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This work undertakes to combine the interests of IsoGeometric Analysis (IGA) and standard Finite Element Methods (FEM) for the global/local simulation of structures. The idea is to adopt a hybrid global-IGA/local-FEM modeling, thereby benefiting from: (i) the superior geometric description and per-Degree-Of-Freedom accuracy of IGA for capturing global, regular responses, and (ii) the ability of FEM to compute local, strongly non-linear or even singular behaviors. For the sake of minimizing the implementation effort, we develop a coupling scheme that is fully non-invasive in the sense that the initial global spline model to be enriched is never modified and the construction of the coupling operators can be performed using conventional FE packages. The key ingredient is to express the FEM-to-IGA bridge, based on B{\'e}zier extraction, to transform the initial global spline interface into a FE one on which the local FE mesh can be constructed. This allows to resort to classic FE trace operators to implement the coupling. It results in a strategy that offers the opportunity to simply couple an isogeometric code with any robust FE code suitable for the modelling of complex local behaviors. The method also easily extends in case the users only have at their disposal FE codes. This is the situation that is considered for the numerical illustrations. More precisely, we only make use of the FE industrial software Code Aster to perform efficiently and accurately the hybrid global-IGA/local-FEM simulation of structures subjected locally to cracks, contact, friction and delamination., Comment: Computational Mechanics, Springer Verlag, 2022

This paper for first time proposes an isogeometric analysis (IGA) for free vibration response of bi-directional functionally graded (BDFG) rectangular plates in the fluid medium. Material properties of the BDFG plate change in both the thickness and length directions via power-law distributions and Mori-Tanaka model. The governing equation of motion of BDFG plate in the fluid-plate system is formulated basing on Hamilton's principle and the refined quasi three-dimensional (3D) plate theory with improved function f(z). The fluid velocity potential is derived from the boundary conditions of the fluid-plate system and is used to determine the added mass. The discrete system of equations is derived from the Galerkin weak form and numerically analyzed by IGA. The accuracy and reliability of the proposed solutions are verified by comparing the obtained results with those published in the literature. Moreover, the effects of the various parameters such as the interaction boundary condition, geometric parameter, submerged depth of plate, fluid density, fluid level, and the material volume control coefficients on the free vibration behavior of BDFG plate in the fluid medium are investigated in detail. Some major findings regarding the numerical results are withdrawn in conclusions.

In the present study, the stress distribution and first ply failure strength of hybrid laminated composites subjected to uniaxial tensile and compression loads are predicted using Isogeometric analysis (IGA) based on non-uniform rational B-splines technology, commonly referred to as non-uniform rational B-splines (NURBS) technology. The obtained results were compared to finite element method results (ANSYS) published in the literature and analytical results using Autodesk Helius Composite software. Graphite-glass/epoxy hybrid composite plates are analyzed for different lamination orientations and used to calculate first ply failure strength. Non-interactive theories such as maximum stress, maximum strain, and fully interactive criteria such as Tsai-Wu, Tsai-Hill and Hoffman are used to predict the failure strength of different laminates. The failure envelopes of the hybrid composites are developed using the same failure criteria used for the graphite-glass/epoxy hybrid composite. The effects of IGA refinement and plate’s dimension on the present analysis were also established. The IGA results showed good accuracy, robustness and good convergence speed with the analytical software results and the finite element method (FEM) reference value.

We propose an adaptive mesh refinement strategy for immersed isogeometric analysis, with application to steady heat conduction and viscous flow problems. The proposed strategy is based on residual-based error estimation, which has been tailored to the immersed setting by the incorporation of appropriately scaled stabilization and boundary terms. Element-wise error indicators are elaborated for the Laplace and Stokes problems, and a THB-spline-based local mesh refinement strategy is proposed. The error estimation .and adaptivity procedure is applied to a series of benchmark problems, demonstrating the suitability of the technique for a range of smooth and non-smooth problems. The adaptivity strategy is also integrated in a scan-based analysis workflow, capable of generating reliable, error-controlled, results from scan data, without the need for extensive user interactions or interventions., Submitted to Journal of Mechanics

A BCMO-ANN algorithm for vibration and buckling optimization of functionally graded porous (FGP) microplates is proposed in this paper. The theory is based on a unified framework of higher-order shear deformation theory and modified couple stress theory. A combination of artificial neural network (ANN) and balancing composite motion optimization (BCMO) is developed to solve the optimization problems and predict stochastic vibration and buckling behaviors of functionally graded porous microplates with uncertainties of material properties. The characteristic equations are derived from Hamilton's principle and approximation of field variables under Ritz-type exponential series. Numerical results are obtained to investigate the effects of the material distribution, material length scale, porosity density and boundary conditions on natural frequencies and critical buckling loads of functionally graded porous microplates. The novel results derived from this paper can be used as future references.

This work introduces a reduced order modeling (ROM) framework for the solution of parameterized second-order linear elliptic partial differential equations formulated on unfitted geometries. The goal is to construct efficient projection-based ROMs, which rely on techniques such as the reduced basis method and discrete empirical interpolation. The presence of geometrical parameters in unfitted domain discretizations entails challenges for the application of standard ROMs. Therefore, in this work we propose a methodology based on i) extension of snapshots on the background mesh and ii) localization strategies to decrease the number of reduced basis functions. The method we obtain is computationally efficient and accurate, while it is agnostic with respect to the underlying discretization choice. We test the applicability of the proposed framework with numerical experiments on two model problems, namely the Poisson and linear elasticity problems. In particular, we study several benchmarks formulated on two-dimensional, trimmed domains discretized with splines and we observe a significant reduction of the online computational cost compared to standard ROMs for the same level of accuracy. Moreover, we show the applicability of our methodology to a three-dimensional geometry of a linear elastic problem., 35 pages, 19 figures, 5 tables. Preprint accepted in Computer Methods in Applied Mechanics and Engineering

Tchebycheffian splines are smooth piecewise functions whose pieces are drawn from (possibly different) Tchebycheff spaces, a natural generalization of algebraic polynomial spaces. They enjoy most of the properties known in the polynomial spline case. In particular, under suitable assumptions, Tchebycheffian splines admit a representation in terms of basis functions, called Tchebycheffian B-splines (TB-splines), completely analogous to polynomial B-splines. A particularly interesting subclass consists of Tchebycheffian splines with pieces belonging to null-spaces of constant-coefficient linear differential operators. They grant the freedom of combining polynomials with exponential and trigonometric functions with any number of individual shape parameters. Moreover, they have been recently equipped with efficient evaluation and manipulation procedures. In this paper, we consider the use of TB-splines with pieces belonging to null-spaces of constant-coefficient linear differential operators as an attractive substitute for standard polynomial B-splines and rational NURBS in isogeometric Galerkin methods. We discuss how to exploit the large flexibility of the geometrical and analytical features of the underlying Tchebycheff spaces according to problem-driven selection strategies. TB-splines offer a wide and robust environment for the isogeometric paradigm beyond the limits of the rational NURBS model., 35 pages, 18 figures

Detailed impact simulations in flexible multibody systems can be simulated based on reduced isogeometric analysis (IGA) models. However, a precise simulation of an impact requires a high element resolution in the contact area. Usually in IGA, global refinement methods are used, which are easy to implement. However, in the literature, also the use of hierarchical local refinement is proposed. The local refinement generates fewer countable degrees of freedom compared to an equivalent global refinement. Numerous application areas can be found in the literature, such as contact simulations, where the computational effort is reduced by local refinement. In this work, we introduce the inclusion of hierarchically refined IGA models within the floating frame of reference formulation. Thereby, the hierarchically refined IGA model is reduced and applied in impact simulations. In two application examples, we simulate the impact of two- and three-dimensional spheres and compare with an analytical solution. The focus here is on the comparison of calculation times and accuracy of globally and locally refined reference models. The third application example consists of two flexible double pendulums and is devoted to systems in which the bodies undergo both arbitrary rigid body motions and small elastic deformations.

In isogeometric analysis (IGA), the boundary representation of computer-aided design (CAD) and the tensor-product non-uniform rational B-spline structure make the analysis of three-dimensional (3D) problems with irregular geometries difficult. In this paper, an IGA method for complex models is presented by reconstructing analysis-suitable models. The CAD model is represented by boundary polygons or point cloud and is embedded into a regular background grid, and a model reconstruction method is proposed to obtain the level set function of the approximate model, which can be directly used in IGA. Three 3D examples are used to test the proposed method, and the results demonstrate that the proposed method can deal with complex engineering parts reconstructed by boundary polygons or point clouds.

We present an isogeometric method for Kirchhoff–Love shell analysis of shell structures with geometries composed of multiple patches and which possibly possess extraordinary vertices, i.e. vertices with a valency different to four. The proposed isogeometric shell discretisation is based on the one hand on the approximation of the mid-surface by a particular class of multi-patch surfaces, called analysis-suitable G1 (Collin et al., 2016), and on the other hand on the use of the globally C1-smooth isogeometric multi-patch spline space (Farahat et al., 2023). We use our developed technique within an isogeometric Kirchhoff–Love shell formulation (Kiendl et al., 2009) to study linear and non-linear shell problems on multi-patch structures. Thereby, the numerical results show the great potential of our method for efficient shell analysis of geometrically complex multi-patch structures which cannot be modelled without the use of extraordinary vertices.

Modern electronic devices are usually subjected to thermo-mechanical loads and prone to buckle during their operation. Thermo-mechanical stability is a crucial standard for their reliable applications. This paper explores the size effect on the thermo-mechanical behavior of the organic solar cells. An effective isogeometric analysis method combined with modified couple stress theory is presented. The thermo-mechanical buckling load-bearing capacities of the organic solar cells subjected to various in-plane loadings, temperatures, and geometrical parameters are discussed. Numerical results show that the size effect has significant effect on the thermo-mechanical load-bearing capacity. The stability region changes minimally when the material length scale parameter $$l$$ to cell thickness $$h$$ ratio is less than 0.2, while the stability region increases remarkably when it is larger than 0.2. Notably, if the material length scale parameter increases to its thickness, the stability region increased almost 25 times than that without size effect. Furthermore, the stability region is narrowest if the temperature is uniform across the thickness direction of the cell.

This article aims to utilize IsoGeometric analysis (IGA) and Level set method for topology optimization of elastoplastic plane stress problems. The IGA is employed to model geometry of the problem and calculate unknown displacements by satisfying equilibrium for materially-nonlinear problems. The von Mises elastoplastic material behavior model with and without isotropic strain hardening is utilized. The normal velocity is derived by the pointwise gradient based sensitivity analysis of the Level set function and the control net is updated at each optimization iteration. The reaction–diffusion equation is also employed to update the design variables, which eliminates the signed distance function dependency, and the algorithm provides capability of hole nucleation. The objective is to maximize the toughness of structure, which is defined as the total external work within a specified displacement, while certain amount of material in the design domain is used. In order to demonstrate the ability and efficiency of the proposed method, several numerical examples are presented.

The purpose of this study is to present a quasi-three-dimensional (quasi-3D) shear deformation theory for static bending and free vibration analyses of porous sandwich functionally graded (FG) plates with graphene nanoplatelets (GPLs) reinforcement. In addition, we propose a novel sandwich plate model with various outstanding features in terms of structural performance. The quasi-3D theory-based isogeometric analysis (IGA) in conjunction with refined plate theory (RPT) is first exploited to capture adequately the thickness stretching effect for porous sandwich FG plate structures reinforced with GPLs. The Non-Uniform Rational B-Splines (NURBS)-based IGA is employed in order to describe exactly the geometry models as well as approximate the unknown field with higher-order derivatives and continuity requirements while the RPT model includes only four essential variables. The sandwich FG plates consist of a core layer containing internal pores reinforced by GPLs and two functionally graded materials (FGMs) skin layers. Effective mechanical properties can be evaluated by employing the Halpin-Tsai model along with the rule of mixture. Various combinations of two porosity distributions and three GPL dispersions in the core layer are thoroughly investigated. Several numerical investigations are conducted to examine the effects of several key parameters on the static bending and free vibration behaviors of sandwich FG plate structures.

Cardiovascular disease has remained the leading cause of death worldwide for the past 15 years, and organizations such as the American Heart Association (AHA) and the National Institute for Health (NIH) spend hundreds of millions of U.S. dollars annually to investigate heart disease and stroke. Local characteristics of blood flow in the heart and the rest of the cardiovascular system provide important information in both understanding progression of and diagnosis of cardiovascular diseases. Unfortunately, current medical imaging techniques cannot provide data with high enough temporal and spatial resolution to extract meaning- ful and accurate research conclusions. Thus, many researchers investigate cardiovascular diseases using a patient-specific blood flow simulation framework. In this framework, a pa- tient’s geometry is constructed on a computer from medical image data, and a numerical simulation, such as finite element analysis (FEA), is used to provide very high detail infor- mation. Typically, the most time consuming step and also one of the most crucial steps in this pipeline is constructing the geometry of interest from the image data. In addition, many of the tools to create an image-based model are commercial, not readily available, or dispersed amongst a variety of software packages. This dissertation discusses two main avenues of research: (1) the development of unique, customized, and open-source tools for vascular model construction and meshing for FEA and (2) the investigation into and the creation of novel model construction methods for an alternative of FEA called isogeometric analysis (IGA). All of the tools developed were implemented using open-source tools such as the Visualization Toolkit (VTK) and have been implemented into the software framework SimVascular. In addition, many of the methods developed were tested for applicability and robustness on the open-source vascular model repository, which is a large database of over 100 vascular models provided by the Open Source Medical Software Corporation (OSMSC).

Fiber-reinforced composite materials have become increasingly popular in the past few decades for lightweight applications, in particular in the aerospace industry where high strength-to-weight and high stiffness-to-weight ratio are considered key design parameters. At the same time, new computational technologies are required to support the design process of increasingly complex structural components and to predict damage growth under non-standard loading conditions. However, the development of accurate and computationally efficient analysis tools, capable of predicting the response of laminated composite structures from the elastic regime to the failure point and beyond, is a complex task. Difficulties stem from the inherent heterogeneous nature of fiber-reinforced polymer composite materials and from their multi-modal failure mechanisms. Composite structures optimized for low weight applications are often laminates, consisting of several layers of fiber-reinforced material, called laminae, bonded together. Intra-laminar damage may occur within a given lamina, and inter-laminar damage, or delamination, may occur when bonds between laminae break down. The unique challenges associated with modeling damage in these structures may be addressed by means of thin-shell formulations which is naturally developed in the context of Isogeometric Analysis. This dissertation presents a novel multi-layer modeling framework based on Isogeometric Analysis, where each ply or lamina is represented by a Non-Uniform Rational B-Spline (NURBS) surface, and it is modeled as a Kirchhoff-Love thin shell. A residual stiffness approach is used to model intra-laminar damage in the framework of Continuum Damage Mechanics. A new zero-thickness cohesive interface formulation is introduced to model delamination as well as permitting laminate-level transverse shear compliance. The gradient-enhanced continuum damage model is then introduced to regularize material instabilities, which are typically associated with strain-softening damage models. This nonlocal regularization technique aims to re-establish mesh objectivity by limiting the dependence of damage predictions on the choice of discrete mesh. To account for the anisotropic damage modes of laminae, the proposed formulation smooths a tensor-valued strain field by solving an elliptic partial differential equation system on each lamina. The proposed approach has significant accuracy and efficiency advantages over existing methods for modeling impact damage. These stem from the use of IGA-based Kirchhoff-Love shells to represent the individual plies of the composite laminate, while the compliant cohesive interfaces enable transverse shear deformation of the laminate. Kirchhoff-Love shells give a faithful representation of the ply deformation behavior, and, unlike solids or traditional shear-deformable shells, do not suffer from transverse-shear locking in the limit of vanishing thickness. This, in combination with higher-order accurate and smooth representation of the shell midsurface displacement field, allows to adopt relatively coarse in-plane discretizations without sacrificing solution accuracy. Furthermore, the thin-shell formulation employed does not use rotational degrees of freedom, which gives additional efficiency benefits relative to more standard shell formulations.

This paper presents a non-classical refined shear deformation theory model in conjunction with the isogeometric analysis for the static bending, free vibration, and buckling behaviors of multilayered microplates. The modified couple stress theory is used to account for the small-scale effect. Taking a five-layer (Al, P3HT: PCBM, PEDOT: PSS, ITO, and Glass) organic solar cell as an example, it is found that the small-scale effects lead to a decrease in deflection, but an increase in the natural frequency and buckling load. With consideration of the size effect (l/h = 1), the stresses are almost 5 times as much as that without the size effect (l/h = 0). This is why the size effect should be taken into account. Besides, the maximum tensile stress occurs in the ITO layer, which is the dangerous layer. In addition, the normalized deflections increase with increasing aspect ratio, but the normalized natural frequencies and normalized buckling loads decrease with increasing aspect ratio.

The Taylor–Couette flow is a classical fluid mechanics problem that exhibits, depending on the Reynolds number, a range of flow patterns, with the interesting ones having small-scale structures, and sometimes even wavy nature. Accurate representation of these flow patterns in computational flow analysis requires methods that can, with a reasonable computational cost, represent the circular geometry accurately and provide a high-fidelity flow solution. We use the Space–Time Variational Multiscale (ST-VMS) method with ST isogeometric discretization to address these computational challenges and to evaluate how the method and discretization perform under different scenarios of computing the Taylor–Couette flow. We conduct the computational analysis with different combinations of the Reynolds numbers based on the inner and outer cylinder rotation speeds, with different choices of the reference frame, one of which leads to rotating the mesh, with the full-domain and rotational-periodicity representations of the flow field, with both the convective and conservative forms of the ST-VMS, with both the strong and weak enforcement of the prescribed velocities on the cylinder surfaces, and with different mesh refinements. The ST framework provides higher-order accuracy in general, and the VMS feature of the ST-VMS addresses the computational challenges associated with the multiscale nature of the flow. The ST isogeometric discretization enables exact representation of the circular geometry and increased accuracy in the flow solution. In computations where the mesh is rotating, the ST/NURBS Mesh Update Method, with NURBS basis functions in time, enables exact representation of the mesh rotation, in terms of both the paths of the mesh points and the velocity of the points along their paths. In computations with rotational-periodicity representation of the flow field, the periodicity is enforced with the ST Slip Interface method. With the combinations of the Reynolds numbers used in the computations, we cover the cases leading to the Taylor vortex flow and the wavy vortex flow, where the waves are in motion. Our work shows that all these ST methods, integrated together, offer a high-fidelity computational analysis platform for the Taylor–Couette flow and for other classes of flow problems with similar features.

We present a set of advanced analytical formulations that facilitates the accurate analysis and efficient implementation of finite deformable thin Kirchhoff–Love beams. This paper enhances the prevailing differential geometry based large deformation beam models by producing geometrically exact formulations for initial curvatures, non-zero force tangents and external stiffness matrix contributions of spatial beams. Though it is not analytically merged in existing beam models, initial curvatures of beams have a significant influence on the integration of forces over beam cross-sections. We reveal this influence through the systematic deduction of the Jacobian in volume integrals of beam forces. Also, this paper demonstrates the applicability of follower loads on beams with necessary adjustments to the global Hessian matrix. We adopt the isogeometric analysis formalism in beam body discretisation and algorithmic implementation of the presented formulations.

This work models spatially uncorrelated (independent) load uncertainty and develops a reduced-order Monte Carlo stochastic isogeometric method to quantify the effect of the load uncertainty on the structural response of thin shells and solid structures. The approach is tested on two demonstrative applications of uncertainty, namely, spatially uncorrelated loading, with (1) Scordelis–Lo Roof shell structure, and (2) a 3D wind turbine blade. This work has three novelties. Firstly, the research models spatially uncorrelated (independent) load uncertainties (including both their magnitude and/or direction) using stochastic analysis. Secondly, the paper advances a reduced-order Monte Carlo stochastic isogeometric method to quantify the spatially uncorrelated load uncertainty. It inherits the merits of isogeometric analysis, which enables the precise representation of geometry and alleviates shell shear locking, thereby reducing the model’s uncertainties. Moreover, the method retains the generality and accuracy of classical Monte Carlo simulation (MCS), with significant efficiency gains. The demonstrative results suggest that there is a cost, which is 3% of the time used by the standard MCS. Furthermore, a significant observation is made from the conducted numerical tests. It is noticed that the standard deviation of the output (i.e., displacement) is strongly influenced when the load uncertainty is spatially uncorrelated. Namely, the standard derivation (SD) of the output is roughly 10 times smaller than the SD for correlated load uncertainties. Nonetheless, the expected values remain consistent between the two cases.

In the context of isogeometric analysis (IGA) of shell structures, the popularity of the solid-shell elements benefit from formulation simplicity and full 3D stress state. However some basic questions remain unresolved when using solid-shell element, especially for large deformation cases with patch coupling, which is a common scene in real-life simulations. In this research, after introduction of the solid-shell nonlinear formulation and a fundamental 3D model construction method, we present a non-symmetric variant of the standard Nitsche’s formulation for multi-patch coupling in association with an empirical formula for its stabilization parameter. An selective and reduced integration scheme is also presented to address the locking syndrome. In addition, the quasi-Newton iteration format is derived as solver, together with a step length control method. The second order derivatives are totally neglected by the adoption of the non-symmetric Nitsche’s formulation and the quasi-Newton solver. The solid-shell elements are numerically studied by a linear elastic plate example, then we demonstrate the performance of the proposed formulation in large deformation, in terms of result verification, iteration history and continuity of displacement across the coupling interface. In the context of isogeometric analysis (IGA), after introduction of the solid-shell nonlinear formulation and a fundamental 3D model construction method, we present a non-symmetric variant of the standard Nitsche’s formulation for multi-patch coupling in association with an empirical formula for its stabilization parameter. An selective and reduced integration scheme is also introduced to address the locking syndrome. In addition, the quasi-Newton iteration format is derived as solver, together with a step length control method. The second order derivatives are totally neglected by the adoption of the non-symmetric Nitsche’s formulation and the quasi-Newton solver. The performance of the proposed formulation in large deformation is demonstrated by several examples.

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 ...

This study proposes a new plate formulation based on a generalized layerwise theory in the isogeometric analysis (IGA) framework to investigate the bending and free vibration behavior of a laminated composite plate. All degrees of freedom in the isogeometric formulation are only associated with the displacements (i.e., rotation-free). In IGA, NURBS functions are used both to construct the geometry and to approximate the field variables. Merits of utilizing IGA include: the exact geometrical description, high accuracy and efficiancy, higher-order smoothness. The displacement-based layerwise theory assumes an individual displacement field expansion inside each layer, and the transverse displacement component is regarded to be $$C^{0}$$ -continuous at the layer interfaces, thus yielding a more precise description of the stress states. The $$C^{0}$$ continuity enforcement across the thickness in the present formulation is easily implemented by virtue of the knot insertion technique of IGA. The capability of the present isogeometric layerwise formulation in analyzing the static and dynamic responses is evidenced by conducting some numerical tests available in the open literature and comparing the computed outcomes with the reference data.

We propose a frictionless contact formulation for isogeometric analysis, which combines a collocated formulation for the contact surfaces with a standard Galerkin treatment of the bulk. We denote it as isogeometric Collocated Contact Surface (CCS) formulation. The approach is based on a simple pointwise enforcement of the contact constraints, performed in this study with the penalty method. Unlike pointwise (node-to-surface or point-to-surface) contact algorithms in the Galerkin framework, the CCS formulation passes the contact patch test to machine precision by naturally exploiting the favorable properties of isogeometric collocation. Compared with approaches where the discretization of both bulk and contact surfaces is based on collocation, the CCS approach does not need enhancements to remove oscillations for highly non-uniform meshes. With respect to integral contact approaches, the CCS algorithm is less computationally expensive, due to the reduced amount of contact evaluation points. In addition, the CCS approach is easy to code and can be added to a pre-existing isogeometric analysis code with minimal effort. Numerical examples in both small and large deformations are investigated to compare the CCS approach with some available contact formulations and to demonstrate its accuracy., Computational Mechanics, 70 (4), ISSN:0178-7675, ISSN:1432-0924

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 deformat...

The bonded repair techniques seem to be the most frequent procedures in the aviation maintenance. The achieved composite repaired perforated thin-walled plate is a complex geometry with high numerical analysis cost. The NURBS-based Isogeometric Analysis (IGA) proposes a sensible and affordable tool to carry out such geometry analysis. In this context, a well-known technique is to divide the original geometry assembly into number of simple neighbors connected geometries. In the present study the free vibration analysis of the perforated plates repaired on one side with an external bonded composite laminated patch is investigated. A multi-patch geometry modeling approach is implemented in line with the first order shear deformation theory of plates. In order to hold the geometry integrity and uniformity, all the degrees of freedom between adjacent geometry patches are completely tied through implementing a Nitsche method. To show the effectiveness and accuracy of the developed formulation, some representative results are extracted and compared with those from literature. The effects of geometrical as well as material parameters including boundary condition, cutout shape, and repair layup on the dynamic response of the repaired perforated plates are then investigated.

An important ingredient of any moving-mesh method for fluid-structure interaction (FSI) problems is the mesh moving technique (MMT) used to adapt the computational mesh in the moving fluid domain. An ideal MMT is computationally inexpensive, can handle large mesh motions without inverting mesh elements and can sustain an FSI simulation for extensive periods of time without irreversibly distorting the mesh. Here we compare several commonly used MMTs which are based on the solution of elliptic partial differential equations, including harmonic extension, bi-harmonic extension and techniques based on the equations of linear elasticity. Moreover, we propose a novel MMT which utilizes ideas from continuation methods to efficiently solve the equations of nonlinear elasticity and proves to be robust even when the mesh undergoes extreme motions. In addition to that, we study how each MMT behaves when combined with the mesh-Jacobian-based stiffening. Finally, we evaluate the performance of different MMTs on a popular two-dimensional FSI benchmark reproduced by using an isogeometric partitioned solver with strong coupling.

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...

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...

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 ...

Topology Optimization (TO) is a powerful numerical technique to determine the optimal material layout in a design domain, which has accepted considerable developments in recent years. The classic Finite Element Method (FEM) is applied to compute the unknown structural responses in TO. However, several numerical deficiencies of the FEM significantly influence the effectiveness and efficiency of TO. In order to eliminate the negative influence of the FEM on TO, IsoGeometric Analysis (IGA) has become a promising alternative due to its unique feature that the Computer-Aided Design (CAD) model and Computer-Aided Engineering (CAE) model can be unified into a same mathematical model. In the paper, the main intention is to provide a comprehensive overview for the developments of Isogeometric Topology Optimization (ITO) in methods and applications. Finally, some prospects for the developments of ITO in the future are also presented.

In this study, a novel refined plate theory (RPT) is developed for the geometrically linear static analysis of FG plates, which is a simplification of the higher-order shear deformation theories (HSDTs). It improves the computational efficiency while preserving the accuracy advantage of HSDTs. The C1-continuity problem is overcome by isogeometric analysis (IGA), which shows more advantages than the C0 elements based finite element analysis. By T-splines, the computational cost is effectively reduced, since compared to NURBS based IGA, T-splines can achieve local refinement and improve the utilization of control points. The rule of mixture with power-law and Mori–Tanaka scheme are adopted to calculate the material properties of the plate. Several numerical experiments are given to prove the efficiency of the proposed method

Analysis of elastic wave propagation in a hollow cylinder with two-dimensional (2D) functionally graded material (FGM) and the curved outer surface under internal moving shock loading is the subject of this study. In the proposed method, there is no restriction on the distribution of material properties, the shape of the outer surface, and the applied shock loading. They are treated with non-uniform rational B-spline (NURBS). The isogeometric approach is developed for solving the problem to ensure precise modeling of the geometry. Also, the Newmark approach is used for full discretization of the isogeometric equations. The distributions of all elastic field quantities are determined for two types of material distributions and shock loadings. The effects of shock loadings, the shape of the outer surface, and the material distribution on the elastic wave are thoroughly examined. Propagation, reflections, and propagation speed inside the hollow cylinder are investigated. It is found that the propagation speeds of elastic waves have a distribution associated with the distribution of the material properties. Also, the shape of the outer surface can affect the amplitude of the elastic wave and the locations of concentration stress. It is concluded that the sonic boom phenomenon occurs in the solids as well as in the air.

Measuring omnidirectional acceleration is highly important for robust control of the vehicle states. A novel omnidirectional accelerometer with three piezoelectric curved-fibers is designed by using the genetic algorithm based optimization method. The isogeometric analysis (IGA) is utilized to analyze the strain induced voltage outputs of curved piezoelectric fibers, which can also guarantee high computation accuracy and significantly reduce the amounts of calculation in the optimization procedure compared to the finite element method. Employing cylindrical piezoelectric three fibers, the cross-axis sensitivities of the x and z axes of the omnidirectional accelerometer is eliminated completely in theory, which ensures the detection precision of magnitude and direction of 3D acceleration. The output voltages of proposed curved three-fiber accelerometer in x and y axes respective are higher than the fully decoupled accelerometer with three orthogonal fibers. The sensor also exhibits high sensitivity in very low frequency range of [0.01 Hz, 5 Hz], and numerical simulated sensitivity can reach 7.42 to 13.41 V/g, which is 78% to 155% higher than that of the omnidirectional accelerometer with three parallel straight-fibers.

A recently introduced NURBS mesh generation method for complex-geometry Isogeometric Analysis (IGA) is applied to building a high-quality mesh for a gas turbine. The compressible flow in the turbine is computed using the IGA and a stabilized method with improved discontinuity-capturing, weakly-enforced no-slip boundary-condition, and sliding-interface operators. The IGA results are compared with the results from the stabilized finite element simulation to reveal superior performance of the NURBS-based approach. Free-vibration analysis of the turbine rotor using the structural mechanics NURBS mesh is also carried out and shows that the NURBS mesh generation method can be used also in structural mechanics analysis. With the flow field from the NURBS-based turbine flow simulation, the Courant number is computed based on the NURBS mesh local length scale in the flow direction to show some of the other positive features of the mesh generation framework. The work presented further advances the IGA as a fully-integrated and robust design-to-analysis framework, and the IGA-based complex-geometry flow computation with moving boundaries and interfaces represents the first of its kind for compressible flows.

In the modelling of fibre-reinforced composites, it is well established to consider the fibre direction in the stored energy in order to account for the transverse isotropy of the overall material, induced by a single family of fibres. However, this approach does not include any length scale and therefore lacks in the prediction of size effects that may occur from the fibre diameter or spacing. By making use of a generalised continuum model including non-symmetric stresses and couple-stresses, the gradient of the fibre direction vector can be taken into account as an additional parameter of the stored energy density function. As a consequence, the enhanced model considers the bending stiffness of the fibres and includes information on the material length scale. Along with additional material parameters, increased continuity requirements on the basis functions follow in the finite element analysis. The isogeometric finite element method provides a framework which can fulfil these requirements of the corresponding weak formulation. In the present contribution, the method is applied to two representative numerical examples. At first, the bending deformation of a cantilever beam is studied in order to analyse the influence of the fibre properties. An increasingly stiff response is observed as the fibre bending stiffness increases and as the fibre orientation aligns with the beam’s axis. Secondly, a fibre-reinforced cylindrical tube under a pure azimuthal shear deformation is considered. The corresponding simulation results are compared against a semi-analytical solution. It is shown that the isogeometric analysis yields highly accurate results for the boundary value problem under consideration.

A simple and effective approach based on refined plate theory (RPT) is proposed to study the static and free vibration characteristics of functionally graded CNT-reinforced composite (FG-CNTRC) plates. Compared to traditional higher order shear deformation theories (HSDTs), the proposed method shows more efficient for FG-CNTRC plates analysis. To solve the C1-continuity requirement of the RPT, we used isogeometric analysis (IGA) to approximate the displacement field, which shows more advantages than the FEA, since it can construct higher-order elements without additional variables. This is an advantage for plate structural analysis because more variables make the calculation cumbersome. Finally, four types of FG-CNTRC plates were investigated and the results show the accuracy and efficiency of the proposed method.

We present computational flow analysis of a vertical-axis wind turbine (VAWT) that has been proposed to also serve as a tsunami shelter. In addition to the three-blade rotor, the turbine has four support columns at the periphery. The columns support the turbine rotor and the shelter. Computational challenges encountered in flow analysis of wind turbines in general include accurate representation of the turbine geometry, multiscale unsteady flow, and moving-boundary flow associated with the rotor motion. The tsunami-shelter VAWT, because of its rather high geometric complexity, poses the additional challenge of reaching high accuracy in turbine-geometry representation and flow solution when the geometry is so complex. We address the challenges with a space–time (ST) computational method that integrates three special ST methods around the core, ST Variational Multiscale (ST-VMS) method, and mesh generation and improvement methods. The three special methods are the ST Slip Interface (ST-SI) method, ST Isogeometric Analysis (ST-IGA), and the ST/NURBS Mesh Update Method (STNMUM). The ST-discretization feature of the integrated method provides higher-order accuracy compared to standard discretization methods. The VMS feature addresses the computational challenges associated with the multiscale nature of the unsteady flow. The moving-mesh feature of the ST framework enables high-resolution computation near the blades. The ST-SI enables moving-mesh computation of the spinning rotor. The mesh covering the rotor spins with it, and the SI between the spinning mesh and the rest of the mesh accurately connects the two sides of the solution. The ST-IGA enables more accurate representation of the blade and other turbine geometries and increased accuracy in the flow solution. The STNMUM enables exact representation of the mesh rotation. A general-purpose NURBS mesh generation method makes it easier to deal with the complex turbine geometry. The quality of the mesh generated with this method is improved with a mesh relaxation method based on fiber-reinforced hyperelasticity and optimized zero-stress state. We present computations for the 2D and 3D cases. The computations show the effectiveness of our ST and mesh generation and relaxation methods in flow analysis of the tsunami-shelter VAWT.

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 tech...

This paper presents an isogeometric approach based on the Non-Uniform Rational B-Splines (NURBS) to investigate static and free vibration responses of smart composite shells integrated with shear piezoelectric actuators. The degenerated shell formulation according to the Mindlin-Reissner shell theory is combined with the isogeometric approach. To model the laminated smart shells, the Equivalent Single Layer (ESL) theory is used. To consider the electric potential in the shear piezoelectric actuator layers, a sub-layer approach is adopted that assumes linear variation in the thickness direction of the sub-layer. The effect of different mechanical and electrical boundary conditions on transverse deformation and natural frequencies of laminated smart shells by applying the electric field have been investigated. In the case studies, two parallel edges of the considered shell structures are assumed simply supported and the other two with an arbitrary combination of boundary conditions including clamped, free or simply supports. Also, open-circuit and closed-circuit conditions are used as electric boundary conditions. Investigation of the effects of the shear piezoelectric actuator layers on various factors, including the simultaneous mechanical and electrical loadings as well as the radius of curvature of the shell are amongst the objects of this paper. Also, several numerical examples are presented to demonstrate the efficiency and accuracy of the isogeometric approach in the study of shear effects of the piezoelectric actuator layers. The obtained results indicate the reliability and desirability of the proposed approach.

An isogeometric approach for solving the Laplace–Beltrami equation on a two-dimensional manifold embedded in three-dimensional space using a Galerkin method based on Catmull–Clark subdivision surfaces is presented and assessed. The scalar-valued Laplace–Beltrami equation requires only$$C^0$$C0continuity and is adopted to elucidate key features and properties of the isogeometric method using Catmull–Clark subdivision surfaces. Catmull–Clark subdivision bases are used to discretise both the geometry and the physical field. A fitting method generates control meshes to approximate any given geometry with Catmull–Clark subdivision surfaces. The performance of the Catmull–Clark subdivision method is compared to the conventional finite element method. Subdivision surfaces without extraordinary vertices show the optimal convergence rate. However, extraordinary vertices introduce error, which decreases the convergence rate. A comparative study shows the effect of the number and valences of the extraordinary vertices on accuracy and convergence. An adaptive quadrature scheme is shown to reduce the error.

This paper concerns a novel isogeometric Timoshenko beam formulation for a geometrically nonlinear analysis of spatial beams using the total Lagrangian description. Constitutive laws for hyperelastic materials, whose behavior varies with their deformations, are widely defined by using strain energy density functions that are written in terms of the Green–Lagrange strain tensor. Many finite element beam formulations for geometrically nonlinear analyses of spatial beams are developed using the Green–Lagrange strain tensor and its energy conjugate, the second Piola–Kirchhoff stress tensor. Unfortunately, there virtually exist no isogeometric Timoshenko beam formulations for this type of analysis that are derived by using this energy conjugate pair. To allow the possibility of considering hyperelastic materials, the present isogeometric beam formulation is developed in the total Lagrangian description using the Green–Lagrange strain tensor and the second Piola–Kirchhoff stress tensor. The proposed formulation is capable of simulating beam structures that are subjected to large displacements and rotations, without any restriction in magnitude. Three-dimensional beam configurations are reduced into one-dimensional structures using the beam axis and director vectors of the cross sections. The cross-sectional rotation along the beam axis is represented by an orthogonal tensor, which is parameterized by a vector-like parameter. Updating the cross-sectional rotations is performed purely by natural exponentiation and superposition of relevant rotational quantities. To show the accuracy and efficiency of the proposed beam formulation, some benchmark and well-established numerical examples with various types of beam, i.e., straight, curved, pre-twisted beams, are analyzed. The obtained results are compared with those results in the literature, obtained from both analytical and numerical methods.

This paper aims to study the buckling and bending analysis of curvilinearly stiffened plates by using an isogeometric approach. First-order shear deformation theory is adopted to model the behaviors of stiffened plates. Based on the employed approach, it is easy to model stiffeners with different sizes and layouts, since the degrees of freedom for the whole structure are integrated into those of the original plate leading to a relatively low computational cost. The performance of the proposed approach is validated via a couple of benchmark problems available in the literature, and the effect of different parameters including bending stiffness, relative mass, cross section, and shape of stiffener on the buckling and bending behavior of curvilinearly stiffened plates is investigated. The results show the relative high accuracy of this method using fewer degrees of freedom for stiffeners, which is beneficial in optimization procedures.

In this study, a three-dimensional discontinuous Galerkin isogeometric analysis framework is presented for the analysis of composite laminates. Non-uniform rational B-splines are employed as basis functions for both geometric and computational implementations. From a practical point of view, modeling with multiple non-uniform rational B-spline patches is required in many different applications due to the complexity of computational domains. Then, a special numerical technique is necessary to couple different non-uniform rational B-spline patches to carry out the isogeometric analysis. In this study, therefore, one of the discontinuous Galerkin methods, namely, symmetric interior penalty Galerkin formulation is utilized to deal with multi-patch isogeometric analysis applications. In order to show the applicability of the proposed framework, composite laminates under sinusoidally distributed load with different stacking sequences are studied in the numerical examples. The predicted results are compared with those obtained by the three-dimensional elasticity solutions and various numerical models available in the literature.