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This paper presents, for the first time, an effective numerical approach based on the isogeometric analysis (IGA) and the six-variable quasi-three dimensional (3D) higher-order shear deformation theory (HSDT) to study the free vibration characteristics of functionally-graded (FG) graphene origami (GOri)-enabled auxetic metamaterial (GOEAM) plates submerged in a fluid medium. The plate theory incorporates the thickness stretching and the effects of transverse shear deformation without using any shear correction factors. The velocity potential function and Bernoulli's equation are used to derive the hydrodynamic pressure acting on the plate surface. Both horizontally and vertically immersed plate configurations are considered here in the form of inertia effects. The plates are composed of multilayer GOEAMs, with the GOri content varying through the plate's thickness in a layer-wise manner. This design results in graded auxetic growth. The material properties are evaluated by mixing rules and a genetic programming (GP)-assisted micromechanical model. The governing equations of motion for the FG-GOEAM plates immersed in a fluid medium are derived by Hamilton's principle. After validating the convergence and accuracy of the present model, a comprehensive parametric study is carried out to examine the effects of the GOri content, GOri distribution pattern, GOri folding degree, fluid level, immersed depth, and geometric parameter on the natural frequencies of the FG-GOEAM plates. The results show that the natural frequencies for the four GOri distribution patterns increase with the increase in the layer number when the lay number is fewer than 10, and then stabilize after the layer number reaches 10. Besides, in general, the natural frequency of the FG-GOEAM plate in a vacuum or fluid increases when the GOri content increases, while decreases when the GOri folding degree increases. Some additional findings related to the numerical results are presented in the conclusions. It is believed that the present results are useful for the precise design and optimization of FG-GOEAM plates immersed in a fluid medium. [ABSTRACT FROM AUTHOR]

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]

In the moving-morphable-component topology optimization, morphable components are introduced as a geometrical model mapped onto the background finite elements, and their shape parameters are utilized as design variables for topology optimization. Whereas a complex curved geometry ensuring C¹ continuity can be generated using existing curved components, the component curvatures cannot be selected as design variables in the existing methods; thus geometric constraints associated with curvatures cannot also be directly imposed. To address this issue, this study proposes a curvature-based morphable component by introducing the curvilinear geometry representation in the strain-based beam formulation. Since the proposed component is parameterized by curvatures using the curvilinear equation, the component curvatures can be utilized as the design variables. This allows for directly imposing curvature constraints on structural members, thereby accounting for the manufacturability of an optimal topology. It is demonstrated that a symmetric placement of the design variables using the midpoint curvilinear coordinate system is critical in ensuring convergence of the proposed curvature-based component optimization. The symmetric curvature component is further extended to account for multiple curvatures within a single component while ensuring C¹ continuity. Several examples are presented to demonstrate the benefits of the proposed multicurvature component for topology optimization. [ABSTRACT FROM AUTHOR]

The Laplace eigenvalue problem on circular sectors has eigenfunctions with corner singularities. Standard methods may produce suboptimal approximation results. To address this issue, a novel numerical algorithm that enhances standard isogeometric analysis is proposed in this paper by using a single-patch graded mesh refinement scheme. Numerical tests demonstrate optimal convergence rates for both the eigenvalues and eigenfunctions. Furthermore, the results show that smooth splines possess a superior approximation constant compared to their C 0 -continuous counterparts for the lower part of the Laplace spectrum. This is an extension of previous findings about excellent spectral approximation properties of smooth splines on rectangular domains to circular sectors. In addition, graded meshes prove to be particularly advantageous for an accurate approximation of a limited number of eigenvalues. Finally, a hierarchical mesh structure is presented to avoid anisotropic elements in the physical domain and to omit redundant degrees of freedom in the vicinity of the singularity. Numerical results validate the effectiveness of hierarchical mesh grading for simulating eigenfunctions of low and high regularity. [ABSTRACT FROM AUTHOR]

Flow diverter implantation has emerged as a highly effective treatment for cerebral aneurysms. However, the variability in patient‐specific vascular anatomy necessitates detailed pre‐operative planning to mitigate potential complications arising from standard, one‐size‐fits‐all devices. To address these challenges, robust predictive simulation tools are essential for optimizing flow diverter design and implantation strategies tailored to the unique characteristics of each patient's anatomy. This study focuses on developing an advanced numerical simulation tool for modeling the mechanical behavior of braided flow diverters during crimping and navigation through patient‐specific vasculature. Using isogeometric analysis (IGA) with NURBS‐based representations in LS‐Dyna, the intricate deformations of the flow diverter wires during catheter crimping are captured with high accuracy. The patient‐specific vessel geometries, derived from imaging data, are integrated into the model to account for variations in vascular structure, ensuring precise alignment and controlled navigation of the device. The navigation process relies on optimizing the central axis of the blood vessel to minimize torsional stress on the flow diverter, reducing the risk of device malfunction or failure during deployment. By incorporating patient‐specific information, such as vessel curvature and tortuosity, the simulation tool enables the prediction of potential issues, thus allowing for intervention planning that is tailored to individual anatomy. This patient‐specific approach enhances the safety and efficacy of flow diverter implantation and serves as a foundation for improved device design prior to prototype development. [ABSTRACT FROM AUTHOR]

The mixed displacement (MD) method was initially developed to mitigate geometrical locking effects in beams, plates, and shells with the intention of having intrinsically locking‐free characteristics while using equal‐order interpolation for all degrees of freedom. In other words, it is an unlocking scheme that works independent of the element shape, polynomial order, and discretization scheme. It includes additional degrees of freedom that adhere to a carefully designed differential relation that can be interpreted as a kinematic law, incorporated in a mixed sense. Certain constraints are to be enforced on these additional degrees of freedom to obtain a well‐posed system of equations. In this work, the MD method is extended for problems in solid mechanics. We present the underlying variational formulation, followed by its application to 2D solid elements. Additionally, we showcase an idea to enforce the additional constraints in a general sense. Various numerical examples, within the framework of the finite element method and isogeometric analysis, are outlined to demonstrate the performance of the MD method in the geometrically linear and geometrically nonlinear cases. [ABSTRACT FROM AUTHOR]

We develop a computational framework to model damage and delamination in laminated polymer composite structures incorporating the effects of temperature and moisture content. The framework is founded on a recently developed comprehensive multi-layer thin-shell formulation based on Isogeometric Analysis, which includes continuum damage, plasticity and cohesive-interface models. To incorporate hygrothermal effects in the modeling, we propose a scaling law that is based on the Arrhenius equation and material glass transition temperature that establishes the dependence of the intra- and interlaminar material properties on the temperature and moisture content. We compute several classical test cases using a combination of environmental conditions and demonstrate that the resulting modeling approach shows a good agreement with the experimental data, both in terms of failure loads reached as well as failure modes predicted. [ABSTRACT FROM AUTHOR]

A general formalism is proposed, based on the definition of a space-time potential, for developing space-time formulations adapted to nonlinear and time dependent behaviors. The focus is given to the case of standard generalized materials that are expressed from the knowledge of two potentials, a strain energy and a dissipation potential in a convex framework with the help of internal variables. Viscoplasticity with isotropic hardening and nonlinear finite viscoelasticity are investigated. Starting from the definition of an appropriate space-time potential, time discontinuous Galerkin forms are developed for use in the case of time singularities (in particular with regard to time integration of internal variables). Furthermore, NURBS approximation are used, such as to propose Space-Time Isogeometric Analysis models. Numerical examples allow to compare the obtained isogeometric space-time models with standard finite-element models (that are based on standard time integration procedures: radial return for viscoplasticity and backward euler for viscosity) and allow to illustrate the new possibilities offered with the proposed space-time formulations. [ABSTRACT FROM AUTHOR]

This paper presents a new mixed finite element model for material and geometric non-linear analysis of composite beams in partial interaction taking into account the non-penetration condition between layers. The Hu–Washizu functional with three independent fields is chosen for the developed mixed formulation. The force fields in the connection are chosen as the redundant forces and approximated using interpolation functions. The remaining force fields are obtained from solving equilibrium equations so that the element equlibrium is verified. Nevertheless, the compatibility as well as the constitutive law is satisfied only in a weak sense. The geometric non-linearity is taken into account by adopting the co-rotational approach. In this paper, the contact condition is imposed at the element level. Augmented Lagrangian method with Uzawa iteration algorithm is used to solve the contact problem. It has been shown that the proposed mixed formulation gives a more accurate result with less elements comparing to classical displacement based model. Besides, the buckling behaviour of delaminated two-layered composite columns has been studied by using the developed mixed formulation model. It has been observed that the buckling strength of the composite column can be overestimated if the uplift is not considered in the model. [ABSTRACT FROM AUTHOR]

We investigate Sobolev regularity of bivariate functions obtained in Isogeometric Analysis when using geometry maps that are degenerate in the sense that the first partial derivatives vanish at isolated points. In particular, we show how the known C 1 -conditions for D-patches have to be tightened to guarantee square integrability of second partial derivatives, as required when computing finite element approximations of elliptic fourth order PDEs like the biharmonic equation. [ABSTRACT FROM AUTHOR]

The geometries constructed using the standard CAD software are always boundary-represented (B-Rep). Due to this, analysis-suitable volumetric parameterization of the geometries constructed using the standard CAD software is necessary for three-dimensional isogeometric analysis (IGA). This paper presents a user-friendly, robust volumetric parametrization tool capable of processing the B-Rep of the geometries constructed in one of the most popular CAD software, i.e. Rhinoceros®. The developed tool traverses multiple stages, starting with reading the standard 3DM CAD files of an arbitrarily shaped geometry. It then extracts surface control points, organizes them to establish an outer structural framework, and employs Coons volume parameterization to generate internal control points based on user-defined specifications. We use the NURBS-Python library for reading 3DM files and the NURBS toolbox to visualize and evaluate NURBS functions in the constructed geometries. We construct several baseline and intricate shape geometries to showcase the robustness and generality of the developed tool. Additionally, to demonstrate the effectiveness and applicability of our tool for IGA of non-linear three-dimensional problems, we simulate frictionless contact between two deformable geometries constructed using the developed tool. [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]

• We present an effective isogeometric shape optimization method to optimize phononic band gaps of periodic plates. • The particle swarm optimization is employed to solve the constrained dynamic maximization problem. • The thickness, i.e., z-component of control point of B-spline surface is defined as optimal design variable. • Several numerical examples for finding optimal phononic band gaps of periodic plates are studied. This work presents an effective isogeometric shape optimization approach for finding and widening the phononic band gaps of single-phase Mindlin plate structures. As the single-phase material phononic plate is easy to be manufactured by additive manufacturing, it has been investigated here by optimized its thickness profile to find and widen the band gaps. The proposed method utilizes a coarse B-spline surface to model the thickness profile of periodic plate and a fine B-spline surface to model the mid-surface of plate structure for simulation. The optimal design variables are the thickness variables, i.e., the z-components of the control points of the coarse B-spline surface. To avoid specifying the initial control point locations manually, the constrained dynamic maximization problem is solved by a particle swarm optimization (PSO) algorithm here. Various numerical examples demonstrate the effectiveness and reliability of the proposed method in finding optimal phononic band gaps of periodic plates. And the numerical results show that there is no band gap for h max = 3 h min , and the band gaps can be found and widen for h max ≥ 5 h min. The obtained band range is 638.9–823.6 Hz with a decreased central frequency of 731.25 Hz for h max = 5 h min and the width and the number of band gaps are increased as the maximum allowable thickness increases. Finally, one optimized design is fabricated through additive manufacturing, and the experimental frequency response is consistent with the results based on isogeometric analysis. [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 modern applications of computer‐aided design (CAD) for the analysis of shell structures, isogeometric analysis is a powerful tool that integrates both design and analysis. An exact geometry description and a straightforward computation without loss of information are advantageous, especially for shell structures such as roofs, satellite hulls, or car bodies. In addition, the scaled boundary method provides a scale separation with a semi‐analytical solution procedure to consider a three‐dimensional linear elastic constitutive law. The presented approach deals with a scaled boundary solid shell formulation in the framework of isogeometric analysis. The formulation utilizes a normal scaling strategy which scales the shell along its normal vector at each point on the discretized bottom surface. This is fundamentally different from the well‐known radial scaling strategy, where each point on the problem domain is obtained from a fixed scaling center. This results in a separation of the analysis into an in‐plane direction and a scaling (normal) direction. By introducing the scaling, a scaled boundary differential equation is derived that is dependent on the scaling parameter only. Choosing a proper set of conditions, the differential equation can be solved by a Padé expansion. While the in‐plane direction is solved in a weak sense, the thickness direction along the normal vector can be solved analytically resulting in a semi‐analytical procedure. The isogeometric description of the CAD structure inherently yields the exact normal vector, its derivatives and a higher order continuity throughout the structure. Herein, the focus is on the solution technique in the thickness direction and the challenges are addressed. The power of the formulation is outlined in several numerical examples of static and dynamic analysis and a comparison to shell formulations in literature is provided. [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]

This study introduces extended isogeometric analysis method (XIGA) as a tool to investigate fracture behavior in isotropic and orthotropic materials under uniaxial and biaxial mechanical loads. Utilizing isogeometric analysis knot spans to discretize the problem domain and second order perturbation technique within XIGA framework derives mean and coefficient of variance values for mixed-mode stress intensity factors (MMSIFs) by considering variations in input parameters, including crack length, crack angle and material elastic properties. Mixed-mode SIF is evaluated using the proper interaction integral method subjected to different loading conditions showcases versatility of the proposed approach. The alignment between the existing literature and Monte Carlo simulations demonstrates a robust correspondence, validating the accuracy and reliability of the stochastic XIGA technique. This research establishes the efficacy of the approach in comprehensively addressing fracture analysis across different mechanical loading scenarios. [ABSTRACT FROM AUTHOR]

This paper introduces a novel method for optimal shape design of thick shells. We consider shells based on the Reissner-Mindlin theory, with the assumption of linear elastic material behavior. The goal is to find the optimal material distribution within the shell’s mid-surface. This is achieved using a cost function that minimizes the volume while considering stress-based constraints, with the material distribution represented by a level set function. The evolution of the shape is driven by the gradient of the cost function within the framework of a Hamilton–Jacobi equation. Both the level set and the displacement fields are described using computer aided design compatible tools, within the framework of isogeometric analysis. This allows for precise definition of the optimal shape and straightforward export of the resulting design to commercial software for manufacturing. Furthermore, the proposed method handles complex, non-conforming multi-patch geometries thanks to an augmented Lagrangian formulation. The latter guarantees strong compatibility with real-world engineering applications. The effectiveness of the method is demonstrated through its application to various three-dimensional multi-patch geometries under different loading conditions. [ABSTRACT FROM AUTHOR]

Common formulations of the eddy current problem involve either vector or scalar potentials, each with its own advantages and disadvantages. An impasse arises when using scalar potential-based formulations in the presence of conductors with non-trivial topology. A remedy is to augment the approximation spaces with generators of the first cohomology group. Most existing algorithms for this require a special, e.g., hierarchical, finite element basis construction. Using insights from de Rham complex approximation with splines, we show that additional conditions are here unnecessary. Spanning tree techniques can be adapted to operate on a hexahedral mesh resulting from isomorphisms between spline spaces of differential forms and de Rham complexes on an auxiliary control mesh. [ABSTRACT FROM AUTHOR]

Spectral and singular value symbols are valuable tools to analyse the eigenvalue or singular value distributions of matrix-sequences in the Weyl sense. More recently, Generalized Locally Toeplitz (GLT) sequences of matrices have been introduced for the spectral/singular value study of the numerical approximations of differential operators in several contexts. As an example, such matrix-sequences stem from the large linear systems approximating Partial Differential Equations (PDEs), Fractional Differential Equations (FDEs), Integro Differential Equations (IDEs), using any discretization on reasonable grids via local methods, such as Finite Differences, Finite Elements, Finite Volumes, Isogeometric Analysis, Discontinuous Galerkin etc. Studying the asymptotic spectral behaviour of GLT sequences is useful in analysing classical techniques for the solution of the corresponding PDEs/FDEs/IDEs and in designing novel fast and efficient methods for the corresponding large linear systems or related large eigenvalue problems. The theory of GLT sequences, in combination with the results concerning the asymptotic spectral distribution of perturbed sequences of matrices, is one of the most powerful and successful tools for computing the spectral symbol f. In this regard, it would be beneficial to design an automatic procedure to compute the spectral symbols of such matrix-sequences and Ahmed Ratnani partially pursued it. Here, in the case of one-dimensional and two-dimensional differential problems, we continue in this direction by proposing an automatic procedure for computing the symbol of the underlying sequences of matrices, assuming that it is a GLT sequence satisfying mild conditions. [ABSTRACT FROM AUTHOR]

The present research applies a 2D refined plate theory and isogeometric analysis (IGA) for free vibration analysis of functionally graded (FG) sandwich plates, whose governing equations are treated based on a unified formulation (UF), and nonuniform rational Lagrange (NURL)-based IGA technique. The constitutive model of FG materials is approximated via a Voigt’s rule of mixture based on an equivalent single-layer (ESL) theory. The present framework offers several advantages, including high precision of vibration response by employing higher-order plate theory and the capability of NURL basis functions to capture the exact form of plate geometries. Moreover, higher-order theories postulated by the UF are exempt from the Poisson locking phenomenon and do not require a shear correction factor. Additionally, by employing UF, the effect of thickness stretching on vibration response is considered. Furthermore, higher-order NURL basis functions effectively mitigate shear locking. A large numerical investigation shows the accuracy of results and investigates the effects of several key parameters, such as gradient index, thickness-to-length ratios, layer-to-thickness ratios, and boundary conditions, on the vibration response of FG sandwich plates. [ABSTRACT FROM AUTHOR]

As the first endeavor in the context of Mindlin's strain gradient theory, this study contributes a systematic and rigorous derivation for governing equations and boundary conditions of planar arbitrarily curved microbeams. The Timoshenko–Ehrenfest beam model is incorporated into a simplified version of Mindlin's strain gradient theory. Kinematic unknowns include displacement components of the beam axis in the local coordinate system and the rotation of cross-section. Since the derived governing equations and boundary conditions are extremely complex, analytical solutions are not achievable for microbeams having non-uniform curvature. To facilitate the numerical analysis, two isogeometric collocation formulations are proposed, that is, displacement-based and mixed formulations. Several tests are designed to evaluate the accuracy and reliability of the proposed isogeometric collocation formulations, especially with respect to the well-known locking pathology. It is found that the mixed formulation is more accurate and robust than the displacement-based one. Therefore, the mixed formulation is then used to numerically investigate the size-dependent behavior and stiffening effect. Furthermore, some informative tests are performed to delineate the significance of the curviness in the prediction of structural responses of planar arbitrarily curved microbeams, which appears to be still an unanswered issue. [ABSTRACT FROM AUTHOR]

The present study aims to develop an original solid-like shell element for large deformation analysis of hyperelastic shell structures in the context of isogeometric analysis (IGA). The presented model includes a new variable to describe the thickness change of the shell and allows for the application of unmodified three-dimensional constitutive laws defined in curvilinear coordinate systems and the analysis of variable thickness shells. In this way, the thickness locking affecting standard solid-shell-like models is cured by enhancing the thickness strain by exploiting a hierarchical approach, allowing linear transversal strains. Furthermore, a patch-wise reduced integration scheme is adopted for computational efficiency reasons and to annihilate shear and membrane locking. In addition, the Mixed-Integration Point (MIP) format is extended to hyperelastic materials to improve the convergence behaviour, hence the efficiency, in Newton iterations. Using benchmark problems, it is shown that the proposed model is reliable and resolves locking issues that were present in the previously published isogeometric solid-shell formulations. [ABSTRACT FROM AUTHOR]

This is Part II of a multipart article on a hyperelastic extended Kirchhoff–Love shell model with out-of-plane normal stress. We introduce an isogeometric discretization method for incompressible materials and present test computations. Accounting for the out-of-plane normal stress distribution in the out-of-plane direction affects the accuracy in calculating the deformed-configuration out-of-plane position, and consequently the nonlinear response of the shell. The return is more than what we get from accounting for the out-of-plane deformation mapping. The traction acting on the shell can be specified on the upper and lower surfaces separately. With that, the model is now free from the "midsurface' location in terms of specifying the traction. In dealing with incompressible materials, we start with an augmented formulation that includes the pressure as a Lagrange multiplier and then eliminate it by using the geometrical representation of the incompressibility constraint. The resulting model is an extended one, in the Kirchhoff–Love category in the degree-of-freedom count, and encompassing all other extensions in the isogeometric subcategory. We include ordered details as a recipe for making the implementation practical. The implementation has two components that will not be obvious but might be critical in boundary integration. The first one is related to the edge-surface moment created by the Kirchhoff–Love assumption. The second one is related to the pressure/traction integrations over all the surfaces of the finite-thickness geometry. The test computations are for dome-shaped inflation of a flat circular shell, rolling of a rectangular plate, pinching of a cylindrical shell, and uniform hydrostatic pressurization of the pinched cylindrical shell. We compute with neo-Hookean and Mooney–Rivlin material models. To understand the effect of the terms added in the extended model, we compare with models that exclude some of those terms. [ABSTRACT FROM AUTHOR]

A curved non-isoparametric Reissner–Mindlin shell element is developed for analyzing thin-walled structures. The standard kinematic description of the element requires the calculation of the director vector. To address this demand accurately, similar to isogeometric analysis (IGA), the geometry is defined by utilization of the non-uniform rational B-splines (NURBS) imported directly from computer-aided design (CAD) files. Then, shape functions of the Legendre spectral element method (SEM) are used to interpolate the displacements. Consequently, the shell director vector and Jacobian of the transformation are calculated properly according to the presented formulation. On the other hand, in Legendre SEM combined with Gauss–Lobatto–Legendre quadrature, the integration points and the element nodes coincide. Thus, the easily computable local coordinate systems at the integration points can be used directly as nodal basis systems. A separate calculation of nodal basis systems at control points, which is the source of either complexity or error in IGA shells, is not required. Given the condition number of the stiffness matrix in the developed method, super high-order elements can also be used. Very high order p-refined elements are used in addition to h-refinement of the mesh to show the capability of higher order elements to analyze problems without mesh refinement. The validity and convergence rate of the method are investigated and verified through various cases of h- and p-refinement in challenging obstacle course problems. [ABSTRACT FROM AUTHOR]

In this paper, we extend our previous work on the dynamic buckling analysis of isogeometric shell structures to the stochastic situation where an isogeometric deterministic dynamic buckling analysis method is combined with spectral-based stochastic modeling of geometric imperfections. To be specific, a modified Generalized-α time integration scheme combined with a nonlinear isogeometric Kirchhoff–Love shell element is used to simulate the buckling and post-buckling problems of cylindrical shell structures. Additionally, geometric imperfections are constructed based on NURBS surface fitting, which can be naturally incorporated into the isogeometric analysis framework due to its seamless CAD/CAE integration feature. For stochastic analysis, the method of separation is adopted to model the stochastic geometric imperfections of cylindrical shells based on a set of measurements. We tested the accuracy and convergence properties of the proposed method with a cylindrical shell example, where measured geometric imperfections were incorporated. The ABAQUS reference solutions are also presented to demonstrate the superiority of the inherited smooth and high-order continuous properties of the isogeometric approach. For stochastic dynamic buckling analysis, we evaluated the buckling load variability and reliability functions of the cylindrical shell with 500 samples generated based on seven nominally identical shells reported in the geometric imperfection data bank. It is noted that the buckling load variability in the cylindrical shell obtained with static nonlinear analysis is also presented to show the differences between dynamic and static buckling analysis. [ABSTRACT FROM AUTHOR]

Usually, detailed impact simulation models within flexible multibody systems have to be set up manually rather than being generated automatically. This is because the process requires prior knowledge of the time and location of the impact, as well as the element resolution within the contact area. If the penalty method is used to determine the occurring contact forces, the corresponding penalty factor also needs to be determined manually. This work, however, presents an adaptive algorithm to simulate impacts within flexible multibody systems fully automatically using reduced isogeometric analysis models, the floating frame of reference formulation, and quasistatic contact models for an efficient but still accurate simulation. The adaptive algorithm detects impacts in the system, determines the contact locations on the bodies, refines the contact area, and determines the penalty factor, and therefore automatically simulates impacts. The work shows how to automatically simulate impacts in flexible multibody systems without user action or prior knowledge of impact location and size. The first application example simulates significant elastodynamic effects within a long flexible rod. The goal is to validate the algorithm by preserving the wave propagation and energy of the system. The second application example simulates the impacts of two flexible double pendulums. This setup is a suitable benchmark for the complete adaptive impact analysis procedure as the flexible double pendulums undergo large rigid body motions. [ABSTRACT FROM AUTHOR]

We study space–time isogeometric discretizations of the linear acoustic wave equation that use splines of arbitrary degree p , both in space and time. We propose a space–time variational formulation that is obtained by adding a non-consistent penalty term of order 2 p + 2 to the bilinear form coming from integration by parts. This formulation, when discretized with tensor-product spline spaces with maximal regularity in time, is unconditionally stable: the mesh size in time is not constrained by the mesh size in space. We give extensive numerical evidence for the good stability, approximation, dissipation and dispersion properties of the stabilized isogeometric formulation, comparing against stabilized finite element schemes, for a range of wave propagation problems with constant and variable wave speed. [ABSTRACT FROM AUTHOR]

The physically based deformable curve models are widely used to simulate thin one-dimensional objects in computer graphics, interactive simulation, and surgery simulation. These models consider objects to be rods described by an adapted frame curve that contains the rod's centerline as well as the orthonormal material frame of each point on the centerline. However, they pose challenges including fine discretization, redundancy in modeling slender rods, and maintaining accuracy and stability. In this paper, we propose a novel physically based deformable B-spline curve model that regards curves as rods consisting of parallel fibers and derive elastic potential energy only from curves' representations. Therefore, our model does not take rotation-based adapted frames into consideration and reduces degree of freedom. Our model divides the curves into infinitesimal elements in parameter space and derives the analytical relationship between elastic potential energy function and curves' representations through the change of total length of infinitesimal elements' fibers. Our model can support material attributes in the real world and maintain the reality and stability of the solution. We employ isogeometric analysis to solve the dynamic equations derived from our deformable model as isogeometric analysis is suitable to solve the dynamic equations of parametric models. We compare the scenarios in the real world, our model's simulation results, and other model's results to demonstrate the reality of our models. The results are in line with expectation. We design several examples to demonstrate our models' applications. [ABSTRACT FROM AUTHOR]

Analysis-suitable G 1 (AS- G 1) multi-patch spline surfaces [7] are particular G 1 -smooth multi-patch spline surfaces, which ensure the construction of C 1 -smooth multi-patch spline spaces with optimal polynomial reproduction properties [20]. We present a local approach for the design of AS- G 1 multi-patch spline surfaces, which is based on the use of Lagrange multipliers. The presented method is simple and generates an AS- G 1 multi-patch spline surface by approximating a given G 1 -smooth but non-AS- G 1 multi-patch surface. Several numerical examples demonstrate the potential of the proposed technique for the construction of AS- G 1 multi-patch spline surfaces and show that these surfaces are especially suited for applications in isogeometric analysis by solving the biharmonic problem, a particular fourth order partial differential equation, with optimal rates of convergence over them. [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]

This paper presents a new approximate solution to study the settlement of rigid footings resting on a soft soil improved with groups of encased stone columns. The solution development is fully analytical, but finite element analyses are used to verify the validity of some assumptions, such as a simplified geometric model, load distribution with depth and boundary conditions. Groups of encased stone columns are converted to equivalent single encased columns with the same cross-sectional area and the same ratio of encasement stiffness to column diameter. In this way, the problem becomes axially symmetric. Soft soil is assumed as linear elastic but plastic strains are considered in the column using the Mohr-Coulomb yield criterion and a non-associated flow rule with a constant dilatancy angle. Soil profile is divided into independent horizontal slices and equilibrium of stresses and compatibility of deformations are imposed in the vertical and horizontal directions. The solution is presented in a closed form and may be easily implemented in a spreadsheet. Comparisons of the proposed solution with numerical analyses show a good agreement for the whole range of common values, which confirms the validity of the solution and its hypotheses. • A new analytical solution to study the settlement of rigid footings on a soft soil improved with encased stone columns. • A simplified model of a single column with the same area and the same ratio of encasement stiffness to column diameter. • The approximate analytical solution may be easily implemented in a spreadsheet. • A simplified calculation example and the corresponding calculation code are presented. • Comparisons with numerical analyses show a good agreement. [ABSTRACT FROM AUTHOR]

In this paper, we implement the finite detail technique primarily based on T-Splines for approximating solutions to the linear elasticity equations in the connected and bounded Lipschitz domain. Both theoretical and numerical analyses of the Dirichlet and Neumann boundary problems are presented. The Reissner–Mindlin (RM) hypothesis is considered for the investigation of the mechanical performance of a 3D cylindrical shell pipe without and with preformed hole problems under concentrated and compression loading in the linear elastic behavior for trimmed and untrimmed surfaces in structural engineering problems. Bézier extraction from T-Splines is integrated for an isogeometric analysis (IGA) approach. The numerical results obtained, particularly for the displacement and von Mises stress, are compared with and validated against the literature results, particularly with those for Non-Uniform Rational B-Spline (NURBS) IGA and the finite element method (FEM) Abaqus methods. The obtained results show that the computation time of the IGA based on the T-Spline method is shorter than that of the IGA NURBS and FEM Abaqus/CAE (computer-aided engineering) methods. Furthermore, the highlighted results confirm that the IGA approach based on the T-Spline method shows more success than numerical reference methods. We observed that the NURBS IGA method is very limited for studying trimmed surfaces. The T-Spline method shows its power and capability in computing trimmed and untrimmed surfaces. [ABSTRACT FROM AUTHOR]

We present an isogeometric analysis (IGA) framework for structural vibrations involving complex geometries. The framework is based on the Complex-Geometry IGA Mesh Generation (CGIMG) method. The CGIMG process is flexible and can accommodate, without a major effort, challenging complex-geometry applications in computational mechanics. To demonstrate how the new IGA framework significantly increases the computational effectiveness, in a set of structural-vibration test computations, we compare the accuracies attained by the IGA and finite element (FE) method as the number of degrees-of-freedom is increased. The results show that the NURBS meshes lead to faster convergence and higher accuracy compared to both linear and quadratic FE meshes. The clearly defined IGA mesh generation process and significant per-degree-of-freedom accuracy advantages of IGA over FE discretization make IGA more accessible, reliable, and attractive in applications of both academic and industrial interest. We note that the accuracy of a structural mechanics discretization, which may be assessed through eigenfrequency analysis, plays an important role in the overall accuracy of fluid–structure interaction computations. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new approach for numerically simulating the growth of cracks in unidirectional composite materials, termed extended isogeometric analysis, evaluating the maximum stress intensity factor and T-stress. To validate our approach, we used a small anisotropic plate with two edge cracks, beginning with formulating the governing equations based on the energy integral method, Stroh's Formula, and the Elastic Law describing the behaviour of anisotropic materials, while considering boundary conditions and initial states. A MATLAB code was developed to solve these equations numerically and to post-process the tensile stress and the stress intensity factor (SIF) in the first mode. The results for the SIF closely match those obtained using the extended finite element method (X-FEM), with a discrepancy of only 0.0021 Pa·m0.5. This finding underscores the credibility of our approach. The extended finite element method has demonstrated robustness in predicting crack propagation in composite materials in recent years, leading to its adoption by several widely used software packages in various industries. [ABSTRACT FROM AUTHOR]

This research aims to analyze the static bending and free vibration behaviors of bidirectional functionally graded porous (BFGP) curved microbeams with elastic boundary conditions resting on a Pasternak’s elastic foundation in a hygro-thermal environment. Isogeometric analysis based on non-uniform rational B-splines, first-order shear deformation theory, nonlocal elasticity theory combined with the modified strain gradient theories, modified Timoshenko beam theory are formulated to depict bending and shear deformations of BFGP curved microbeams. Especially, because using the modified Timoshenko beam theory, this study removes the requirement for a shear correction factor and describes shear stress by zero at the upper and lower cross-sectional sites of the BFGP curved microbeam. Different from traditional boundary conditions, where the beginning and end positions of a curved beam are connected by an elastic system of straight and torsion springs. This allows for greater flexibility in controlling the stiffness of the springs to obtain arbitrary boundaries. To assess the accuracy and convergence of the proposed approach, validation numerical examples were conducted in the various examples. [ABSTRACT FROM AUTHOR]

An innovative approach that combines isogeometric analysis (IGA), limit analysis, machine learning, and the multivariate adaptive regression splines (MARS) model is presented in this paper to investigate sinkhole stability of circular cavity. The upper bound limit analysis method using IGA and second-order cone programming (SOCP) is employed to analyze circular cavity stability. Based on Bézier extraction, the non-uniform rational B-spline (NURBS) is used to generate a set of NURBS surfaces that define the boundary of the soil domain. The proposed approach is validated through comparative analysis with previous studies, demonstrating its effectiveness in accurately predicting soil stability. A large dataset consisting of 5000 randomly generated runs is used to train the machine learning algorithm that is integrated with the MARS model. The results show high accuracy, with a small mean squared error of 10–3, in predicting the undrained stability of circular cavities. The integration of IGA, limit analysis, machine learning, and the MARS model contributes significantly to advancing computational techniques for assessing soil stability. The proposed approach offers a comprehensive and precise tool for engineers and researchers, providing an accurate design formula for evaluating the undrained stability of circular cavities. [ABSTRACT FROM AUTHOR]

Over the past few decades, early osteoporosis detection using ultrasonic bone quality evaluation has gained prominence. Specifically, various studies focused on axial transmission using ultrasonic guided waves and have highlighted this technique's sensitivity to intrinsic properties of long cortical bones. This work aims to demonstrate the potential of low-frequency ultrasonic guided waves to infer the properties of the bone inside which they are propagating. A proprietary ultrasonic transducer, tailored to transmit ultrasonic guided waves under 500 kHz, was used for the data collection. The gathered data underwent two-dimensional fast Fourier transform processing to extract experimental dispersion curves. The proposed inversion scheme compares experimental dispersion curves with simulated dispersion curves calculated through the semi-analytical iso-geometric analysis (SAIGA) method. The numerical model integrates a bone phantom plate coupled with a soft tissue layer on its top surface, mimicking the experimental bone phantom plates. Subsequently, the mechanical properties of the bone phantom plates were estimated by reducing the misfit between the experimental and simulated dispersion curves. This inversion leaned heavily on the dispersive trajectories and amplitudes of ultrasonic guided wave modes. Results indicate a marginal discrepancy under 5% between the mechanical properties ascertained using the SAIGA-based inversion and those measured using bulk wave pulse-echo measurements. [ABSTRACT FROM AUTHOR]

The vast majority of heart attacks occur when vulnerable plaques rupture, releasing their lipid content into the blood stream leading to thrombus formation and blockage of a coronary artery. Detection of these unstable plaques before they rupture remains a challenge. Hemodynamic features including wall shear stress (WSS) and wall shear stress gradient (WSSG) near the vulnerable plaque and local inflammation are known to affect plaque instability. In this work, a computational workflow has been developed to enable a comprehensive parametric study detailing the effects of 3D plaque shape on local hemodynamics and their implications for plaque instability. Parameterized geometric 3D plaque models are created within a patient-specific coronary artery tree using a NURBS (non-uniform rational B-splines)-based vascular modeling pipeline. Realistic blood flow features are simulated by using a Navier–Stokes solver within an isogeometric finite-element analysis framework. Near wall hemodynamic quantities such as WSS and WSSG are quantified, and vascular distribution of an inflammatory marker (VCAM-1) is estimated. Results show that proximally skewed eccentric plaques have the most vulnerable combination of high WSS and high positive spatial WSSG, and the presence of multiple lesions increases risk of rupture. The computational tool developed in this work, in conjunction with clinical data, -could help identify surrogate markers of plaque instability, potentially leading to a noninvasive clinical procedure for the detection of vulnerable plaques before rupture. [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]

Curved nanobeams are one of the essential components in manufacturing nano-electromechanical systems needing nonlinear stability design. In the current investigation, the nonlinear buckling characteristics of functionally graded porous reinforced curved (FGPRC) nanobeams having different degrees of curvature are analyzed by counting the higher-order gradients of the classical strain tensor as well as nonlocal-type interatomic interactions. In this regard, two independent length-scale constants within the framework of the nonlocal strain gradient theory (NSGT) of continuum elasticity are taken into account. Via employing the promising low computational cost and geometrically adaptable method of isogeometric collocation, various branches of NSGT-based equilibrium graphs of FGPRC nanobeams are plotted relevant to each considered degree of curvature. It is extrapolated that the quantity of graphene platelet (GPL) weight fraction has a negligible influence on the significance of nonlocal-type of interatomic size dependency as well as the strain gradient kind of small-scale effect in the value of the maximum deflections or lateral loads at the detected limit points, especially attributed to a higher degree of curvature. Besides, it can be remarked that, in the FGPRC nanobeam owning a small degree of curvature, lessening the quantity of porosity index results in an increment in the significance of the nonlocal-type of interatomic size dependency as well as the strain gradient kind of small-scale effect on the maximum deflection at both upper and lower limit points. However, in the FGPRC nanobeams owning medium and large degrees of curvature, it gets lesser at the upper limit point, but becomes higher at the lower limit one. [ABSTRACT FROM AUTHOR]