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• Free vibration of matrix cracked FG-GPLRC plates coupled with stationary fluid is developed using the C0-HSDT and isogeometric analysis. • Matrix crack is considered based on self-consistent micromechanical model. • Three fluid-plate interaction boundary conditions are investigated carefully. • Parametric studies are carried out to research influences of various parameters on free vibration. This paper for the first time proposes an efficiently C0-higer order shear deformation theory (HSDT) and isogeometric analysis (IGA) for the free vibration analysis of matrix cracked functionally graphene nanoplatelets reinforced composite (FG-GPLRC) plate coupled with stationary fluid. This case represents essential components of sophisticated structures utilized in industries such as shipbuilding, nuclear, marine, and naval. The properties of the four GPLs distributions of FG-GPLRC are evaluated by using a combination of the modified Halpin-Tsai micromechanics model and the rule of mixtures, while the degraded stiffness of cracked layers is predicted by the self-consistent micromechanical (SCM) model. The fluid is assumed to be homogeneous, inviscid, incompressible and irrotational, so the free-surface waves and hydrostatic pressure effects on structures are neglected. The governing equation of motion is derived by the Hamilton's principle, where three different fluid-plate interaction systems are taken into consideration. After validating the proposed method against existing literature, the effect of various parameters such as crack density, interaction boundary conditions (IBC), fluid level, GPLs distribution pattern, total number of layers, and geometric parameter on the free vibration of matrix cracked FG-GPLRC plate are investigated. It is believed that the finding in this paper may be helpful for the accurate design and analysis of matrix cracked FG-GPLRC plate submerged in fluid. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive analysis of the free vibrations of functionally graded porous (FGP) triangular plates with arbitrary shapes and elastic boundary conditions using Isogeometric Analysis (IGA). We express the triangular shapes by using non-uniform rational B-splines (NURBS). The impact of porosity, geometry, and boundary conditions on the natural frequencies is investigated, with a focus on three key factors: porosity coefficient, geometric shape, and type of boundary conditions. Results show that increasing porosity generally leads to an increase in natural frequencies for thin plates, while thicker plates exhibit the opposite trend. The effect of geometric shape, characterized by different angles, is investigated and reveals distinct trends in natural frequencies. The study also investigates both classical and elastic boundary conditions, illustrating the impact of arbitrary boundary conditions on the natural frequency response. Validation against previous references and finite element methods establishes the accuracy of the presented results. The paper concludes with an extension of the analysis to various scenarios, offering valuable insights into the intricate interplay of porosity, geometry, and boundary conditions on the vibrational behavior of FGP triangular plates. • This paper presents a comprehensive examination of the free vibrations of porous FGM triangular plates with arbitrary shapes and elastic boundary conditions using IGA. • The study systematically investigates the influence of key factors such as porosity coefficient, geometric shape, and boundary conditions on natural frequencies. • The paper addresses challenges in creating triangular geometries using NURBS, proposing a reliable approach to enhance convergence and accuracy in Isogeometric Analysis. • Convergence analysis underscores the importance of higher-order NURBS for triangular shapes, balancing accuracy with computational efficiency. • presented results offer valuable insights for researchers and practitioners, contributing to the advancement of structural analysis methodologies for complex materials and geometries. [ABSTRACT FROM AUTHOR]

• A nested non-invasive SIGA method is presented for the random vibration of FGM plates. • SIGA-RBFNN demonstrates exceptional accuracy and robustness in high-dimensional stochastic analysis. • A generalized technique is proposed to accelerate the convergence of QMCS utilizing SIGA-RBFNN. • The effects of gradient index and temperature on the dynamic response were investigated. This paper introduces an adaptive nested non-invasive dynamic SIGA method based on RBFNN for the nonlinear thermal vibration analysis of FGM plates under random loading. This method is robust and accurate in high-dimensional input spaces regardless of the sample sequence, addresses the low convergence rate of QMCS, and solves the stochastic dynamic response probability density function under random loading. Firstly, the multidimensional input space for random loading is constructed based on several mutually independent random variables via the stationary Gaussian stochastic process simulation technique. The nonlinear FGM plate model subjected to random loading in the thermal environment is modeled using HSDT with von Kármán strain-displacement relation within the IGA framework. Subsequently, a nested non-invasive dynamic response surface analysis method, SIGA-RBFNN, is proposed based on the RBFNN technique. Analysis of the FGM plate response under random loading demonstrates that SIGA-RBFNN, compared to tensor-product-based SIGA methods, is less affected by sample sequence types. It effectively addresses high-dimensional stochasticity and offers significant advantages in robustness, accuracy, and efficiency. Finally, SIGA-RBFNN compensates for the low convergence speed of QMCS and successfully solves the FGM plate displacement response statistics and probability density function under random loading. [ABSTRACT FROM AUTHOR]

In this research effort, a novel multiscale analysis scheme is proposed for damage modeling of composite laminates, sandwich structures, and stiffened plates relying on capabilities of the parametric HFGMC and isogeometric RZT { 3 , 2 } formulations. The Ramberg Osgood (RO) model is incorporated into the micromechanics model to reflect polymer matrix material nonlinearities on the overall homogenized composite behavior. Carbon fibers are assumed to behave in a linear transversely isotropic manner. The higher order RZT { 3 , 2 } theory employed at the macro level facilitates efficient applicability of the model to thick composite laminates and soft core sandwiches. On the other hand, it generates all three-dimensional stress components and thus ensures dimensional consistency between micro and macro levels. Numerical discretization and prediction of RZT { 3 , 2 } kinematic variables are enabled by performing NURBS based isogeometric analysis (IGA) thereby enhancing modeling efficacy to a significant degree. Soft core plasticity and failure in the composite are evaluated at the macro level through the RO model and Hashin criteria, respectively. Applicability of the method is presented for thin and thick flat composite and sandwich laminates; and further extended to stiffened plates via developing a multipatch formulation. A comprehensive validation of our analysis is conducted by comparing the results with established benchmarks from the literature, experimental data, and three-dimensional finite element method (3D-FEM) simulations. Initially, a moderately thick, simply supported square laminate under transverse loading is examined, a common verification benchmark. Then, results from standard mechanical tests, including tensile, shear, and four-point bending tests on thin laminates, followed by experiments on moderately thick sandwich structures subjected to four-point bending, are presented. Finally, the analysis is extended to a stiffened plate under uniform pressure, demonstrating the method's accuracy and applicability across diverse structural configurations. • A new multiscale scheme with HFGMC and RZT { 3 , 2 } enhances damage modeling in composites. • Integrating the Ramberg–Osgood model captures polymer matrix nonlinearity in composites. • NURBS-based isogeometric analysis improves kinematic variable prediction in composites. • The method's effectiveness is proven by experiments and 3D finite element analysis comparisons. [ABSTRACT FROM AUTHOR]

• Simultaneous shape and size optimization of the stiffened shells using isogeometric analysis. • Analysis model created by coupling the isogeometric degenerated shell and beam elements. • Analytical definition ensuring stiffeners perpendicular to the curved surface. • Analytical sensitivity with the positions, heights, and thicknesses as design variables. A shape and size optimization framework is developed to improve the structural performance of the stiffened shell using isogeometric analysis. To accurately model the stiffened shell, the Lagrange multiplier method is employed to establish the coupling relationship of isogeometric degenerated shell elements and isogeometric degenerated beam elements. Due to the advantages of the non-uniform rational B-spline (NURBS), the unit normal direction vectors of the shell can be defined analytically, which guarantees stiffeners perpendicular to the skin. Additionally, the stiffeners can be easily generated based on the mapping relationship of the parametric space and the physical space of the shell. Analytical sensitivity is derived in detail, and the gradient-based optimization method can be used to solve the minimum compliance optimization problem owing to the high order continuity of NURBS. Three numerical illustrative examples are presented to verify the effectiveness of the proposed framework for the shape and size optimization of stiffened shells, consisting of a cylindrical shell patch, a hyperbolic shell, and a complex engineering segment. It is worth noting that the proposed framework is especially suitable for optimization problems of the stiffened shell, eliminating the need of complex feature extraction. [Display omitted] [ABSTRACT FROM AUTHOR]

• A new shell coupling approach inspired by the concept of solid coupling is proposed. • A framework for 5 degrees of freedom (5-DOFs) shell that accommodates different geometric continuities without introducing additional DOFs has been developed. • Implemented the Nitsche, Penalty, and Mortar methods within the proposed framework. • Comparison of the three methods and the selection of related parameters. In the aerospace field, there are numerous assembled thin-walled structures with complex geometric continuity conditions. This makes isogeometric analysis (IGA) inevitably meet multi-patch issues. In previous work on 5-DOFs shell, when encountering G 0 continuity or kinks, the approach often involved converting two local coordinate system rotations into three global coordinate system rotations to achieve multi-patch coupling. This often introduces additional DOFs and may destabilize the stiffness matrix. In this study, inspired by the concept of solid coupling, a new shell coupling approach is proposed, developing a 5-DOFs shell coupling framework suitable for different geometric continuities, providing a more efficient and simpler framework. When calculating the coupling stiffness matrix, there is no need for prior classification of the control points. Within this framework, the Nitsche, Penalty, and Mortar methods based on IGA are implemented. To demonstrate the effectiveness of the proposed framework in static and linear buckling analyzes, four different numerical examples were constructed, including G 1, G 0 continuity, and kinks. Under different continuity conditions, the results are sensitive to the parameter selection of the Nitsche and Penalty methods. Appropriate parameter selection can lead to better results for them. Compared to others, the Mortar method avoids this problem, making it easier to apply in engineering. The core codes are publicly available at https://github.com/tasteofbbq/ICA4ATWS. [ABSTRACT FROM AUTHOR]

The aim of this study was to analyze the effect of fluid presence on the dynamic response characteristics of the thin circular plate and the distortions associated with the wet mode shapes. To this end, series of numerical calculations and experimental measurements were performed to investigate the free vibration characteristics of clamped circular plate under in-vacuo conditions and when it is partially in contact with fluid. In the experimental studies, the clamped boundary conditions are imposed on the circular end plate of the horizontal rigid cylindrical tank by closely-spaced bolts, and measurements were performed based on roving hammer impact technique. The proposed numerical approach was divided into two parts based on linear hydroelasticity theory. In the first stage, the thin circular plate is considered to be under in-vacuo conditions, and the mathematical model for this problem is developed based on the isogeometric finite element method (IGAFEM). The fluid environment is introduced in the second stage of the study in which the generalized in-vacuo modal displacements constitute the boundary conditions of the potential flow problem. The influence of fluid medium is incorporated in the system of equations in the form of fluid added mass, and the corresponding fluid forces are calculated by the isogeometric boundary element method (IGABEM). It is observed that the fluid presence has significant effects on the dynamic response characteristics of the test structure, and the specifically, the distortions of wet mode shapes were noticeable due to presence of free surface of the water. Overall, it is found that the natural frequencies and corresponding mode shapes obtained by conducted experiments and adapted numerical framework are in favorable agreement. • Free vibration characteristics of a circular plate in the air and when it interacts with various levels of fluid are investigated. • For numerical analysis, hybrid isogeometric-based finite element — boundary element approach based on linear hydroelasticity theory is adopted. • Experimental measurements for thin circular plate attached to rigid cylindrical tank are performed by roving hammer impact technique. • Comparisons between in-vacuo and wet dynamic characteristics for various fluid depths are performed. [ABSTRACT FROM AUTHOR]

This paper proposes an effective numerical method for shape control of bi-directional functionally graded plates (2D-FGPs) with piezoelectric layers. Isogeometric analysis (IGA) based on non-uniform rational B-splines (NURBS) related to third-order shear deformation theory (TSDT) is employed for the static analysis of the 2D-FGPs with piezoelectric layers. The B-spline basis functions are utilized to represent the distribution of the ceramic volume fractions, where the control points placed along the plane corresponding to the ceramic volume fraction and the applied voltages are taken as the design variables. In addition, an improved moth flame optimization algorithm is utilized to solve the optimization problem of minimizing the static shape error, which effectively balances the exploratory and exploitative capabilities of the algorithm. Various numerical examples of square, skew, and dart-shaped 2D-FGPs are analyzed to validate the proposed method and demonstrated the superior mechanical performance of 2D-FGPs over 1D-FGPs. • The mechanical behavior of 2D-FGPs with piezoelectric layers is studied by IGA-TSDT. • Material layout and control voltages of 2D-FGPs with piezoelectric layers are optimized. • An improved moth flame optimization algorithm is employed as the optimization solver. • The effectiveness of the proposed method is demonstrated through numerical experiments. [ABSTRACT FROM AUTHOR]

This article first introduces a novel optimization-driven reduced order model (ROM) to the dynamics of plates utilizing isogeometric analysis (IGA). The proposed paradigm uses an iterated improved reduced system (IIRS) technique to condense the system's dynamic properties. This model takes account of inertia items, the consistent mass matrix is therefore preserved. Moreover, master degrees of freedom (DOFs) defined at control points of the IGA in ROM are optimized via the derivative-free adaptive hybrid evolutionary firefly algorithm (AHEFA). Accordingly, the accuracy and the correlation of high-order shape modes can be improved. The Galerkin discretization is employed to establish the IGA-based ROM for the plate's dynamic analysis with proportional damping. In which, its weak form relied upon a generalized shear deformation theory (GSDT) is derived from the Hamilton's principle. Consequently, the reduced IGA can deal with both thick and thin plates without shear correction coefficients and the shear locking phenomenon. The Newmark- β method is then employed to achieve time-history responses of the reduced dynamic equation system. Several numerical examples are tested to illustrate the reliability and efficiency of the present methodology. Obtained outcomes have shown their useful and potential applications to the structural health monitoring (SHM) field, especially when the number of sensors is limited. • A novel optimization-based ROM using IGA is proposed for the dynamics of plates. • IIRS is utilized to condense dynamic properties with consistent mass conservation. • Master DOFs defined at control points are optimized by AHEFA. • Examples of plates' transient analysis with proportional damping are investigated. [ABSTRACT FROM AUTHOR]

• An isogeometric method for buckling analysis of composite cylindrical shells under external pressure is proposed. • Based on Reissner–Mindlin shell theory, effects of large deformation is considered in this method, and a modified arc-length method is proposed to track the equilibrium path after limit points. • Post-buckling analysis of different composite pressure shell models are computed and verified, both snap-instability behavior and bifurcation behavior are observed. • For linear buckling analysis of variable stiffness composite shell cases, the efficiency of the proposed method is confirmed for achieving same precision as FEM with fewer elements. Composite cylindrical pressure hulls are thin-walled structures widely used for autonomous underwater vehicles. Buckling failure is one of the most important failure modes for these shells under external pressure. In existing buckling studies of cylindrical pressure hulls, FEM is the most popular analysis method but not efficient enough when dealing with structures with complex material distributions such as the variable stiffness composite shells. Motivated by this, an isogeometric method for buckling prediction and post-buckling analysis of variable stiffness composite underwater pressure shell is proposed in this article. In this method, based on Reissner–Mindlin shell formulas undergoing large deformation, a buckling analysis framework in IGA forms is established. Then a modified arc-length method is proposed based on kinematics used in the shell formulas, and is used to overcome the inaccuracy caused by the 2 degrees of freedom node rotation in the prediction step of arc-length method. In addition, the influence of bifurcation is considered, which may seriously affect the precision of buckling behavior simulation when the limit point is close to a bifurcation point. The computational accuracy of this framework has been validated in a series of constant stiffness composite shell cases involving buckling load prediction and post-buckling behavior simulation. For variable stiffness composite hull cases, this framework achieves the same precision as FEM with fewer elements. Therefore, the proposed framework provides an efficient way for the buckling design of underwater variable stiffness composite pressure hulls. [ABSTRACT FROM AUTHOR]

• A general semi-analytical modeling method of bolted composite conical-conical shells with flanges is proposed. • A bolted joint model considering the non-uniform distribution of interface pressure is proposed. • The accuracy of the proposed modeling method is confirmed through incremental validation using finite element method and experimental testing. • The proposed modeling method can efficiently guide the dynamic design of bolted composite conical shell structures with flanges. This paper proposes a general semi-analytical modeling method of bolted composite conical-conical shells with flanges based on the first-order shear deformation theory. The coupling connections between conical shells and flanges are achieved by using the penalty function method. A bolted joint model that considers the non-uniform distribution of interface pressure is proposed, which can efficiently simulate any number of bolt connections between flanges and boundaries and between flanges and flanges. The correctness and effectiveness of the proposed modeling method are confirmed through step-by-step comparisons with finite element analysis and experimental testing. Then, the influence of various parameters on the frequency trajectories and modal shapes of bolted composite conical-conical shells with flanges is analyzed, with a particular focus on frequency veering and modal coupling vibration behaviors in these structures. The analyses indicate that the proposed modeling method can flexibly adjust structural geometric parameters, material parameters, bolt parameters, fiber layer parameters, and so on, which can efficiently guide the dynamic design of bolted composite conical shell structures with flanges. [ABSTRACT FROM AUTHOR]

• The stiffness matrix of thin-walled composite laminates is linearized by the lamination parameters in the isogeometric continuum shell model. • The optimal search direction in the nonlinear-buckling optimization is directly determined by the sensitivity analysis of the critical buckling state. • A suitable initial estimate of multiple Newton's iterations in the line-search of the constrained optimization is provided by a continuous following strategy. • The continuity of the critical buckling points in the optimization is properly preserved when passing through two typical cases of singularity. Nonlinear buckling optimization of variable stiffness (VS) composite shells is computationally expensive due to frequent nonlinear analyses. Although the generalized path-following method can serve to reduce the redundant computation, it is weakened by two kinds of discontinuity. First, the design variables may not always be searched continuously in the constrained optimization. Second, the critical buckling states may not be continuous at singular points on the search path. To address this issue, a hybrid path-following approach is proposed to trace the critical buckling states in the nonlinear-buckling optimization with constraints on the realizability of the lamination parameters and the amplitude range of geometric imperfections. Firstly, the optimal search direction is determined with the sensitivity analysis of the critical buckling equations in the isogeometric continuum shell model. Then, a continuous following strategy is adopted to provide a proper initial estimate for the Newton iterations at a disconnected point. Moreover, an investigation into the singularity of the critical buckling equations is conducted to identify the discontinuous points of the critical states in a line-search. Upon detection of the singularity, a segment of path in state space is inserted to recover the continuity. Numerical experiments show that the continuity of the critical states in the optimization is well maintained, which leads to a more efficient optimization for the VS shell with shape imperfections. [ABSTRACT FROM AUTHOR]

• Shape sensing of stiffened thin-shell structures is investigated using isogeometric iFEM. • A methodology based on the use of Lagrange multipliers is proposed to deal with non-conforming interfaces. • Displacement field reconstruction for a set of case studies, including a wingbox. • High accuracy demonstrated through numerical analysis. The capability of reconstructing the displacement field of a structure based on in-situ strain measurements is referred to as "shape sensing" and constitutes a fundamental unit for the real-time monitoring of critical structural components. The Inverse Finite Element Method (iFEM) is one of the most promising innovative techniques for accomplishing this task. This study explores the application of iFEM in conjunction with Isogeometric Analysis (IGA) for the shape sensing of stiffened thin-shell structures. The use of IGA allows for the exact representation of computational geometry, simplifies mesh refinement, and potentially reduces the number of installed sensors. In the context of IGA, when the geometry of a structure is composed of multiple surfaces, non-conforming interfaces are typically involved. To overcome this issue, we propose an assembly process based on the Lagrange multiplier method to jointly apply iFEM and IGA to shell structures assemblies. The methodology is numerically validated using FEM models both to generate the in-situ strain data and as a comparison for iFEM reconstruction results. The case studies include a T-beam, a reinforced hyperbolic paraboloid, and a wingbox. Convergence analyzes are performed to investigate the shape sensing accuracy as the number of inverse elements increases. Additionally, contour plots of displacement field components are compared with the reference solution, revealing a high degree of agreement. [ABSTRACT FROM AUTHOR]

• Size-dependent behaviors of auxetic honeycomb sandwich nanoplates is developed. • The proposed approach utilizes a nonlocal strain-gradient isogeometric analysis which incorporates the effects of both nonlocality and strain gradient. • The sandwich nanoplate consists of a core layer featuring an auxetic honeycomb and two outer skin layers reinforced with graphene nanoplatelets. • The length scale parameters can high-efficiently predict size effects. • Some novel benchmark numerical results are illustrated and introduced. Honeycomb structures, which are known for being lightweight and stiff, are still being researched and developed. They have been used in a wide range of industries, but their full potential has not yet been realized. In this study, a novel computational approach for exploring the size-dependent behaviors of auxetic honeycomb sandwich nanoplates is developed. The proposed approach employs a nonlocal strain-gradient isogeometric analysis integrating the influences of nonlocality and strain gradient into the nanoplate structures. The sandwich nanoplate consists of a core layer featuring an auxetic honeycomb with a negative Poisson's ratio, complemented by two outer skin layers reinforced with graphene nanoplatelets (GNPs). This configuration not only achieves exceptional lightweight characteristics through the utilization of auxetic honeycomb cells but also enhances structural stiffness by incorporating GNPs into the skin layers. The material properties of the core layer are determined using cellular cell formulas, while the reinforcement of the two outer skin layers with GNPs is calculated using the modified Halpin-Tsai model. Numerous numerical examples are conducted to investigate the influence of various parameters on the frequencies of the auxetic honeycomb sandwich nanoplates. Notably, the geometrical dimensions of the auxetic honeycomb cells and the nonlocal and length scale parameters emerge as significant influencers on the results. As the first analysis of honeycomb structures at small dimensions, our findings stand as valuable benchmarks for future analyses. [ABSTRACT FROM AUTHOR]

• A new isogeometric analysis model for MEEFG microplate is proposed. • Static and dynamic responses with square and elliptical plates are investigated. • The accuracy and convergence of the numerical solution are verified. • The microstructure effect becomes more pronounced as the structure size and stiffness decrease. • Adjusting the graded index can improve the mechanical and electromagnetic properties of the plate. In this study, an accurate numerical method for the static and dynamic response analysis of magneto-electro-elastic functionally graded (MEEFG) microplates with complex geometries is proposed with the application of isogeometric analysis (IGA). Leveraging Hamilton's principle and the extended modified couple stress theory, the weak form of motion equations is derived. By performing convergence analysis, the accuracy of the proposed numerical method is verified. To show the applicability of the new method, the influences of the microstructure effect and gradient index on the static and dynamic behaviors of both the MEEFG square and elliptical microplates with various boundary conditions are discussed in detail. Results illustrate that the microstructure effect dominated by the couple stress effect has an obvious impact on both the mechanical and electromagnetic behavior of structures with microscopic scales which will cause hardening of microstructural stiffness, whereas the macrostructures are minimally affected by the couple stress effect. Besides, microstructures with lower stiffness exhibit a more pronounced microstructure effect and a greater degree of stiffness hardening. The proposed IGA method could serve as a basis for the design and optimization of microelectromechanical devices with complex shapes. [ABSTRACT FROM AUTHOR]

• Post flutter analysis of FG-CNTRC plates using the Isogeometric Approach (IGA). • Post-flutter analysis of plates with arbitrary shapes. The current investigation deals with the aeroelastic behavior of quadrilateral plates composed of Functionally Graded Carbon Nanotubes Reinforced Composites (FG-CNTRC) with different distribution models in supersonic airflow using Isogeometric Analysis (IGA). To fulfill this aim, the aeroelastic equations of the mentioned plates are constituted utilizing extended Hamilton's Principle. Hence, First-order Shear Deformation Theory (FSDT) and von Karman's nonlinear strains are exploited to extract structural dynamics equations. The first-order piston theory is utilized to include aerodynamic forces in aeroelastic equations. Carbon nanotube distribution is assumed to be across the thickness either uniformly or non-uniformly and estimated by using the extended rule of mixture. The Isogeometric approach is operated to discretize the obtained relations. The natural frequencies and the flutter boundaries are then attained by applying eigenvalue analysis to the linear aeroelastic model. The flutter behavior of the plates is studied by applying the well-known Newmark method to the mentioned equation. The post-flutter analysis is also conducted by simultaneously applying the Newton–Raphson and Newmark methods to the nonlinear aeroelastic equation. The impacts of nanotube distribution and its volume fraction, flow yaw angle, and geometry on the plates' behavior are investigated. The results are also validated by comparing them with well-known references presented in the literature. [ABSTRACT FROM AUTHOR]

• A new 3D corotational isogeometric shear deformable geometrically exact beam element undergoing arbitrarily large deformation is presented. • By constructing a co-rotated frame, the pure deformations are extracted to derive the spatial exact invariant strain measure with lie derivative formalism. • The consistent tangent stiffness matrix belonging to proposed element are derived in closed form of the discrete variables for deformation field of arbitrary order. In this paper, a new 3D generic order corotational geometrically exact beam element undergoing arbitrarily large deformations is presented. The novelty of the formulation lies in the use of the standard corotational framework, that is the decomposition into rigid body motion and pure deformation, to derive not only the objective, path-independent and singularity-free spatial exact strain measure but also the internal force and the consistent tangent stiffness matrix. The new formulation is derived by firstly conducting the consistent linearization of the weak formulation for the equilibrium equations of Reissner–Simo theory in the spatial form. By constructing a co-rotated frame that continuously rotates and translates with the element, the nodal strain-producing deformations can be extracted with the rigid-body translations and rotations removed from the element total motion. Subsequently, the corotational deformation variables are exploited to establish the distribution of deformation field within the beam element through B-spline basis functions, and derive the invariant and path independent exact strain measure in the spatial form by Lie derivative formalism. Through performing the variational operations of the compact transformation between corotational and global variables, the consistent tangent stiffness matrix are derived in closed form of the discrete variables for deformation field of any order. The proposed formulation is applicable to not only low-order two-node geometrically exact elements but also high-order multi-node straight or curved ones. The accuracy and robustness of the new formulation are demonstrated through the solutions of various benchmark problems. [ABSTRACT FROM AUTHOR]

• An interpolatory basis lumped mass isogeometric formulation is proposed for accurate frequency computation of Kirchhoff plates. • Nodal quadrature rules are developed to formulate isogeometric lumped mass matrices with interpolatory basis functions. • A frequency equivalence is rationally established between different isogeometric mass matrix formulations. • Rigorous theoretical frequency error estimates are presented for the lumped mass isogeometric formulation with interpolatory basis functions. • The 4th and 6th order accuracy of the proposed method with cubic and quartic basis functions contrasts sharply to the 2nd order accuracy of standard approach. A noticeable drawback associated with the isogeometric free vibration analysis of Kirchhoff plates with lumped mass formulation is that its frequency accuracy is strongly limited to 2nd order, no matter what degrees of basis functions are used. This issue is resolved herein by a lumped mass isogeometric formulation using a set of interpolatory basis functions. These interpolatory basis functions are constructed via transforming the standard isogeometric basis functions with respect to the Greville nodes. A direct consequence of the basis interpolation property is that the resulting lumped mass matrices can be realized with a nodal integration technique, and the corresponding nodal quadrature rules are then developed for cubic and quartic basis functions. Furthermore, based upon the transformation relationship between the standard and interpolatory basis functions, a frequency equivalence is rationally established between the standard and transformed isogeometric formulations, which enables a rigorous analytical study of the frequency accuracy for the proposed approach. In particular, the theoretical frequency error estimates are obtained for both cubic and quartic basis functions, which clearly illustrate the frequency accuracy superiority of the proposed method over the standard lumped mass isogeometric formulation for Kirchhoff plates. The theoretical observations are simultaneously demonstrated by numerical results. [ABSTRACT FROM AUTHOR]

This paper for the first time attempts to find the simultaneously optimal three-dimensional distribution of porosity and material phases in functionally graded materials (FGMs) model that altogether maximize the natural frequency of porous FG plates. By using the same concept of non uniform rational B-splines (NURBS) based interpolation for the material distribution, the problem of finding the optimal porosity distribution is enabled. An upper bound of porosity is pointed out, which is necessary for considering the porosity design variables. Generalized shear deformation theory (GSDT) in the framework of isogeometric analysis (IGA) for free vibration analysis of the porous FG plates is verified with previous works. The findings are: in the optimal design of material only, the uniformly distributed pores have a neutral or detrimental effect on 4-side constrained plates but slightly increase the frequency for the cantilever plate; and with that same amount of porosity, the simultaneously optimal distributions of pores, similar to those in bio-materials or natural bones in the way that are most foam-like in the center or at the furthest from the boundaries, result in lighter yet of significantly elevated vibration frequency structures. • Simultaneously optimal 3D material and porosity distribution in FG plates. • An upper bound for porosity in porous FG plates is presented. • Verification of generalized shear deformation theory and isogeometric analysis. • Significantly elevated natural frequencies and lighter weights. [ABSTRACT FROM AUTHOR]

This paper develops a multi-patch isogeometric Kirchhoff–Love shell method for post-buckling of functionally graded graphene platelets reinforced composite (FG-GPLRC) cylindrical, spherical, and conoidal shell structures, which are built with single or multiple NURBS patches. A penalty strategy is employed to weakly couple nonconforming interfaces between adjacent patches. The coupling work induced by enforcing displacement continuity and rotational continuity is added to the equilibrium equation, and the corresponding stiffness matrix is derived in detail. A simplified arc-length method is utilized to capture the complex equilibrium paths including snap-through and snap-back behaviors. Five distribution patterns of the shells including uniform (UD), V-type, A-type, O-type, and X-type are considered. The cylindrical and spherical shells are subjected to concentrated loadings at central points while for conoidal shells the concentrated loadings are enforced at the center points of an edge. The post-buckling of isotropic and laminated shell structures is first studied to validate the developed formulations by comparing the obtained results with those given in existing literature. Then a series of numerical examples considering nonlinear FG-GPLRC shell problems are conducted to explore the effect of various parameters like geometric dimensions, GPL distribution patterns, and shell thickness on the mechanical performance. Finally, the post-buckling of a cylindrical shell subjected to an offset concentrated load, with extremely complicated equilibrium paths, is modeled and analyzed by using the developed multi-patch isogeometric method. The numerical results reveal that the X-type GPL distribution pattern demonstrates better performance in load–deflection responses and provides the largest buckling critical load among the five patterns. Additionally, the increase in height ratio could deteriorate the stability performance of FG-GPLRC conoidal shells. • Post-buckling of FG-GPLRC shells is explored by using Kirchhoff–Love shell theory. • A penalty–based IGA method is developed to weakly couple adjacent NURBS patches. • The coupling stiffness matrix is derived and given explicitly in the matrix form. • Snap-instability behaviors are well–captured and verified in various examples. • Effect of geometric and material parameters on post-buckling performance is studied. [ABSTRACT FROM AUTHOR]

Abstract A novel and effective computational approach within the context of isogeometric analysis (IGA) is developed for analyzing size-dependent mechanical behaviors of functionally graded (FG) microbeams. To capture the size effects, an extension of quasi-3D theory is established to integrate with the modified couple stress theory. The nonuniform rational B-spline (NURBS) basis functions are employed and can directly meet the first-order derivative demand of the quasi-3D theory, where four variables are involved at each node. In this new setting, both normal and shear deformations are considered, while the shear correction factor is avoided. Numerical examples are studied, in which the effects of several factors, including material gradient factor, boundary conditions, parameter of material length scale, and aspect ratio, on deflections, stresses, and fundamental frequencies of FG microbeams are explored. Highlights • An effective computational approach is presented for size-dependent behaviors of thick functionally graded microbeams. • A non-classical quasi-3D theory is used to capture the size-dependent effect. • Both thickness stretching effects and shear deformations are considered without the use of shear correction factor. • NURBS-based isogeometric analysis can squarely meet the first-order derivative demand. • The influences of material parameters, boundary conditions, and aspect ratios on deflections, stresses, and vibration responses of functionally graded microbeams are investigated. [ABSTRACT FROM AUTHOR]

Abstract This study attempts at analyzing buckling responses of functionally graded material (FGM) plates under diverse types of thermal loadings. An accurate and effective numerical approach based on isogeometric analysis (IGA) to predict the nonlinear thermal buckling behavior is developed. A refined higher-order shear deformation theory (HSDT) which accounts for the geometric nonlinearity in the von Kármán sense is presented and used to derive the equilibrium and governing equations for FGM plate in thermal environments. Two different types of transverse shear functions are considered in the refined HSDT. IGA uses non-uniform rational B-spline (NURBS) basis functions which enable to accomplish easily the smoothness of arbitrary continuity order. Thus, the present method satisfies the C 1 -continuity of the displacement field required by the proposed HSDT. Several numerical examples involving buckling behavior of various kinds of FGM plates subjected to uniform, linear and nonlinear temperature distributions across the thickness are simulated, and the results are compared to the analytical solutions for the verification purpose. Parametric studies are also carried out on FGM plates under the different through-thickness temperature variations to scrutinize the thermal buckling features. Temperature gradient through the thickness by the one-dimensional (1-D) heat conduction and thermal profile developed by the three-dimensional (3-D) heat conduction are also taken into account. Results demonstrate that the proposed IGA method can be used as an accurate and effective numerical tool for analyzing the thermal buckling responses of FGM plates, and the 3-D heat conduction needs to be considered in the buckling analysis of FGM plates subjected to thermal conduction. Highlights • Isogeometric analysis (IGA) method for investigating nonlinear thermal bucking behavior of FGM plates is presented. • Refined higher-order shear deformation theory (HSDT) with four unknowns is designed and employed. • The present method satisfies the C1-continuity of the displacement field required by the refined HSDT. • Temperature gradient developed by the 3-D heat conduction is taken into account. • The IGA approach based on the refined HSDT can accurately predict the thermal buckling behavior. [ABSTRACT FROM AUTHOR]

• A new large deformation locking-free shell element in updated lagrangian formulation is proposed. • The assumed natural strain field for the green-lagrange strain are constructed to alleviate locking pathologies in the context of isogeometric analysis. • The corotational procedure available for high order isogeometric shell element is developed on the basis of euler parameters. A new general geometric nonlinear curved quadrilateral shell element, which can handle large displacements and large rotations, is presented in this paper. It is formulated based on the incremental virtual work equation in updated Lagrangian formulation for general large displacement analysis. The kinematics of shell element is described using non-uniform B-spline patch, which results in the element displacement field with higher order continuity and the element performance more resistive to shear locking and membrane locking. In order to perfectly avoid such membrane locking and shear locking behaviors, the assumed in-plane membrane strain field and the assumed transverse shear strain field for the incremental covariant Green-Lagrange strain are constructed as linear combinations of non-uniform B-spline basis functions with degrees lower than those adopted by the original displacement field interpolation. In addition, based on Euler parameters, the corotational procedure available for high order isogeometric shell element is developed to extract the strain-producing deformational displacements and rotations and to update the element stresses and realistic internal force vectors. The accuracy and robustness of proposed shell element are demonstrated through the solutions of various benchmark problems. [ABSTRACT FROM AUTHOR]

• A novel general numerical method, discrete Ritz method (DRM), is proposed for buckling analysis of arbitrarily shaped plates with arbitrary cutouts. • DRM combines the extended interval integral, Gauss quadrature, and variable stiffness, and builds a discrete energy system over a standard rectangular domain. • Cutouts with zero stiffness are used to simulate the shape of plates as well as inner cutouts. • Using variable stiffness and Gauss integration points in combination, DRM discretizes energy and uses cutouts to control the geometric boundary of the plate. • Standard energy functionals are established within a rectangular domain in terms of cutouts for arbitrarily shaped perforated plates, making the computation procedure standard. To overcome the difficulties of the Ritz method when dealing with complex geometric domain problem, a novel general numerical approach, discrete Ritz method (DRM), is proposed for buckling analysis of arbitrarily shaped plates with arbitrary cutouts. Accounting for a variety of boundary conditions, Legendre polynomials are adopted to construct the admissible function. By using the global trial function with variable stiffness properties within a virtual rectangular design domain, the deformation of arbitrarily shaped plates can be captured with the help of numerical integration using Gauss quadrature. The shapes and cutouts of plates are both numerically simulated by using cutouts, where the stiffness is assigned zero within the cutouts in the virtual rectangular domain. Moreover, boundary conditions and load potential can be applied to any contour of the plate. Based on the above formulation, standard energy functionals and computation procedures are established to extract the buckling eigenvalues and mode shapes. Variously shaped plates with arbitrarily shaped cutouts are investigated. Under several boundary conditions, multiple inplane loads are applied, and the results are compared with those obtained by other numerical and analytical methods in the literature. Demonstrating the stability and accuracy of the DRM. [ABSTRACT FROM AUTHOR]

• Tensile behaviour of origami bellows with polygonal cross-section was investigated. • The energy absorption of the bellows increased with the number of polygonal sides. • Two types of non-rigid deployment modes were discovered. • Analytical model of mean tensile force for each deployment mode was derived. • The predicted results were validated against numerical results. The mechanical behaviour and energy absorption (EA) of origami bellows with polygonal cross-sections under quasi-static axial tension were numerically and theoretically investigated. The finite element analysis results showed that the plateau force increased with the number of polygon sides N , leading to increases in the mean tensile force (P m) and specific energy absorption (SEA). Two types of basic deployment elements during the tensile process of hexagonal cross-section bellows were defined based on two corresponding deployment modes, namely non-rigid deployment mode I and non-rigid deployment mode II. The bellows exhibiting deployment mode II had approximately 60 % greater SEA and P m than those exhibiting mode I. Theoretical predictions of the mean tensile force for each mode were derived based on a rigid, perfectly plastic material model and superfolding elements. The predicted results showed reasonable agreement with the finite element analysis results in terms of force – displacement history and P m. This work reveals the fundamental mechanics involved and can facilitate design of origami bellows with optimized geometric and material parameters for desired EA behaviour. [ABSTRACT FROM AUTHOR]

• Isogeometric Analysis based on HSDT is developed for dynamic responses of BFGSW nanoplates subjected to dynamic loading. • Monte Carlo Simulation is employed to capture distribution characteristics of vibration responses of BFGSW nanoplates with random input parameters. • The nonlocal theory is used to take into account the small-scale effect that appears in BFGSW nanoplates. • Effects of geometrical parameters and material properties on dynamic responses of BFGSW nanoplates are investigated as new numerical results. • The proposed method can be developed to be the FEM standard solution for predicting the behavior of BFGSW nanoplates with random input parameters. In this paper, we present a novel approach that combines isogeometric analysis (IGA) with the higher-order shear deformation theory (HSDT) and Monte Carlo simulation (MCS). Our objective is to investigate uncertain vibration characteristics of bi-functionally graded sandwich (BFGSW) nanoplates under dynamic loading. The small-scale effect observed in nanostructures is achieved by employing the nonlocal elasticity theory. This theory allows for the consideration of the mechanical behavior that arises at the nanoscale level. Within the stochastic design approach, the state function for design conditions is commonly formulated by incorporating input random variables, assumed distribution functions, and random responses obtained from computational models. This work primarily focuses on investigating vibrational characteristics of BFGSW nanoplates when the model parameters are considered as random quantities. The obtained results show that distribution characteristics of vibration of the BFGSW nanoplate depend significantly on the standard deviation of input parameters. [ABSTRACT FROM AUTHOR]

Understanding the nonlinear behavior of advanced engineering structures is of great importance in supporting the analysis, design, and manufacturing processes. The primary objective of this paper, therefore, is to focus on exploring the nonlinear free vibrational characteristics of bi-directional functionally graded (FG) plates considering internal pores under various conditions. To accomplish this, we present an approximate numerical model derived based on the framework of NURBS-based isogeometric analysis (IGA), in conjunction with four-variable refined plate theory (RPT) and the von Kármán assumption, to reckon the displacement field. The mechanical properties of bi-directional FG plate models can smoothly and continuously vary along two in-plane directions according to a power law. Additionally, it is assumed that internal porosities in the matrix materials can be dispersed into two independent patterns, either the even or uneven porosity distributions. The nonlinearity in free vibration, assessed by means of the nonlinear-to-linear frequency ratio related to the central deflection amplitude, can be obtained using an iterative scheme with a displacement control strategy. The accuracy and effectiveness of the current numerical model are demonstrated through a comparison with existing solutions. Comprehensive parametric investigations are subsequently carried out to provide insight into the impact of various factors on the nonlinear free vibration characteristics of plate structures under different conditions. The new insights obtained from this research could serve as valuable benchmark outcomes as well as contribute to a more comprehensive understanding of the nonlinear responses in future analysis and design processes. • Nonlinear free vibration characteristics of bi-directional FG porous plates are explored. • Numerical model is developed using four-variable RPT and NURBS-based IGA. • Iterations with displacement control strategy are implemented to obtain nonlinear responses. • Significant influence of input factors is examined and evaluated thoroughly. [ABSTRACT FROM AUTHOR]

• A novel shape sensing method is proposed for the full displacement field reconstruction of thin shell structures. • The inherent advantages of adaptive isogeometric analysis with the superior capabilities of iFEM are integrated. • The adaptive hierarchical mesh refinement is automatically implemented with high accuracy and flexibility. • In-situ discrete strain data are enriched by the smoothing technique to effectively support inverse reconstruction. As the preventive maintenance paradigm transfers to condition-based maintenance, deformation monitoring has become a fundamental system capacity in aerospace engineering. In this study, a novel shape sensing method is proposed for accurate and efficient reconstruction of full-field deformation of thin shell structures from discrete strain measurements. Firstly, a flexible isogeometric approach based on the geometry-independent field approximation is developed for characterizing the geometric and physical domains, which fully unlocks the potential of local refinement while preserving the original exact geometry without re-parameterization. On this basis, a posteriori error estimation algorithm is put forward to automatically drive the adaptive refinement procedure, reducing the discretization error with a fast convergence rate. Subsequently, according to the Kirchhoff-Love theory and the least-squares variational principle, an isogeometric inverse-shell element is created to integrate the inherent advantages of adaptive isogeometric analysis with excellent shape-sensing capabilities of the inverse finite element method. Moreover, a smoothing technique is applied to replenish strain data into each inverse shell element, by which the compatibility between the interpolated and measured strain components is also enforced. Finally, the excellent accuracy and efficiency of the proposed deformation reconstruction framework are verified using both experimental and numerical strain data for two thin-shell spaceborne antennas. [ABSTRACT FROM AUTHOR]

Abstract For the first time, the parametric instability regions of variable stiffness laminated composite quadrilateral plates subjected to uniform in-plane loadings are studied. The static as well as time-varying inplane loadings are assumed distributed throughout the whole geometry. The isogeometric analysis finite element formulation based on non-uniform rational B-splines is developed in order to address the dynamic instability of quadrilateral panels. The problem has been formulated by utilizing the principle of virtual work based on first order shear deformation plate theory. In terms of tow-steered reinforcements, the fiber orientations in every lamina is assumed to change linearly in the panel longitudinal direction. In order to demonstrate the capabilities of the developed formulation in predicting the structural parametric dynamic behavior, some representative results are obtained and compared with those available in the literature. The effects of geometry layout, loading frequency and amplitude, changes in curvilinear fiber orientations, and material orthogonality on the parametric instability regions are studied by applying Bolotin's first order approximation. Highlights • The parametric instability regions of variable stiffness laminated composite quadrilateral plates are studied, for the first time. • The static as well as time-varying inplane loadings are assumed distributed throughout the whole geometry. • Isogeometric analysis finite element formulation based on first order shear deformation plate theory is developed. • The reinforcing fibers' orientations in every ply is assumed to change in the panel longitudinal direction. • The effects of geometry layout, loading frequency and amplitude, changes in curvilinear fiber orientations, material orthogonality, thickness and layup on the parametric instability regions are investigated. [ABSTRACT FROM AUTHOR]

Abstract In this study, the nondeterministic structural responses of functionally graded material (FGM) plates under static loads with uncertain material property is investigated. The considered spatially dependent uncertainties are modelled as random fields with Gaussian distribution. A novel spectral stochastic isogeometric analysis (SSIGA) framework is proposed for such uncertainty quantification through the first-order shear deformation theory. Within the SSIGA framework, the non-uniform rational B-spline (NURBS) is adopted for both the geometry modelling of the random fields of the uncertain material properties and random field discretization through the Karhunen-Loève (K-L) expansion. Such new feature provides an effective and practically applicable random field modelling technique, especially for uncertain parameters over complex physical domains. The polynomial chaos expansion (PCE) is employed for estimating the statistical characteristics (e.g., mean and standard deviation) of any concerned structural responses (e.g., displacement and stress). By further implementing various statistical inference techniques, the probability density functions (PDF) and cumulative distribution functions (CDF) of structural responses can be established to determine both serviceability and strength limits of FGM plate. Two numerical examples are thoroughly investigated to illustrate the applicability, effectiveness and efficiency of the proposed computational approach. Graphical abstract fx1 Highlights • Spectral stochastic isogeometric analysis (SSIGA) is fruitfully introduced to uncertain static analysis of FGM plates. • Spatially dependent uncertain Young's modulus of FGM plate is investigated. • Exact geometry of FGM plate between design model and stochastic analysis model is promised. • Strength and serviceability limits of FGM plate can be determined through the CDFs. • Effectiveness and efficiency of SSIGA is verified against large-scale sampling method. [ABSTRACT FROM AUTHOR]

This paper presents a unified theory for modelling composite thin-walled beams (TWB) of arbitrary planar axial curvature, variable cross-section and general material layup, complemented by the development of an Isogeometric Analysis (IGA) formulation for the discretization and solution of the equilibrium equations. To this end, the standard formulation of composite TWB with rectilinear axes is combined with a general framework for describing the kinematics of arbitrary three-dimensional curves based on the Frenet-Serret frame field. The theory includes explicit terms accounting for curvature gradients within the IGA stiffness matrix, allowing for the treatment of cases with highly curved geometry. Also included is an advanced shear-modification adjustment previously derived for rectilinear TWB, here reformulated for the case of curved TWB, improving the description of the in-plane shear-strain coupling and thus increasing the accuracy for cases with axial-bending-torsional structural coupling. Results from three numerical test cases indicate that this unified formulation effectively transfers all the advantages associated with rectilinear TWB to curved TWB models, yielding an accuracy comparable to more complex models while maintaining a competitive computational economy. [ABSTRACT FROM AUTHOR]

In the current study, 1D refined beam theories on the basis of Carrera Unified Formulation (CUF) are combined with Isogeometric approach (IGA) for the static and free vibration analysis of thin-walled beam structures. The B-spline basis functions utilized in IGA are employed to approximate displacement field due to their interesting attributes in analysis. N-Order Taylor-like expansions are utilized in the framework of CUF which presents finite element matrices in the form of fundamental nuclei that is independent of the type and order of expansion. Higher-order B-spline basis functions attenuate the effect of shear locking properly and higher-order theories presented by CUF are free from Poisson locking phenomenon and utilizations of shear correction factor. Several numerical results including both solid and thin-walled structures are investigated and it is shown that coupling IGA and CUF ends in a suitable methodology to analyze beam structures. [ABSTRACT FROM AUTHOR]

This paper studies static and free vibration of multilayered plates based on isogeometric analysis (IGA) and higher-order shear and normal deformation theory. In which, the plate model with higher-order terms in the displacement fields can capture both shear deformation and thickness stretching effects. Consequently, it passes shear locking and achieves more accurate results in deflection, shear stress distributions, which are satisfied with traction free and interlaminate continuity conditions, and natural frequencies especially for sandwich plates. Utilizing non-uniform rational B-splines (NURBS) basis function fulfills C 1 -continuity required by the plate model without additional variables. [ABSTRACT FROM AUTHOR]

Presented in this paper is a size-dependent analysis of the surface stress and nonlocal influences on the free vibration characteristics of rectangular and circular nanoplates. Nanoplates are assumed to be made of functionally graded materials (FGMs) with two distinct surface and bulk phases. The nonlocal and surface effects are captured by the Eringen and the Gurtin-Murdoch surface elasticity theories, respectively. The Mori-Tanaka distribution scheme is also used for obtaining material properties of nanoplate. In addition to the conventional procedure of deriving the formulation, a novel matrix-vector form of the governing differential equations of motion is presented. This form has the capability of being used directly in the finite element method or isogeometric analysis. To show the effects of surface parameters and small scale influences on the vibrational behavior of rectangular and circular FGM nanoplates with various boundary conditions, several case studies are presented. [ABSTRACT FROM AUTHOR]

The paper presents an effective methodology for modeling and simultaneously optimizing the layer thicknesses (shape) and the ceramic volume fraction distribution (size) of functionally graded (FG) sandwich plates under free vibration in the framework of isogeometric analysis (IGA). The multi-patch B-spline basis functions separately defined in each of the layer thicknesses are used to represent the ceramic volume fraction distribution. Accordingly, the C 0 − continuity at layer interfaces can be naturally satisfied without any additional conditions. Furthermore, this multi-patch B-spline representation still ensures the continuously and smoothly varying material properties across each layer thickness. The effective material properties are then estimated by either the rule of mixture or the Mori-Tanaka scheme. A non-uniform rational B-splines (NURBS)-based isogeometric finite element model associated with the third-order shear deformation theory (TSDT) is utilized for the plate free vibration analysis. A recently developed adaptive hybrid evolutionary firefly algorithm (AHEFA) with the improvement on the convergence speed and the solution accuracy is employed as an optimizer. Design variables are the layer thicknesses and the ceramic volume fractions at control points located in the thickness direction. Several numerical examples of two types of optimization problems of the FG sandwich plates, including (i) the first natural frequency maximization with volume constraints, and (ii) mass minimization with frequency constraints, are presented to illustrate the effectiveness and reliability of the proposed method. [ABSTRACT FROM AUTHOR]

During the last decades, the constant evolution of the construction systems has led to the possibility of carrying out increasingly complex architectural project. Among the wide range of construction systems, thin concrete shells with corrugated-edge stand out for their relevance. In this paper, the mechanical behaviour of thin concrete corrugated-edge shell inspired by Nervi's Flaminio dome has been analysed in detail, considering different load configurations (self-weight, uniform normal pressure and antisymmetric vertical load) and constraints (pure membrane vs. displacements restrained boundary conditions). Non-linear static analysis has been performed to assess the vertical load-bearing capacity of the corrugated-edge shell considering a Concrete Damaged Plasticity (CDP) constitutive model and linear and non-linear buckling analyses have been carried out to evaluate the effects of the corrugation on buckling behaviour. The results obtained from linear and non-linear analyses have been compared with those obtained for a concrete thin smooth-edge shell having the same geometric global characteristics. The comparison highlighted improvements provided by corrugated-edge in terms of structural behaviour. • Corrugation to increase structure stiffness, inspired by Flaminio Dome of Nervi. • Exact analytical geometry of corrugated-edge spherical shells. • Static analyses to highlight the structural enhancement due to corrugated shape. • Nonlinear analyses taking into account plasticity and buckling behaviour. [ABSTRACT FROM AUTHOR]

This paper presents a new microplate model for the static bending, free vibration, and buckling analysis of functionally graded (FG) porous plates. The model is based on the third-order shear deformation theory (TSDT) and incorporates the microstructural effect using the modified couple stress theory (MCST), as well as the surface stress effect using the Gurtin–Murdoch theory. The accuracy and reliability of the proposed model are evaluated using NURBS-based isogeometric analysis (IGA), which demonstrates excellent validation results. Furthermore, this study provides new insights into the mechanical behavior of FG porous microplates, investigating the influences of boundary conditions, surface effects, length scale parameters, porosity coefficients, plate aspect ratios, and buckling load conditions. Novel conclusions are drawn based on the analysis of deflection, stress, natural frequency, and buckling load. • A new TSDT microplate model combined with microstructural effect and surface effect is established for the FG porous plates. • The microstructural effect is described by MCST, and the surface stress effect is captured by Gurtin–Murdoch theory. • The present model is assessed with the NURBS based isogeometric analysis. • Validation studies show that the present theory has excellent accuracy and reliability. • Some new results are presented, and some novel conclusions are drawn. [ABSTRACT FROM AUTHOR]

In this study, a numerical model based on three-dimensional isogeometric analysis and adaptive hybrid evolutionary firefly algorithm is developed to concurrently optimize the shape and material distribution of multi-directional functionally graded plates. The optimization problems focus on maximizing the fundamental frequency of the plates subjected to thermal effects, while the volume fraction of ceramic constituent material and volume of the plates are considered as side constraints. Isogeometric multi-mesh design approach is employed to generate design and analysis domain. The free vibration analysis of multi-directional functionally graded plates with variable thickness is conducted within the framework of three-dimensional elasticity theory and isogeometric analysis. The generalized numerical framework developed in this study could accurately capture the thermal effects on the behavior of nonhomogeneous plates with variable thickness. Various numerical examples are conducted to illustrate the optimal shapes and material distributions within square, rectangular, and circular plates. Influences of temperature field, boundary conditions, and geometries of the plates on the optimal results are also addressed. • A numerical model based on 3D IGA and AHEFA is developed to optimize MFGM plates. • Isogeometric multi-mesh design approach is employed to develop shape design, size design, and analysis domains. • The objective function is to maximize the fundamental vibration frequency of MFGM plates under thermal effects. • Square, rectangular, and circular plates are taken into investigation. [ABSTRACT FROM AUTHOR]

We present a rotation free isogeometric analysis formulation based on Kirchhoff-Love theory, which aims to address free vibration and buckling behaviors of functionally graded thin plates with in-plane material inhomogeneity. For Kirchhoff-Love thin plate analysis, construction of C 1 conforming finite element approximation is not straightforward, while isogeometric analysis with high-order continuity splines basis functions is ideally suited for Kirchhoff-Love elements. We first explain the formulations and then provide verification of the present method through numerical examples. Studies on convergence and comparison with reference solutions are demonstrated to show the effectiveness and accuracy of the proposed method. Effects on natural frequencies, critical buckling loads and mode shapes originated from the material inhomogeneity and boundary conditions are numerically investigated. [ABSTRACT FROM AUTHOR]

The isogeometric analysis (IGA) proposed by Hughes is a new approach in which Non-Uniform Rational B-Splines (NURBS) are used as a geometric representation of an object. It has superiorities of capturing exact geometry, simplifying refinement strategy, easily achieving degree elevation with an arbitrary continuity of basic functions and getting higher calculation accuracy. In this paper, the IGA approach is extended to solve the free vibration problem of curvilinearly stiffened cylindrical and shallow shells. The first-order shear deformation theory (FSDT) and the Reissner-Mindlin shell theory are used to model the shells, and the three-dimensional curved beam theory is employed to model the stiffener which can be placed anywhere within the shell. Some numerical examples are solved to study the vibration behavior of the curvilinearly stiffened shells. The effects of shell and stiffener element numbers, boundary conditions, stiffener ply modes and shell thicknesses on the natural frequency are investigated. Results have shown the correctness and superiorities of the present method by comparing the results with those from commercial finite element software and some numerical methods in existing literatures. One of the advantages is that the element number is much less than commercial finite element software, whereas another is that the mesh refinement process is much more convenient compared with traditional finite element method (FEM). [ABSTRACT FROM AUTHOR]

IsoGeometric Analysis (IGA) has been applied in hull structural analysis and proved to be efficient and accurate. Nevertheless, the advantages of IGA have not been fully utilized. In this paper, IGA technics for hull structural analysis are further developed. A 3 Degrees-Of-Freedoms C 1 -continuous Kirchhoff–Love shell element is used to analyze hull structures, and the weighted non-symmetric Nitsche's method is used to couple connected patches. With the proposed shell elements and coupling method, the modeling of hull structures for IGA is greatly simplified. A typical hull block structure with complex interfaces is used to verify the correctness and accuracy of non-conforming multi-patch IGA. The commercial software ANSYS 17.0 is used to obtain reliable reference solutions. An extreme non-conforming IGA model with 231 non-conforming interfaces is adopted to test the robustness of IGA. When using the weighted non-symmetric Nitsche's method, the maximum relative error of displacements is 1.7%, and the maximum relative error of von Mises stresses is 1.0%, which is acceptable in engineering. The correctness and robustness of non-conforming multi-patch IGA for the hull structural analysis are verified. The engineering practicability of IGA is proved. [ABSTRACT FROM AUTHOR]

The comment published by Dehrouyeh-Semnani (2023) is based on an incorrect assumption which results in completely erroneous conclusions. In the present paper, the invalidity of claims given by that comment are proved clearly to avoid any possible mistake for readers. [ABSTRACT FROM AUTHOR]

Modeling and analysis of stiffened panels are two key technologies in the design of aerospace thin-walled structures. For the stiffened panels with complex geometry, classical finite element analysis (FEA) and conventional isogeometric analysis (IGA) based on explicit geometry usually require time-consuming and labor-intensive geometric processing, and additional coupling matrices to be ready for analysis. In this study, a new method for modeling and buckling analysis of stiffened panels is proposed, which provides a more efficient and simpler way. During the modeling process, the stiffeners are treated as curves on surfaces, which is not explicitly defined using the control-point-based representation of curves, but implicitly defined using parameter curves in the parametric space of the surface. Mapping modeling provides more accurate geometric description and transfer the complex modeling problems (three-dimensional space) of stiffeners on free-form surface into simple modeling problems in the regular parametric space (two-dimensional space). During the buckling analysis process, a new mapped stiffener element based on mapping modeling is proposed, which can model the section of the eccentric stiffener without changing the geometry. The precise normal information of the Non-Uniform Rational B-Splines (NURBS) surface can ensure that the stiffeners are perpendicular to the skin. In addition, the coupling of the stiffener and the skin is automatic, without any additional coupling matrix. This buckling analysis framework realizes the complete integration of modeling and analysis. Furthermore, for the stiffened panels with cutouts, the trimmed surface analysis (TSA) method is extended to be used for the numerical integration of the trimmed stiffeners, which means that no additional geometric process is required. Finally, four numerical examples of different types of stiffened panels are constructed, involving metal, trimmed surface, classical grid-stiffener, free-form surface, variable-stiffness composites, and curvilinear grid-stiffener. Several numerical examples of static and buckling analysis of stiffened panels with high fidelity demonstrate the effectiveness of the proposed framework. • A new mapped stiffener element formulation is proposed for isogeometric modeling and buckling analysis. • Automatic coupling relationship between the degrees of freedom of the shell element and the stiffener element. • The extended Trimmed surface analysis (TSA) method deals with both trimmed surface and trimmed stiffener. [ABSTRACT FROM AUTHOR]

In this paper, a nonlinear FGM plate analysis model is presented based on IGA, which suppresses shear locking and is applicable to plates with a wide range of thickness-to-length ratios. Furthermore, the nonlinear aerodynamic characteristics of FGM plate subjected to the combined effect of transverse load, in-plane load, and supersonic flow are investigated. HSDT is used to construct a displacement field suitable for nonlinear vibration analysis of FGM plates with a wide range of thickness-to-length ratios. For the problem that shear locking cannot be avoided entirely in the nonlinear analysis of plates, the first derivative of transverse displacement is adopted as the first term of HSDT, which weakens the effect of shear strain. Therefore, the shear locking is effectively restrained. The nonlinear FGM plate analysis model is derived using NURBS, which meets the C1 continuity requirement of HSDT. The computational efficiency, accuracy and the suppressing capacity to shear locking are verified in three aspects: static displacement, eigenfrequency, and nonlinear frequency ratio. The Bathe method is used to obtain the displacement response of an FGM plate subjected to supersonic flow, in-plane load, and transverse load. The dynamic characteristics of the FGM plate are studied using time history, bifurcation diagrams, PSD curves, phase diagrams, and Poincaré maps. • A nonlinear functionally graded plate model is presented using the isogeometric approach. • This model suppresses shear locking and applies to plates of a wide range of thickness-to-length ratios. • This model has high efficiency and accuracy as it uses higher-order basis functions. • Airflow and functionally graded materials affect plates' dynamic characteristics. [ABSTRACT FROM AUTHOR]

In this paper, the geometrically nonlinear behaviors of functionally graded composite shells under large displacements and large rotations are analyzed. Instead of constructing conventional layer-wised models, equivalent single-layer composite shell elements based on general displacement fields are developed to model the inhomogeneity of composite materials. The mixed interpolation of tensorial components technique is used to eliminate membrane locking and shear locking phenomena. The assumed covariant strain fields are initially constructed before being used to evaluate the second Piola–Kirchhoff stress and construct stiffness matrices in local Cartesian coordinates. The standard full Newton–Raphson method is utilized to solve a system of nonlinear equations. Geometrically nonlinear analyses are performed on different thin-walled composite structures including thin cantilever beams, slit annular plates, pinched cylindrical shells, and hemispherical shells. Obtained results demonstrate good convergence characteristics and modeling capability of the developed quadrilateral composite shell elements in analyzing thin-walled composite structures. • Four-node and nine-node composite shell finite elements are presented. • Geometrically nonlinear behaviors of thin-walled composite structures are examined. • MITC technique is used to eliminate membrane-locking and shear-locking phenomena. • Analyses on composite beam, plate, cylindrical and hemispherical shells are performed. • Developed finite elements show good modeling capability for geometrically nonlinear analysis of thin-walled composites. [ABSTRACT FROM AUTHOR]

This paper is the second part in a two-part series that examines the role of geometric imperfections in load–displacement response and collapse behavior of cold-formed steel (CFS) structural members. In part I (Farzanian et al., 2023) a review of the basics and a summary of efforts geared towards modeling geometric imperfections was provided. This included the ingredients needed for systematic identification of elastic buckling mode shapes, due to their frequent use in approximating geometric imperfections, and the development of high fidelity shell finite element (FE) nonlinear collapse analysis of CFS members seeded with different geometric imperfection models. Part II is the companion to the analysis in part I that revealed a noticeable variability in the collapse behavior and load carrying capacity of CFS members as a result of adopting different imperfection modeling strategies. In this part we provide the necessary steps to build a probabilistic framework that rests on machine learning, polynomial approximation, and parametric and non-parametric statistical inference and uses imperfection data to build a consistent stochastic field model of geometric imperfections. This data-driven model is then used to generate the much needed realizations of geometric imperfections that are faithful to the underlying statistics of measured data and therefore can be seeded, directly, in nonlinear collapse analysis of CFS members. Nonlinear shell FE analysis, within a stochastic simulation framework, is finally used to (statistically) quantify the impact of geometric imperfections and to enable probabilistic validation of geometric imperfection models. • The impact of random geometric imperfections on nonlinear response of CFS members is studied. • A data-driven framework for building stochastic field models over measured imperfection data is presented. • Realizations of geometric imperfections, faithful to the underlying statistics of measured data, are generated. • Statistically consistent realizations of imperfections are used in stochastic nonlinear analysis of CFS members. • The statistics of nonlinear response are used for the validation of geometric imperfection models. [ABSTRACT FROM AUTHOR]

With the wide application of lightweight structures, it is necessary to precisely and efficiently predict dynamic response of sandwich plates for the dynamic safety of sandwich structures in service life. Due to the weak normal stiffness of the core, the used higher-order shear deformation theories (HSDTs) are required to consider the transverse normal strain. To the best knowledge of authors, the most efficient and accurate higher-order theory including transverse normal strain merely contains six independent unknowns. However, the existing six-unknown higher-order theories may be incapable of accurately forecasting the dynamic response of the soft-core sandwich plates attributing to the huge mismatches of mechanical properties. Therefore, a novel Gaussian higher-order plate theory (NGHPT) with six independent variables has been developed for the free and forced vibration of sandwich plates, where the transverse shear function is defined by Gaussian function and Fourier transformation to approximately fulfill the continuity requirement of transverse shear stresses at the interfaces. Meanwhile, the isogeometric analysis (IGA) is utilized to handle complex geometries. Compared to the existing HSDTs with six unknowns, the NGHPT can more accurately predict the dynamic behaviors of sandwich plates, which is verified by several experimental tests. Furthermore, a comprehensive parametric study on various sandwich plates including square, circular, elliptical and annular shapes, has been carried out to evaluate the influence of fiber orientation, distribution of internal pores and porosity coefficient on the dynamic response, which can provide suggestions for the future designs of porous sandwich plates to meet specific dynamic requirements. • A novel Gaussian higher-order plate theory is developed by Gaussian function and Fourier transformation. • Several vibration tests on the CFRP sandwich plates with various fiber orientations are carried out. • Effects of fiber orientation and porosity coefficient on free and forced vibration are investigated. [ABSTRACT FROM AUTHOR]

This paper presents the axisymmetric thermal postbuckling analysis of functionally graded graphene platelets-reinforced composite (FG-GPLRC) annular plates with various geometric imperfections within the framework of first-order shear deformation theory and von Kármán geometric nonlinearity. An imperfection model composed of trigonometric and hyperbolic functions is used to simulate possible imperfections with different shapes, amplitudes and locations. The 3D Halpin–Tsai model is employed to estimate the effective modulus of graphene nanocomposites. Nonlinear governing equations are derived by the variational principle and are then solved by the generalized differential quadrature method combined with the modified Newton–Raphson iteration. Parametric studies are conducted to highlight the influences of imperfection amplitude, localization degree, location and half-wave number on the thermal postbuckling behaviour of FG-GPLRC annular plates. It is found that the thermal postbuckling resistance is reduced due to the existence of geometric imperfections, and this effect become more/less significant as the imperfection amplitude/half-wave number increases. • Thermal postbuckling of FG-GPLRC annular plates with geometric imperfections is investigated for the first time. • The 3D Halpin–Tsai model is introduced to evaluate the elastic modulus of 3D-random graphene nanocomposites. • Thermal postbuckling resistance is more weakened by the global imperfections than the localized ones. • Thermal postbuckling behaviour is less sensitive to the imperfections with a smaller amplitude or more half-waves. [ABSTRACT FROM AUTHOR]

In the present work, nonuniform rational B-spline (NURBS) based isogeometric formulation in conjunction with refined higher-order theory is used to investigate the linear buckling, post-buckling, and post-buckled vibration behaviour of initially imperfect skew sandwich plates. The face sheets are functionally graded carbon nanotube-reinforced composite (FGCNTRC), and the core layer is made up of aluminium foam. The effects of three types of CNT distributions (uniform, FGX and FGO) in the face sheets, two types (uniform, symmetric) of porosity distribution functions for the core layer and five types of in-plane compressive loads are examined in the present investigation. The pre-buckling stresses are calculated using static analysis to evaluate accurate, critical loads. The post-buckling paths are traced using the modified Riks method. The accuracy of the present results is ascertained by comparing the results for critical loads and post-buckling paths with those available in the literature. Subsequently, the influence of CNT distribution functions, porosity functions, compressive loads, skew angle and the side-to-thickness ratio is studied on the nonlinear stability and free vibration behaviour of the post-buckled skew sandwich plates. The obtained results highlight that the buckling strength can be improved by increasing the skew angle, increasing the concentration of CNTs towards the surface of the face sheets and by using a metal foam core with nonuniform porosity distribution. • Isogeometric formulation is based on a refined higher order theory. • Vibration behaviour of postbuckled sandwich skew plates. • Sandwich plate with FGCNTRC facesheets and aluminium foam core. • Various types of non-uniform compressive edge loads are considered. [ABSTRACT FROM AUTHOR]