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This article investigates the nonlinear analysis of hyperelastic planar curved beams based on the total Lagrangian Timoshenko theory. The fully incompressible neo-Hookean model has been selected as the constitutive relation to accurately capture large deformations. The nonlinear equations and boundary conditions derived from the virtual work principle are solved using the Newton–Raphson method. Employing isogeometric analysis with NURBS functions to discretize the unknown kinematics, including displacements and rotation, and the linearized governing equations. The study accounts for conservative and non-conservative forces, validating results against available experimental and numerical results reported in the literature, confirming the proposed formulation's effectiveness and precision. [ABSTRACT FROM AUTHOR]

AbstractThe free vibration analysis of rotating pre-twisted composite beams with arbitrary cross-section geometry is investigated using an isogeometric-based dimensional reduction method. The three-dimensional beam problem is decomposed into a two-dimensional cross-sectional analysis and a one-dimensional beam problem, significantly reducing the numerical cost compared to three-dimensional finite element method. The simultaneous influences of pre-twist and rotational speed are carefully studied for various composite beams. This approach benefits from the numerical advantages of isogeometric analysis, with results showing better agreement with three-dimensional finite element method than other studies in the literature. [ABSTRACT FROM AUTHOR]

This article performs the buckling and vibration studies of the sandwich plates with a negative Poisson's ratio honeycomb core. Based on the isogeometric analysis in conjunction with the refined shear deformation theory, the discrete equilibrium equations of the sandwich plate are established. Numerical results show that the plate with negative Poisson's ratios of the honeycomb core layer has a higher load-bearing capacity than that with positive Poisson's ratios. In addition, the optimal inclined angles of honeycomb core for negative Poisson's ratios subjected to different loading types are obtained. The normalized natural frequency of the plate almost decreases by 10% when the Poisson's ratio ν12 of honeycomb core decreases from −0.3 to −5.5. [ABSTRACT FROM AUTHOR]

AbstractFunctionally graded triply periodic minimal surface (FG-TPMS) structures are known as bio-inspired structures. They possess some remarkable advantages such as porous structures with high inter-connectivity, mathematically controllable geometry features and smooth surfaces. As another advantage, FG-TPMS structures can be fast and numerously manufactured by 3D printing technology. Nevertheless, modeling these structures is a challenging task. This paper investigates static bending and free vibration behaviors of FG-TPMS shells. The proposed formulation is established upon isogeometric analysis (IGA) and first-order shear deformation shell theory (FSDT). The governing equations are discretized by a Galerkin weak form and numerically solved by using non-uniform rational B-Spline (NURBS) basis functions. Exact geometries of structures are described via NURBS basis functions. A fitting technique is used to compute the mechanical characteristics of FG-TPMS materials. We investigate behaviors of FG-TPMS shells considering three types of cell geometries which are primitive (P), gyroid (G), I-graph and wrapped package-graph (IWP), and six porosity distribution patterns. The present solutions are verified with the reference ones in the literature. Effects of boundary, type of cell geometry, porosity distribution pattern, length-to-radius and thickness ratios on behaviors of FG-TPMS shells are rigorously studied. Especially, many numerical results of FG-TPMS shells are first proposed in this paper. [ABSTRACT FROM AUTHOR]

In this study, the thermo-mechanical dynamic buckling analysis of two-directional functionally graded porous (2D-FGP) shallow microshells resting on elastic foundations with arbitrary boundary conditions is performed using the isogeometric approach. The isogeometric approach takes advantage of non-uniform rational B-spline basic functions to exactly represent the structure geometry models and the attainment of higher order approximation conditions. The characteristics of the material vary in both the thickness and axial x orientation. Especially, a new point in this material length-scale parameter of microshell is analyzed as a function of spatial coordinates and as a function of the material gradient parameters. Using Hamilton's principle, the modified couple stress theory, and Kirchhoff-Love's shell theory, the governing equations of a 2D-FGP microshell lying on a Pasternak medium are obtained. A computer program that employs an isogeometric analysis method to analyze the static and dynamic buckling of a 2D-FGP doubly curved shallow microshell with various boundary conditions. The numerical results for thin cylindrical, spherical, and hyperbolic paraboloidal shallow microshells with various planforms, such as rectangular and circular, are presented. Several special cases are used to demonstrate the accuracy and efficacy of the developed model by comparing the numerical results obtained by the proposed formulations with other published data. In addition, the effects of certain parameters, such as the length scale parameters, the power-law indexes, the thickness-to-sides ratio, and the radius ratio, on the dynamic thermo-mechanical buckling response of the 2D-FGP shallow microshells with double curvature are explored in depth. [ABSTRACT FROM AUTHOR]

In this article, we apply NURBS-based isogeometric method to solve a nonlocal degenerate parabolic problem. The isogeometric method has advantages over classical finite element method in terms of exact geometry representation and higher order smooth basis functions. We consider the NURBS-based semi-discretization of the problem. The second-order Crank–Nicolson method is applied for the complete discretization of the problem. Error estimates of the semi-discrete and fully-discrete problems are derived. Few numerical examples are provided to verify the theoretical findings. [ABSTRACT FROM AUTHOR]

AbstractIsogeometric high-order analysis of a sandwich beam is presented in this article. The kinematic and geometric modeling is applied using the higher order modeling based on the stretchable models. The suggested model in this article can be applied for the sport equipment specially for analysis of diving beams boards and beams. The Variational-based approach is extended to derive governing equations. The results are analytically obtained in order to seek impact of significant parameters of the problem on the responses. The results are confirmed through comparison with available ones in the literature. [ABSTRACT FROM AUTHOR]

AbstractThis study addresses the multi-material optimization problem by the effective and robust isogeometric proportional topology optimization (IGA-PTO) approach. Non-uniform rational B-spline basis functions are used for descriptions of geometry, displacement field, and density fields of material phases. The alternating active-phase algorithm is employed to convert the optimization problem with multiple constraints into a series of sub-problems of single constraint. Several examples are exhibited, and intensive comparisons with the gradient-based optimality criteria (OC) algorithm are presented to highlight the superior performance of the proposed PTO algorithm. Finally, the optimized topologies are prototyped using 3D printing technology to evidence the manufacturing feasibility. [ABSTRACT FROM AUTHOR]

In the present article, the panel flutter behavior of nanocomposite hybrid laminated quadrilateral panel is studied. A three-phase carbon-nanotube (CNT)/polymer/fiber laminated composite is considered where the probable agglomeration of the CNT phase in the nano-matrix mixture is also addressed. Diverse use of fiber phase material in different plies is assumed in the context of hybrid laminated composite. A combination of nanocomposite polymer matrix, tow-steered curvilinear reinforcing fibers within the plies, and hybrid multi-material laminate is considered. The panel flutter behavior of the arbitrary quadrilateral hybrid laminated nanocomposite plate is formulated by a non-uniform rational B-splines-type isogeometric analysis method based on the first-order shear deformation plate theory. The nonideal mixture of the nanocomposite is also concerned about through applying a micromechanics approach. Representative results are obtained and compared with those available in the literature to demonstrate the quality of the proposed formulation. The effects of different parameters including the layup, mixture quality, boundary condition, geometry, and flow direction on the flutter behavior are investigated by performing parametric studies. [ABSTRACT FROM AUTHOR]

AbstractTo solve the multi-physical coupling characteristics of piezoelectric structures, the thermal-mechanical-electrical coupling isogeometric analysis method (TMEC-IGA) is proposed to explore the structures of piezoelectric materials. Based on the basic equations and boundary conditions of piezoelectric materials, NURBS basis function is introduced to construct displacement and electrical potential functions, and the control equation of TMEC-IGA is derived. Numerical examples show that TMEC-IGA is effective in solving the thermal-mechanical-electro coupling problem of piezoelectric structures, and has broad application prospects in the design, development and performance analysis of piezoelectric devices. [ABSTRACT FROM AUTHOR]

Sandwich structures have been increasingly used in aerospace engineering, while local vibration modes of sandwich plates might occur earlier than global vibration modes attributing to the weak stiffness of the core layer, and it is difficult to predict such vibration modes. Therefore, local vibration modes are often discarded in the process of structural design, so that potential dangers might be encountered when the frequency of external load is close to the natural frequency of local vibration. To avoid such an issue, an extended Legendre higher-order theory (ELHT) is developed to accurately forecast the local dynamic behaviors of sandwich plates for the first time. Subsequently, an effective multi-objective optimization platform will be constructed to optimize the distribution of graphene-nanoplatelets (GPLs) in the core layer, so that natural frequencies of local vibration modes will be improved and largely more than the fundamental frequency. The B-spline basis functions are employed to describe various GPLs distributions, which is more convenient to produce original data for the machine learning method in the optimization process. Then, extreme gradient boosting optimized by Sparrow Search Algorithm (SSA-XGBoost) is utilized as the high-fidelity surrogate model to construct the objective functions to accelerate the interaction of the ELHT and non-dominated sorting sparrow search algorithm (NSSSA). By optimizing for minimum global and local fundamental frequency ratio and total mass of GPLs reinforced sandwich plates, the Pareto-optimal solutions are obtained from the present algorithm which can give an alternative suggestion for the future designer to ensure the structural dynamic safety of thick sandwich plates. [ABSTRACT FROM AUTHOR]

AbstractThis study delves into the impact of material and fabrication uncertainties on the natural frequencies of rim-driven rotating structures. Utilizing a higher-order shear deformation theory (HSDT), an isogeometric analysis (IGA) model predicts these frequencies. Sensitivity analysis via a radial basis function network (RBFN) model, validated with Monte Carlo simulation, highlights parameter influence. Parametric investigations unveil sensitivity patterns and influential parameters. Employing a stochastic approach, the study compares the effects of random material properties on the free vibration response of rotating and non-rotating plates. Additionally, the RBFN-based surrogate model assesses reliability parameters concerning resonance failure in rim-driven rotating composite structures. [ABSTRACT FROM AUTHOR]

In this communication, it is mathematically proved that the modified couple stress theory-based stability trend (buckling-post-buckling) of the size-dependent porous functionally graded (metal-ceramic) shear deformable microplates with fully simply supported edges was wrongly predicted in the aforementioned paper. [ABSTRACT FROM AUTHOR]

This work presents analyses of interfacial crack in piezoelectrics bimaterial plate under electromechanical loading environment by extended isogeometric analysis (XIGA) approach using Bézier extraction of NURBS. Asymptotic crack–tip branch functions and discontinuous Heaviside function are implemented for local enrichment in the approximation of isogeometric analysis for capturing singularity at cracktip and discontinuity across surfaces of a crack. Bézier extraction of NURBS–based basis functions are implemented in discretization of domain for approximating both unknown field solution and geometries. The Bézier extraction operation decomposes the NURBS basis functions into a set of linear combination of Bernstein polynomials and a set of C 0 –continuity Bézier elements. Domain–form interaction integral is implemented to obtain generalized fracture parameters. To assess the robustness and accuracy in results obtained from XIGA, numerical results are first validated from analytical ones and then additionally, few numerical problems are solved for calculating the fracture parameters in terms of normalized intensity factors with respect to shear loads, electrical loads, crack orientation angle and angle of polarization. [ABSTRACT FROM AUTHOR]

Energy-dependent self-adaptive mesh refinement algorithms are developed for a symmetric interior-penalty scheme for a discontinuous Galerkin spatial discretization of the multi-group neutron diffusion equation using NURBS-based isogeometric analysis (IGA). The spatially self-adaptive algorithms employ both mesh (h) and polynomial degree (p) refinement. The discretized system becomes increasingly ill-conditioned for increasingly large penalty parameters; and there is no gain in accuracy for over penalization. Therefore, optimized penalty parameters are rigorously calculated, for general element types, from a coercivity analysis of the bilinear form. Local mesh refinement allows for a better allocation of computational resources; and thus, more accuracy per degree of freedom. Two a posteriori interpolation-based error measures are proposed. The first heuristically minimizes local contributions to the discretization error, which becomes competitive for global quantities of interest (QoIs). However, for localized QoIs, over energy-dependent meshes, certain multi-group components may become under-resolved. The second employs duality arguments to minimize important error contributions, which consistently and reliably reduces the error in the QoI. [ABSTRACT FROM AUTHOR]

Energy-dependent self-adaptive mesh refinement algorithms are developed for a continuous Bubnov-Galerkin spatial discretization of the multi-group neutron diffusion equation using NURBS-based isogeometric analysis (IGA). The spatially self-adaptive algorithms employ both mesh (h) and polynomial degree (p) refinement. Constraint-based equations are established across irregular interfaces with hanging-nodes; they are based upon master-slave relationships and the conservative interpolation between surface meshes. A similar Galerkin projection is employed in the conservative interpolation between volume meshes to evaluate group-to-group source terms over energy-dependent meshes; and to evaluate interpolation-based error measures. Enforcing continuity over an irregular mesh does introduce discretization errors. However, local mesh refinement allows for a better allocation of computational resources; and thus, more accuracy per degree of freedom. Two a posteriori interpolation-based error measures are proposed. The first heuristically minimizes local contributions to the discretization error, which becomes competitive for global quantities of interest (QoIs). However, for localized QoIs, over energy-dependent meshes, certain multi-group components may become under-resolved. The second employs duality arguments to minimize important error contributions, which consistently and reliably reduces the error in the QoI. [ABSTRACT FROM AUTHOR]

An optimal electric machine design task can be posed as a constrained multi-objective optimization problem. While the objectives require time-consuming finite element analysis, constraints, such as geometric constraints, can often be based on mathematical expressions. This article investigates this mixed computationally expensive optimization problem and proposes a computationally efficient optimization method based on evolutionary algorithms. The proposed method always generates feasible solutions by using a generalizable repair operator and also addresses time-consuming objective functions by incorporating surrogate models for their prediction. The article successfully establishes the superiority of the proposed method over a conventional optimization approach. This study demonstrates how a complex engineering design task can be optimized efficiently for multiple objectives and constraints requiring heterogeneous evaluation times. It also shows how optimal solutions can be analysed to select a single preferred solution and harnessed to reveal vital design features common to optimal solutions as design principles. [ABSTRACT FROM AUTHOR]

In linear isogeometric analysis of beams, the success of selective reduced integration and B ¯ projection methods in mitigating the locking phenomenon has been proved. This study further extends these methods to the geometrically nonlinear analysis with two isogeometric Timoshenko–Ehrenfest beam formulations, that is, C 0 -continuous NURBS selective reduced integration and B ¯ formulations. Three numerical examples are presented examining overall structural responses, strain energy, recovery of cross-sectional stress resultants, and convergence properties. Although the two proposed formulations exhibit the locking-free behavior for highly flexible beam structures, the B ¯ formulation offers higher accuracy, and the proper recovery of strain measures and cross-sectional stress resultants. [ABSTRACT FROM AUTHOR]

In this study, the nonlinear bending behavior of multi-directional functionally graded plates with variable thickness is investigated. To this regard, the governing equation of the plate problem is developed based on the principle of virtual work, while the third-order shear deformation plate theory proposed by Reddy is employed to describe the kinematic relations. The geometrical nonlinearity is taken into account by adopting the von Kármán's assumptions for nonlinear problems with small strains and moderate rotations. The plates investigated in this study are assumed to be made from two different material constituents, whose volume fractions vary spatially within the plate domain. The effective material properties are calculated based on the mixture approach. The Isogeometric Analysis approach is used as a numerical method to solve the governing equations. NURBS basis functions are used as interpolation functions for geometrical modeling and discretization procedure, where the C1-continuity requirement is meet efficiently. Various numerical examples are conducted to validate the accuracy of the proposed approach and investigate the influences of geometrical and material factors on the nonlinear bending responses of the plates. [ABSTRACT FROM AUTHOR]

Stiffness properties of structural members, such as beam, plate and shell, can change drastically in the presence of axial forces due to geometric effects of the nonlinear strain components. In this paper, the stability behaviour of beam-column is investigated using the governing differential equation and compared with the geometrically nonlinear finite element analysis. The lateral deflection obtained from the theoretical model matches quite accurately with the numerical values for wide range of axial to critical load ratio P/Pcr. It is shown that bending stiffness decreases linearly with the axial load. By extending the theory, an expression for the membrane stiffness of the beam-column is presented in this paper. The geometrically nonlinear finite element analysis can capture exactly the parabolic variation of the membrane stiffness as per the derived expression. It increases initially up to P/Pcr = 0.35 and decreases rapidly to negligible value near the critical load indicating buckling instability. [ABSTRACT FROM AUTHOR]

A unified shape and non-shape design optimization for lattice structures is performed to obtain extremal band gaps in an isogeometric computational framework, which uses the same NURBS basis functions as used in CAD description. Using a precise numerical model in both response and shape sensitivity analyses, enhanced response and sensitivity can be obtained, which leads to a precise optimal design. A plane wave propagation in infinite periodic lattice is analyzed within a representative unit cell using the Bloch theory with periodic boundary conditions. The ligaments of lattice structures are modeled using geometrically exact beams whose cross-sectional area and configuration are regarded as design variables, which are parameterized by the NURBS basis functions. The design variables are controlled by a mathematical programming algorithm with efficient adjoint design sensitivity. The obtained optimal lattice structures of triangular, squared, hexagonal, and Kagomé structures are fabricated using a 3D printing machine to be validated by physical experiments. Through harmonic response analysis and physical experiment for the optimal and the original designs, the wave attenuation properties are compared to demonstrate the validity of the obtained optimal design. [ABSTRACT FROM AUTHOR]

The current work presents the combination of isogeometric approach (IGA) and Carrera unified formulation (CUF) to perform the buckling analysis of isotropic thin-walled and orthotropic beams. Toward this end, the layerwise (LW) theory based CUF and B-spline basis functions in IGA have been used. The LW theory uses Lagrangian expansion (LE) to estimate the displacement field in the cross-section. However, in the present study, B-spline basis functions in both longitudinal direction and cross-section have substituted the corresponding functions. The CUF expresses the 3 D displacement fields as a set of 1 D generalized unknown displacement. Combined model in the present study obliterates the costly use of 3 D finite element analysis with its high accuracy and loyalty to 3 D problems. The principle of virtual displacement (PVD) is used to obtain the fundamental nuclei. One of the features of CUF is that it's higher-order expansion is free of the Poisson locking phenomenon. Also, there is no need to use the shear correction factor. Some examples of the isogeometric analysis of laminated composite beams with different geometries and boundary conditions are conducted and comparison of the critical buckling load results illustrate the proper validation and formulation of the present study. [ABSTRACT FROM AUTHOR]

Creating a formal model for timbre is one of the most compelling open questions in music research. In contrast to more traditional perceptually-oriented approaches, often aimed at sound analysis, we introduce a three-dimensional geometric model of timbre, specifically designed for sound synthesis. The proposed model relies on the properties of space-filling curves for multidimensional scaling, and represents via three parameters, any static combination of sinusoidal partials with an additional noisiness component. We detail the construction of the model and its properties and discuss future implications for music research. [ABSTRACT FROM AUTHOR]

This exploration deals with the nonlinear large deflection behavior of nanocomposite plates reinforced with functionally graded carbon nanotube (FG-CNT) having various shapes with variable thickness. To accomplish this end, a hybrid quasi-3D plate model is constructed by incorporating trigonometric normal and sinusoidal transverse shear functions. The applied plate formulations have the capability to model the nanocomposite plate with only four independent variables which results in a significant reduction in the computational cost of computational calculations. Four different dispersion schemes for the CNT reinforcement are considered, the effective mechanical properties of each one are achieved via an extension of the rule of mixture. In addition, plate thickness is assumed to vary in convex, concave and linear patterns. For solving nonlinear problem, isogeometric technique using non-uniform rational B-spline basis functions is employed to integrate an accurate geometric description. It is revealed that at deeper parts of flexural response, the role of CNT dispersion pattern on the nonlinear flexural stiffness of FG-CNT reinforced composite plates gets lower importance. Moreover, it is demonstrated that by substituting linear thickness variation scheme with convex one, the influence of CNT dispersion pattern reduces, but by changing from the linear type to the concave one, this influence increases. [ABSTRACT FROM AUTHOR]

Recently, non-prismatic beams have been considered as perfect substitutes to replace uniform cantilever beam structures in harvester design. This is due to their tendencies to provide uniform strain distribution, which enhances piezoelectric (PZT) charge generation when coupled with the beams. As the voltage produced by the PZT depends largely on the geometrical shape of the substrate, thus there is need for formulations to analyze the behavior of the shim prior to practical implementation. In this paper, analytical and finite element models were developed to study deflection and strain distribution of a non-prismatic beam termed, wedge edged cantilever (WEC) for patch-like harvester application. The analyses offer possibility for maximum utilization of strain location along the beam span for efficient harvester design. Vibration energy harvesting characteristics of the WEC beam with partially covered PZT material forming three configurations namely: Config1, Config2 and Config3 were studied. Both numerical and experimental results show that Confg3 with macro fiber composite (MFC) as the PZT material covering the determined optimal strain position yielded 2 to 3 times more peak output voltage than Config1 and Config2 with the MFC bonded at non-optimal positions. [ABSTRACT FROM AUTHOR]

Although fiber reinforced polymers (FRPs) have become the most widely used material to strengthened existing concrete structures in shear, premature debonding of externally bonded FRP remains a significant cause of material under-utilisation. In an effort to suppress debonding failure, research has shown that the use of ±45° bidirectional fabric patch anchors can delay the occurrence of FRP debonding. However, most research to date on patch anchors has been based on joint-level tests and the data available on full-scale beam applications has been very limited. One means by which additional data can be generated on the performance of patch anchors when applied to full-scale beams is using finite element simulations. This paper presents a 2D and 3D non-linear finite element model calibrated using available data on prestressed T-beams strengthened in shear with FRP laminates and patch anchors. The models captured the failure modes, strains in the FRP and crack patterns of the specimens very well and predicted the failure load for the control, strengthened and anchored specimens within a margin of difference of 6–9%, 4–13% and 1–2%, respectively. Parametric studies involving variation of concrete strength and FRP thickness were conducted to generate additional data and the research findings are presented. [ABSTRACT FROM AUTHOR]

This article describes the process of topology optimisation (TO) of three components of an electric scooter, namely the neck, platform, and suspension bracket. We use these example parts to investigate the additive manufacturing (AM) workflow, from re-design to nesting and support approach that has an impact on the total costs and time required for product development and manufacturing, with a focus on Direct Metal Laser Sintering (DMLS) technology. Due to the mathematically generated shape, components that are topology optimised and fabricated through AM have improved structural load-to-weight ratio. The article elaborates on the cost of manufacturing these new geometrical structures and re-designing existing components. Recognising topology-optimised design features for the LPBF manufacturing process like creating touch points between parts in 3D nesting orientations and lattice structure integration reduces cost in volume production. Our study shows that it is beneficial for the DMLS process to perform finite element analysis (FEA) and optimise components using TO and lattice structures, as weight reduction also translates to cheaper fabricating parts. Defining and implementing a streamlined workflow for editing the complex automatically generated support structures improves manufacturability. Such approaches encourage companies to adopt wider LPBF processes in mainstream industries. Abbreviations: AM = additive manufacturing; DMLS = direct metal laser sintering; TO = topology optimisation; SLS = selective laser sintering; FEA = finite element analysis; CAD = computer-aided design; CAM = computer-aided manufacturing; 3D = three dimension; CAE = computer-aided engineering [ABSTRACT FROM AUTHOR]

Isogeometric analysis is a spline-based discretization method to partial differential equations which show the approximation power of a high-order method. The number of degrees of freedom, however, is as small as the number of degrees of freedom of a low-order method. This does not come for free as the original formulation of isogeometric analysis requires a global geometry function. Since this is too restrictive for many kinds of applications, the domain is usually decomposed into patches, where each patch is parameterized with its own geometry function. In simpler cases, the patches can be combined in a conforming way. However, for non-matching discretizations or for varying coefficients, a non-conforming discretization is desired. An symmetric interior penalty discontinuous Galerkin method for isogeometric analysis has been previously introduced. In the present paper, we give error estimates that are explicit in the spline degree. This opens the door towards the construction and the analysis of fast linear solvers, particularly multigrid solvers for non-conforming multipatch isogeometric analysis. [ABSTRACT FROM AUTHOR]

This paper investigates the bending and vibration characteristics of metallic and functionally graded (FG) beam structures. The weak form of governing equations and boundary conditions are derived using Carrera unified formulation (CUF). The isogeometric analysis (IGA) is employed to solve the static and free vibration problems. NURBS basis functions approximate the displacement field unknowns and material gradations in cross-section. In contrast, the axial displacements are evaluated by either NURBS or Lagrange basis functions. In this framework, the equations are extracted in the form of a fundamental nucleus, which allows the study of different beam theories in a constant formulation. Several numerical examples are presented and compared with results available in the literature to address the accuracy and effectiveness of the current approach. It is found that the present results are validated for different aspect ratios, boundary conditions, and material distribution with more accuracy and low computational cost. [ABSTRACT FROM AUTHOR]

A porosity-dependent nonlinear postbuckling analysis for microplates prepared from a porous functionally graded material (PFGM) is performed based on the modified couple stress theory of elasticity (MCSTE). To accomplish this purpose, the modified couple stress-based nonlinear differential equations are derived by third-order shear deformation plate theory (TSDPT). To extract PFGM microplate effective mechanical properties, a power-law function is utilized which is capable of incorporating porosity dependency and material gradient, simultaneously. Thereafter, the non-uniform rational B-spline (NURBS)-based isogeometric analytical method is employed as an effective discretization method which could satisfy C−1 continuity condition. It is demonstrated that the gap between equilibrium paths relevant to various couple stress length scales reduces by going deeper in postbuckling regime. Also, one can see that for certain porosity and material property gradient index values, by boundary condition transformation from simply supported to clamped, the contribution of the effect of couple stress size in PFGM microplate postbuckling response becomes more significant, especially for a higher maximum deflection values. [ABSTRACT FROM AUTHOR]

The size-dependent bending and free vibration of bi-directional functionally graded graphene nanoplatelets reinforced composite (BDFG-GPLRC) microbeams are investigated based on the Timoshenko beam theory and isogeometric analysis (IGA). The modified couple stress theory (MCST) is employed to describe the scale effect of microbeams. GPLs are distributed as power functions along the thickness and axis directions and four types of distribution patterns are taken into account. Employing the minimum potential energy principle and Hamilton's principle, the government equations are established and solved by IGA. Correctness and accuracy of this method are verified by comparing with a published paper. By means of several numerical examples, the effects of GPL weight fraction, power-law indexes, boundary conditions and scale parameter on bending and free vibration behaviors of BDFG-GPLRC microbeams are studied in detail. [ABSTRACT FROM AUTHOR]

Free vibration and bending of laminated plates on Winkler foundations are investigated based on a combination of generalized layerwise theory (LW) for higher-order shear deformation theory (HSDT) and the meshless radial point interpolation method (RPIM). The shape function of the meshless radial interpolation method is used to discretize the weak form control equations derived from the principle of virtual work. The shape functions have the properties of Kronecker functions. The slope components associated with the first-order derivatives of the transverse displacements are defined as approximate variables. The transverse shear stresses at each layer interface are continuous. A comparative study with literature solutions verified the numerical stability and applicability of the combined generalized LW-HSDT and meshless RPIM methods. The effect of Winkler modulus parameters on the vibration performance and bending performance of the laminated plate was investigated. The results of bending, vibration frequencies and modes of the laminated plates on different Winkler foundations are presented. It is found that initially, the Winker foundation had a significant effect on the frequency magnitude and bending deformation, but little influence on vibration mode. After the influence of the foundation on the frequency enters the stable period, the influence of foundation on the mode shape will be significant. With the relaxation of the boundary conditions, the vibration mode will still be affected when the foundation parameters are small. It is for the first time that the laminated plates on Winker foundations were investigated using a combination of higher-order layerwise theory and meshless radial interpolation method. In the proposed model, the slope component related to the first-order derivative of the transverse displacement is defined as an approximate variable and does not require the boundary to be treated by the isogeometric method. The transverse shear stresses at the interface of each layer are continuous for the bending analysis of laminated panels. The meshless results reveal the influence of the Winker foundation parameters on the vibration characteristics of the laminated plate [ABSTRACT FROM AUTHOR]

This research aims to develop a finite element model of nonpneumatic tires (NPTs) with different spoke shapes to study the geometric effects on the NPT for the maximum stiffness and minimum local stress. Four types of spoke structure were classified from reviewed articles and intellectual property. These were based on a few criteria including (1) manufacturability using polyurethane or engineering polymer as the material and (2) simplicity of the shape, the shape with less complexity and simple patterns. The finite element models of NPTs with different four spoke types were created using the same tread, shear band and the overall dimension. The spoke component of each model was created using 2D elements, with the different thickness to give the same mass. The hyperelastic constitutive equations were used to model behavior of NPT tread and spokes. The finite element analysis of vertical stiffness testing was performed on the NPT models using the maximum load required for skid-steer loaders. The analysis results were then compared to give an overview of load capacity of each model along with each advantage/disadvantage. The model with highest vertical stiffness by weight ratio was selected for the optimum number of spoke. Parabolic trends in vertical stiffness and maximum local stress at different spoke numbers were observed. This study found that the upper design limitation of spoke number was 24 spokes. Thus, the optimized number of spokes can be observed and the finite element model can be used to define the optimum geometry for a novel NPT. [ABSTRACT FROM AUTHOR]

This article presents the critical speed analysis of spinning laminated composite shaft under the different coupling mechanism effects based on isogeometric analysis. The analysis of the layered tubular composite shaft is usually performed using shell elements, but the present study concerns with the equivalent single layer theory (ESLT) obtained from the transformation of the cylindrical coordinates to the Cartesian coordinates and therefore, it avoids the use of non-uniform rational Bsplines. The results obtained are in good agreement with the modified EMBT and the modified SHBT. It is found that the proposed approach can yield highly accurate solutions compared with other existing methods available in the literature. In addition, the numerical results of critical speeds are obtained and investigated under the Poisson's effects and different mechanism coupling effects, length-to-mean diameter ratios, and stacking sequence of layers. [ABSTRACT FROM AUTHOR]

The current literature deals with the multi-objective optimal material distribution of porous functionally graded plates subjected to free vibration in the framework of Carrera Unified Formulation (CUF) based on isogeometric analysis (IGA). The objective function is to maximize the natural frequencies and minimize the weight of the PFG plate, considering the material properties and porosity through the thickness of the plate. The governing equation of the PFG plate is obtained by using the principle of virtual displacement (PVD) based on the CUF. A non-uniform rational B-splines (NURBS)-based isogeometric finite element model associated with CUF is utilized for the plate free vibration analysis. The Legendre polynomials are used to approximate the thickness direction of plates. The rule of mixture is used to estimate the effective material properties. The Multi-Objective Particle Swarm Optimization (MOPSO) algorithm is employed as an optimizer. Design variables are the power and porosity indices. For verification, several structural design examples are compared with those available in the literature. Several numerical examples for optimizing the PFG plates, including maximization of the first natural frequency and minimization of mass, illustrate the effectiveness and reliability of the proposed method. The results show that the optimum values for the power and porosity indices depend on the objective function and boundary conditions. Furthermore, the clamped boundary condition leads to less mass than the simply-supported boundary condition for each desired first natural frequency. [ABSTRACT FROM AUTHOR]

The current work presents an investigation on size-dependent nonlinear free vibration of porous skew and elliptical nanoplates. Formulations are based on a four-variable higher-order shear deformation plate theory to satisfy automatically the traction-free condition, von Kármán geometric nonlinearity to account for the mid-plane stretching, and Eringen's nonlocal elasticity theory to capture the scale effect. The isogeometric analysis and a displacement control strategy are employed synthetically to obtain large amplitude responses of the nanoplates. New results show the influences of porosity distribution pattern, porosity coefficient, and nonlocal parameter on the behaviors of vibration behaviors of the skew and elliptical nanoplates. [ABSTRACT FROM AUTHOR]

In this work, the extended isogeometric analysis (XIGA) is presented for the analysis of cracks in elastic material subjected to thermal, mechanical, and thermo-mechanical loading. The comparative study on the effect of mechanical and combined thermo-mechanical load on stress intensity factors (SIFs) is performed. Two types of cracks, i.e., isothermal and adiabatic crack, is considered for the simulation. The crack is modeled using suitable enrichment functions. A modified domain-based interaction integral approach is used to extract the SIFs. Several simulations are performed to validate the accuracy of the results. Moreover, the effect of discontinuities (e.g., voids) on SIFs is analyzed. [ABSTRACT FROM AUTHOR]

This article intends to study the performance of sandwich panels consisting of four isotropic flat plates and three trapezoidal or sinusoidal cores. The sandwich panels, subjected to the uniform loading resting on simply supported edges, are analyzed by an analytical method based on the classical plate theory and commercially available software. The homogenization method is used for the analytical method to replace the core by a flat plate with an equivalent stiffness. Results show that the deflected shape of the equivalent sandwich plate with the flat core is similar to that of the original corrugated plate measured by using shell elements in ABAQUS. The effects of geometric characteristics on the deflection and Von-Mises's stress are also studied by the finite element method analysis. Results show that the trapezoidal-core panel has better performance as compared to the sinusoidal-core one. Moreover, results show that the corrugation thickness and amplitude have considerable effects on the performance of the panel. A wide validity range is also obtained for the thickness of the sinusoidal-core panel as compared to the trapezoidal-core panel. [ABSTRACT FROM AUTHOR]

In the present work, we consider weakly-singular integral equations arising from linear second-order elliptic PDE systems with constant coefficients, including, e.g. linear elasticity. We introduce a general framework for optimal convergence of adaptive Galerkin BEM. We identify certain abstract conditions for the underlying meshes, the corresponding mesh-refinement strategy, and the ansatz spaces that guarantee that the weighted-residual error estimator is reliable and converges at optimal algebraic rate if used within an adaptive algorithm. These conditions are satisfied, e.g. for discontinuous piecewise polynomials on simplicial meshes as well as certain ansatz spaces used for isogeometric analysis. Technical contributions include the localization of (non-local) fractional Sobolev norms and local inverse estimates for the (non-local) boundary integral operators associated to the PDE system. [ABSTRACT FROM AUTHOR]

In the recent years, isogeometric analysis (IGA) has found wide application in modeling different types of discontinuities produced by cracks, contact surfaces and bi-material interfaces. This technique eliminates the geometry discretization errors associated with the representation of complex geometries. The present paper employs the extended isogeometric analysis (XIGA) and the coupled finite element-isogeometric analysis (FE-IGA) to model large elasto-plastic deformations in bi-material engineering components. XIGA models all types of discontinuities independent of the grid chosen for analysis. Instead, the standard displacement-based approximation is enriched with additional enrichment functions to include the effects of these discontinuities in the formulation. In the coupled FE-IGA technique, IGA is used in the weak portion of the domain to eliminate the problems of mesh distortion and conventional finite element method is used in the stronger portion where mesh distortions do not occur. The transition elements are employed to couple the finite element and isogeometric portions of the domain. Finally, several numerical problems are solved by XIGA and coupled FE-IGA techniques to illustrate the applicability, efficiency and accuracy of the proposed techniques in modeling large elasto-plastic deformations in bi-material specimens. The results obtained in the present study are compared with finite element solutions which have been taken as the reference solution for the given problems. [ABSTRACT FROM AUTHOR]

Graphene-based reinforcements can enhance mechanical performances of composite structures by altering the distributions of graphene platelets (GPLs), which determines wave propagation characteristics. Dispersion behaviors of elastic waves in the nanocomposite annular plates are investigated in this work. Utilizing the modified micromechanical model and the rule of mixtures, four types of distribution patterns are considered to evaluate the effective material properties of the nanocomposites. Elastodynamic equations of wave motion are expressed and parameterized in the semi-analytical formulation based on Reddy's higher-order shear deformation theory and the isogeometric analysis. Dispersion characteristics of the in-plane and out-of-plane wave modes are studied in detail. The cutoff frequencies are discussed in order to confirm the accuracy of the results. Besides, parametric studies are conducted to analyze the influences of distribution, weight fraction and size parameters of GPLs on phase-velocity and group-velocity curves of waves. The results indicate that the concentration of GPLs on the boundaries of composite plates can improve the propagation characteristics of wave modes. In the case of FG-V, there exists the interesting phenomenon of mode conversion. It is concluded that dispersion characteristics of elastic waves in nanocomposite annular plates can be flexibly modulated by changing significant parameters of the reinforcement GPLs. [ABSTRACT FROM AUTHOR]

The paper aims to evaluate the performance of the Lagrange-based finite element method and the non-uniform rational B-splines isogeometric analysis of time-harmonic acoustic exterior scattering problems using high-order local absorbing boundary conditions, in particular based on the Karp's and Wilcox's far-field expansions. The analysis of accuracy and convergence of both methods is achieved by observing the effect of the order of the approximating polynomial, the number of degrees of freedom, the wave number, and the absorbing boundary conditions tuning parameters. It is concluded that, regardless of the polynomial order, IGA provides a higher accuracy per degree of freedom compared to the traditional Lagrange-based finite element method. [ABSTRACT FROM AUTHOR]

In the Isogeometric Analysis (IGA) framework, the computational domain has very often a multipatch representation. The multipatch domain can be obtained by a volume segmentation of a boundary represented domain, e.g. provided by a Computer Aided Design model. Typically, small gaps and overlapping regions can appear at the patch interfaces of such multipatch representations. In the current work, we consider multipatch representations having only small overlapping regions between the patches. We develop a Discontinuous Galerkin (DG)-IGA method that can be immediately applied to these representations. Our method appropriately connects the fluxes of the one face of the overlapping region with the flux of the opposite face. We provide a theoretical justification of our approach by splitting the whole error into two components: the first is related to the incorrect representation of the patches (consistency error) and the second to the approximation properties of the IGA space. We show bounds for both components of the error. We verify the theoretical error estimates in a series of numerical examples. [ABSTRACT FROM AUTHOR]

Flexoelectricity is a symmetry independent electromechanical coupling phenomenon that outperforms piezoelectricity at micro and nanoscales due to its size-dependent behavior arising from gradient terms in its constitutive relations. However, due to this gradient term flexoelectricity, to exhibit itself, requires specially designed geometry or material composition of the dielectric material. First of its kind, the present study put forward a novel strategy of achieving electric field gradient and thereby converse flexoelectricity, independent of geometry and material composition of the material. The spatial variation of the electric field is established inside the dielectric material, Ba0.67Sr0.33TiO3 (BST), by manipulating electrical boundary conditions. Three unique patterns of electrode placement are suggested to achieve this spatial variation. This varying direction of electric field gives rise to electric field gradient, the prerequisite of converse flexoelectricity. A multi-physics coupling based theoretical framework is established to solve the flexoelectric actuation by employing isogeometric analysis (IGA). Electromechanically coupled equations of flexoelectricity are solved to obtain the electric field distribution and the resulting displacements thereby. The maximum displacements of 0.2 nm and 2.36 nm are obtained with patterns I and II, respectively, while pattern III can yield up to 85 nm of maximum displacement. [ABSTRACT FROM AUTHOR]

In our previous research, we proposed a speedy double bootstrap method for assessing the reliability of statistical models with maximum log-likelihood criterion. It can provide 3rd order accurate probabilities. In this study, our focus switches to the mathematical proof. We propose an alternative proof of the third order accuracy in the context of the multivariate normal model. Our proof is based on tube formula differential geometric methodology and an Taylor series approach to the asymptotic analysis of the bootstrap method. [ABSTRACT FROM AUTHOR]

The exact geometry four-node solid-shell element formulation using the sampling surfaces (SaS) method is developed. The SaS formulation is based on choosing inside the shell N not equally spaced SaS parallel to the middle surface in order to introduce the displacements of these surfaces as basic shell unknowns. Such choice of unknowns with the use of Lagrange basis polynomials of degree N − 1 in the through-thickness interpolations of displacements, strains, stresses and material properties leads to a very compact form of the SaS shell formulation. The SaS are located at Chebyshev polynomial nodes that make possible to minimize uniformly the error due to Lagrange interpolation. To implement efficient 3D analytical integration, the extended assumed natural strain method is employed. As a result, the proposed hybrid-mixed solid-shell element exhibits a superior performance in the case of coarse meshes. To circumvent shear and membrane locking, the assumed stress and strain approximations are utilized in the framework of the mixed Hu-Washizu variational formulation. It can be recommended for the 3D stress analysis of thick and thin doubly-curved functionally graded shells because the SaS formulation with only Chebyshev polynomial nodes allows the obtaining of numerical solutions, which asymptotically approach the 3D solutions of elasticity as the number of SaS tends to infinity. [ABSTRACT FROM AUTHOR]

This paper presents an isogeometric (IGA) solver for time-dependent, incompressible magnetohydrodynamics (MHD). In this paper, a combination of inf-sup stable mixed discretisations is considered to discretise the hydrodynamic pair (i.e. velocity and pressure) and magnetic pair (i.e. magnetic field and magnetic pressure). The one step θ-method is used for the temporal discretisation. Manufactured and analytical solutions are considered to assess convergence, accuracy and performance of the IGA solver. Moreover, benchmark problems involving a MHD flow over an obstacle and MHD flow under non-uniform magnetic field are considered to examine the effect of the magnetic field on the flow behaviour. [ABSTRACT FROM AUTHOR]

Adopting an updated Lagrangian approach, a "general" and "exact" framework for the geometrically non-linear analysis of thin-walled framed structures are developed. The generality of such framework stands for the wide range of its applicability for different types of beam cross-sections, support conditions, and loading patterns including configuration-dependent behavior of applied moments; while the exactness stands for the utilization of a number of closed-form solutions of a class of torsionally loaded thin-walled beams to formulate a two-node element for spatial buckling analysis. The key in this formulation relates to the use of the "exact" solution for the displacement fields as opposed to the more conventional finite element approach in which polynomial/Lagrangian-type interpolation function is employed. Further, emphasizes are given to the effect of finite rotations in space on the non-linear kinematic descriptions as well as the configuration-dependent behavior of externally applied moment vector of the conservative/non-conservative type. Results obtained in a number of numerical simulations of beam assemblages subjected to different loading patterns illustrated the usefulness, robustness and fast convergence of the developed model in predicting the lateral torsional buckling. [ABSTRACT FROM AUTHOR]

In this contribution we consider cardiovascular hemodynamic modelling in patient-specific artery branches. To this aim, we first propose a procedure based on non-uniform rational basis splines (NURBS) to parametrise the artery volume which identifies the computational domain. Then, we adopt an isogeometric hierarchically reduced model which suitably combines separation of variables with a different discretization of the principal and of the secondary blood dynamics. This ensures the trade-off desired in numerical modelling between efficiency and accuracy, as shown by the good performances obtained in the numerical assessment of the last section. [ABSTRACT FROM AUTHOR]

In the present work, a NURBS-based Extended Isogeometric Analysis (XIGA) code has been developed for fracture analysis of orthotropic lamina. The XIGA code is capable of an efficient analysis of crack problems using non-uniform rational B-spline basis functions for both the solution field and geometric description of model. The level set approach is used to track the crack geometry. Crack faces are enriched by Heaviside enrichment function and crack tip singularity is captured by asymptotic crack tip enrichment functions. The interaction integral (M-Integral) method is used to calculate mixed mode stress intensity factor for further stable crack growth. The Paris crack growth law is used to simulate the crack propagation and fatigue life estimation in orthotropic media using life cycle increment approach. The developed code has been validated for static and fatigue analysis. The effect of varying angle of orthotropy on fatigue life of 2D plate is investigated using XIGA methodology leading to an optimized ply orientation of orthotropic plate. [ABSTRACT FROM AUTHOR]