References of "Rabczuk, Timon"
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See detailConstructing IGA-suitable planar parameterization from complex CAD boundary by domain partition and global/local optimization
Xu, Gang; Li, Ming; Mourrain, Bernard et al

in Computer Methods in Applied Mechanics & Engineering (2018), 328

In this paper, we propose a general framework for constructing IGA-suitable planar B-spline parameterizations from given complex CAD boundaries. Instead of the computational domain bounded by four B ... [more ▼]

In this paper, we propose a general framework for constructing IGA-suitable planar B-spline parameterizations from given complex CAD boundaries. Instead of the computational domain bounded by four B-spline curves, planar domains with high genus and more complex boundary curves are considered. Firstly, some pre-processing operations including B´ezier extraction and subdivision are performed on each boundary curve in order to generate a high-quality planar parameterization; then a robust planar domain partition framework is proposed to construct high-quality patch-meshing results with few singularities from the discrete boundary formed by connecting the end points of the resulting boundary segments. After the topology information generation of quadrilateral decomposition, the optimal placement of interior B´ezier curves corresponding to the interior edges of the quadrangulation is constructed by a global optimization method to achieve a patch-partition with high quality. Finally, after the imposition of C1/G1-continuity constraints on the interface of neighboring Bezier patches with respect to each quad in the quadrangulation, the high-quality Bezier patch parameterization is obtained by a local optimization method to achieve uniform and orthogonal iso-parametric structures while keeping the continuity conditions between patches. The efficiency and robustness of the proposed method are demonstrated by several examples which are compared to results obtained by the skeleton-based parameterization approach. [less ▲]

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See detailModelling hydraulic fractures in porous media using flow cohesive interface elements
Nguyen, Vinh Phu; Lian, Haojie; Rabczuk, Timon et al

in Engineering Geology (2017), 225

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See detailGeometry-Independent Field approximaTion (GIFT) for spline based FEM for Linear Elasticity: a Diffpack implementation
Hossain, Md Naim; Xu, Gang; Bordas, Stéphane UL et al

Scientific Conference (2015, June 01)

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See detailIsogeometric analysis: an overview and computer implementation aspects
Nguyen, Vinh-Phu; Anitescu, Cosmin; Bordas, Stéphane UL et al

in Mathematics and Computers in Simulation (2015)

Isogeometric analysis (IGA) represents a recently developed technology in computational mechanics that offers the possibility of integrating methods for analysis and Computer Aided Design (CAD) into a ... [more ▼]

Isogeometric analysis (IGA) represents a recently developed technology in computational mechanics that offers the possibility of integrating methods for analysis and Computer Aided Design (CAD) into a single, unified process. The implications to practical engineering design scenarios are profound, since the time taken from design to analysis is greatly reduced, leading to dramatic gains in efficiency. In this manuscript, through a self-contained Matlab⃝R implementation, we present an introduction to IGA applied to simple analysis problems and the related computer implementation aspects. Furthermore, implementation of the extended IGA which incorporates enrichment functions through the partition of unity method (PUM) is also presented, where several examples for both two-dimensional and three-dimensional fracture are illustrated. We also describe the use of IGA in the context of strong-form (collocation) formulations, which has been an area of research interest due to the potential for significant efficiency gains offered by these methods. The code which accompanies the present paper can be applied to one, two and three-dimensional problems for linear elasticity, linear elastic fracture mechanics, structural mechanics (beams/plates/shells including large displacements and rotations) and Poisson problems with or without enrichment. The B ́ezier extraction concept that allows the FE analysis to be performed efficiently on T-spline geometries is also incorporated. The article includes a summary of recent trends and developments within the field of IGA. [less ▲]

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See detailProbabilistic multiconstraints optimization of cooling channels in ceramic matrix composites
Ghasemi, Hamid; Kerfriden, Pierre; Bordas, Stéphane UL et al

in Composites : Part B, Engineering (2015), 81

This paper presents a computational reliable optimization approach for internal cooling channels in Ceramic Matrix Composite (CMC) under thermal and mechanical loadings. The algorithm finds the optimal ... [more ▼]

This paper presents a computational reliable optimization approach for internal cooling channels in Ceramic Matrix Composite (CMC) under thermal and mechanical loadings. The algorithm finds the optimal cooling capacity of all channels (which directly minimizes the amount of coolant needed). In the first step, available uncertainties in the constituent material properties, the applied mechanical load, the heat flux and the heat convection coefficient are considered. Using the Reliability Based Design Optimization (RBDO) approach, the probabilistic constraints ensure the failure due to excessive temperature and deflection will not happen. The deterministic constraints restrict the capacity of any arbitrary cooling channel between two extreme limits. A “series system” reliability concept is adopted as a union of mechanical and thermal failure subsets. Having the results of the first step for CMC with uniformly distributed carbon (C-) fibers, the algorithm presents the optimal layout for distribution of the C-fibers inside the ceramic matrix in order to enhance the target reliability of the component. A sequential approach and B-spline finite elements have overcome the cumbersome computational burden. Numerical results demonstrate that if the mechanical loading dominates the thermal loading, C-fibers distribution can play a considerable role towards increasing the reliability of the design. [less ▲]

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See detailInterfacial shear stress optimization in sandwich beams with polymeric core using non-uniform distribution of reinforcing ingredients
Ghasemi, Hamid; Kerfriden, Pierre; Muthu, Jacob et al

in Composite Structures (2015)

Core shearing and core/face debonding are two common failure states of sandwich beams which are mainly the result of excessive shear stresses in the core. Generally, the core made of homogeneous Fiber ... [more ▼]

Core shearing and core/face debonding are two common failure states of sandwich beams which are mainly the result of excessive shear stresses in the core. Generally, the core made of homogeneous Fiber Reinforced Polymer (FRP) shows better shear resistance in comparison with that made of pure polymer. Usually, this enhancement is however somewhat limited. This paper proposes a methodology to decrease interfacial stresses by presenting the optimal distribution of reinforcing ingredients in the polymeric matrix. For this purpose, a Non-Uniform Rational Bspline (NURBS) based reinforcement distribution optimizer is developed. This technique aims at the local stress minimization within any arbitrary zone of the design domain. In our methodology, optimization and model analysis (calculation of the objective function and the design constraints) have common data sets. The quadratic NURBS basis functions smoothly define the reinforcement distribution function as a NURBS surface. The core and face sheets are modeled as multi-patches and compatibility in the displacement field is enforced by the penalty method. An adjoint sensitivity method is devised to minimize the objective function within areas of interest defined over arbitrary regions in the design domain. It is also used for efficient updating of design variables through optimization iterations. The method is verified by several examples. [less ▲]

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See detailCardiff/Luxembourg Computational Mechanics Research Group
Bordas, Stéphane UL; Kerfriden, Pierre; Hale, Jack UL et al

Poster (2014, November)

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See detailUncertainty quantification of dry woven fabrics: A sensitivity analysis on material properties
Akmar, Ilyani; Lahmer, Tom; Beex, Lars UL et al

in Composite Structures (2014), 116

Based on sensitivity analysis, we determine the key meso-scale uncertain input variables that influence the macro-scale mechanical response of a dry textile subjected to uni-axial and biaxial deformation ... [more ▼]

Based on sensitivity analysis, we determine the key meso-scale uncertain input variables that influence the macro-scale mechanical response of a dry textile subjected to uni-axial and biaxial deformation. We assume a transversely isotropic fashion at the macro-scale of dry woven fabric. This paper focuses on global sensitivity analysis; i.e. regression- and variance-based methods. The sensitivity of four meso-scale uncertain input parameters on the macro-scale response are investigated; i.e. the yarn height, the yarn spacing, the yarn width and the friction coefficient. The Pearson coefficients are adopted to measure the effect of each uncertain input variable on the structural response. Due to computational effectiveness, the sensitivity analysis is based on response surface models. The Sobol’s variance-based method which consists of first-order and total-effect sensitivity indices are presented. The sensitivity analysis utilizes linear and quadratic correlation matrices, its corresponding correlation coefficients and the coefficients of determination of the response uncertainty criteria. The correlation analysis, the response surface model and Sobol’s indices are presented and compared by means of uncertainty criteria influences on MataBerkait-dry woven fabric material properties. To anticipate, it is observed that the friction coefficient and yarn height are the most influential factors with respect to the specified macro-scale mechanical responses. [less ▲]

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See detailReduced order modelling: towards tractable computational homogenisation schemes
Kerfriden, Pierre; Goury, Olivier; Akbari, Ahmad et al

Presentation (2014, May 15)

Towards rationalised computational expense for simulating fracture over multiple scales The project focuses on the numerical simulation of the failure of complex, heterogeneous structures. The simulation ... [more ▼]

Towards rationalised computational expense for simulating fracture over multiple scales The project focuses on the numerical simulation of the failure of complex, heterogeneous structures. The simulation of such physical phenomena is of particular interest to practitioners as it enables to limit the number of destructive tests required to design and assess structures, and, ultimately, to decrease the safety factors used in design. In such heterogeneous media, the description of crack or damage initiation and propagation must be done at the scale of the inhomogeneities (e.g. aggregates in a concrete structure) in order for the results to be predictive. If one uses such a fine-scale material model to simulate structures at an engineering scale (e.g. an aircraft composite panel or a concrete beam), very large numerical problems need to be solved. In addition, there is a strong need for engineers to run their models numerous times, for different sets of the design parameters (e.g. loading conditions, geometry or material properties). Tackling such parametric multiscale problems is prohibitively expensive when using brute force parallel computing. However, one can use the fact that solutions to parametric problems usually evolve in a relatively coarse space: solutions to nearby parameter sets are usually close in a certain sense. This idea is classically used in Model Order Reduction, which proposes to reduce the size of the initial problem by several order of magnitude by simply reusing the information generated when solving the initial problem for several different sets of parameters. However, in the case of fracture, the information provided by the initial problem is most of the time insufficient to describe the behaviour of the system for arbitrary parameters. Crack paths, defects, and subsequent ultimate strengths are strongly influenced by an even slight variation in the parameter set. Fortunately, we showed in our previous research that this characteristic only affects a local region surrounding the structural defects, whilst the behaviour far from these regions is remains relatively unchanged for a wide range of parameter values. The proposed project will make use of this observation in a generic way, by coupling Reduced Order Modeling and Domain Decomposition. The structure will be divided in smaller subcomponents, on which Reduced Order Modeling will be applied separately. The consequence will be that the computational efforts will be greatly decreased in the regions that are far away from the damaged zone. Within the process zone itself, the substructuring framework will allow us to automatically switch to classical direct solvers. In this sense, the research aims at rationalising the computational costs associated to the simulation of parametrised multiscale fracture simulations, by concentrating the numerical effort where it is most required and with minimal intervention of the user. [less ▲]

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See detailIsogeometric analysis suitable trivariate NURBS representation of composite panels with a new offset algorithm
Nguyen, Vinh-Phu; Kerfriden, Pierre; Bordas, Stéphane UL et al

in Computer-Aided Design (2014), 55

Trivariate NURBS (non-uniform rational B-splines) representation of composite panels which is suitable for three-dimensional isogeometric analysis (IGA) is constructed with a new curve/surface offset ... [more ▼]

Trivariate NURBS (non-uniform rational B-splines) representation of composite panels which is suitable for three-dimensional isogeometric analysis (IGA) is constructed with a new curve/surface offset algorithm. The proposed offset algorithm, which is required by IGA, is non-existent in the CAD literature. Using the presented approach, finite element analysis of composite panels can be performed with the only input being the geometry representation of the composite surface. The method proposed provides a bi-directional system in which one can go forward from CAD to analysis and backwards from analysis to CAD. This is believed to facilitate the design of composite structures. Different parts (patches) can be parametrized independently of each other and glued together, in the finite element solver, by a discontinuous Galerkin method. A stress analysis of curved composite panel with stiffeners is provided to demonstrate the proposed framework. © 2014 Elsevier Ltd. All rights reserved. [less ▲]

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See detailAn integrated design-analysis framework for three dimensional composite panels
Nguyen, Vinh-Phu; Kerfriden, Pierre; Bordas, Stéphane UL et al

in Computer-Aided Design (2014)

We present an integrated design-analysis framework for three dimensional composite panels. The main components of the proposed framework consist of (1) a new curve/surface offset algorithm and (2) the ... [more ▼]

We present an integrated design-analysis framework for three dimensional composite panels. The main components of the proposed framework consist of (1) a new curve/surface offset algorithm and (2) the isogeometric concept recently emerged in the computational mechanics community. Using the presented approach, finite element analysis of composite panels can be performed with the only input is the geometry representation of the composite surface. In this paper, non-uniform rational B-splines (NURBS) are used to represent the panel surfaces. A stress analysis of curved composite panel with stiffeners is provided to demonstrate the proposed framework. [less ▲]

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See detailExplicit finite deformation analysis of isogeometric membranes
Chen, Lei; Nguyen-Thanh, Nhon; Nguyen-Xuan, Hung et al

in Computer Methods in Applied Mechanics & Engineering (2014)

NURBS-based isogeometric analysis was first extended to thin shell/membrane structures which allows for finite membrane stretching as well as large deflection and bending strain. The assumed non-linear ... [more ▼]

NURBS-based isogeometric analysis was first extended to thin shell/membrane structures which allows for finite membrane stretching as well as large deflection and bending strain. The assumed non-linear kinematics employs the Kirchhoff-Love shell theory to describe the mechanical behaviour of thin to ultrathin structures. The displacement fields are interpolated from the displacements of control points only, and no rotational degrees of freedom are used at control points. Due to the high order Ck (k ≥ 1) continuity of NURBS shape functions the Kirchhoff-Love theory can be seamlessly implemented. An explicit time integration scheme is used to compute the transient response of membrane structures to time-domain excitations, and a dynamic relaxation method is employed to obtain steady-state solutions. The versatility and good performance of the present formulation is demonstrated with the aid of a number of test cases, including a square membrane strip under static pressure, the inflation of a spherical shell under internal pressure, the inflation of a square airbag and the inflation of a rubber balloon. The mechanical contribution of the bending stiffness is also evaluated. [less ▲]

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See detailQuasicontinuum-based multiscale approaches for plate-like beam lattices experiencing in-plane and out-of-plane deformation
Beex, Lars UL; Kerfriden, Pierre; Rabczuk, Timon et al

in Computer Methods in Applied Mechanics & Engineering (2014), 279

The quasicontinuum (QC) method is a multiscale approach that aims to reduce the computational cost of discrete lattice computations. The method incorporates small-scale local lattice phenomena (e.g. a ... [more ▼]

The quasicontinuum (QC) method is a multiscale approach that aims to reduce the computational cost of discrete lattice computations. The method incorporates small-scale local lattice phenomena (e.g. a single lattice defect) in macroscale simulations. Since the method works directly and only on the beam lattice, QC frameworks do not require the construction and calibration of an accompanying continuum model (e.g. a cosserat/micropolar description). Furthermore, no coupling procedures are required between the regions of interest in which the beam lattice is fully resolved and coarse domains in which the lattice is effectively homogenized. Hence, the method is relatively straightforward to implement and calibrate. In this contribution, four variants of the QC method are investigated for their use for planar beam lattices which can also experience out-of-plane deformation. The different frameworks are compared to the direct lattice computations for three truly multiscale test cases in which a single lattice defect is present in an otherwise perfectly regular beam lattice. [less ▲]

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See detailStochastic modelling of clay/epoxy nanocomposites
Silani, Mohammad; Talebi, Hossein; Ziaei-Rad, Saeed et al

in Composite Structures (2014), 118

This paper presents a numerical investigation of the mechanical properties of exfoliated clay/epoxy nanocomposites. The large scatter in the material properties and distribution of the inclusions and ... [more ▼]

This paper presents a numerical investigation of the mechanical properties of exfoliated clay/epoxy nanocomposites. The large scatter in the material properties and distribution of the inclusions and matrix is taken into account by introducing an appropriate stochastic damage modelling at the nano scale. Then, the overall properties of the nanocomposite are upscaled using computational homogenisation. Two mechanical properties are investigated: the random distribution of the homogenised Young’s modulus and the overall loss of stiffness observed in the case of extreme loading. The results obtained in the former case are in good agreement with experimental results from the literature. In the second case, we show that exfoliation does not significantly affect the overall strength of the nanocomposite. [less ▲]

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See detailIsogeometric finite element analysis using polynomial splines over hierarchical T-meshes
Nguyen-Thanh, Nhon; Nguyen-Xuan, Hung; Bordas, Stéphane UL et al

in IOP Conference Series: Materials Science and Engineering (2014), 10(1),

Isogeometric finite element analysis has become a powerful alternative to standard finite elements due to their flexibility in handling complex geometries. One major drawback of NURBS based isogeometric ... [more ▼]

Isogeometric finite element analysis has become a powerful alternative to standard finite elements due to their flexibility in handling complex geometries. One major drawback of NURBS based isogeometric finite elements is their less effectiveness of local refinement. In this study, we present an alternative to NURBS based isogeometric finite elements that allow for local refinement. The idea is based on polynomial splines and exploits the flexibility of T-meshes for local refinement. The shape functions satisfy important properties such as non-negativity, local support and partition of unity. We will demonstrate the efficiency of the proposed method by two numerical examples. [less ▲]

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See detailIsogeometric analysis: an overview and computer implementation aspects
Nguyen, Vinh-Phu; Anitescu, Cosmin; Bordas, Stéphane UL et al

Learning material (2013)

Isogeometric analysis (IGA) represents a recently developed technology in computational mechanics that offers the possibility of integrating methods for analysis and Computer Aided Design (CAD) into a ... [more ▼]

Isogeometric analysis (IGA) represents a recently developed technology in computational mechanics that offers the possibility of integrating methods for analysis and Computer Aided Design (CAD) into a single, unified process. The implications to practical engineering design scenarios are profound, since the time taken from design to analysis is greatly reduced, leading to dramatic gains in efficiency. The tight coupling of CAD and analysis within IGA requires knowledge from both fields and it is one of the goals of the present paper to outline much of the commonly used notation. In this manuscript, through a clear and simple Matlab⃝R implementation, we present an introduction to IGA applied to the Finite Element (FE) method and related computer implementation aspects. Furthermore, implemen- tation of the extended IGA which incorporates enrichment functions through the partition of unity method (PUM) is also presented, where several examples for both two-dimensional and three-dimensional fracture are illustrated. The open source Matlab⃝R code which accompanies the present paper can be applied to one, two and three-dimensional problems for linear elasticity, linear elastic fracture mechanics, structural mechanics (beams/plates/shells including large displacements and rotations) and Poisson problems with or without enrichment. The B ́ezier extraction concept that allows FE analysis to be performed efficiently on T-spline geometries is also incorporated. The article includes a summary of recent trends and developments within the field of IGA. [less ▲]

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See detailOptimization of elastic properties and weaving patterns of woven composites
Abu Bakar, Ilyani Akmar; Kramer, Oliver; Bordas, Stéphane UL et al

in Composite Structures (2013), 100

Predictions of geometric characteristics and elastic properties of patterns in woven fabric composites are proposed based on unit cells. This study addresses the optimization of the elastic properties ... [more ▼]

Predictions of geometric characteristics and elastic properties of patterns in woven fabric composites are proposed based on unit cells. This study addresses the optimization of the elastic properties within woven fabric composite unit cells with multiple designs based on periodic boundary conditions and evolutionary algorithms. Furthermore, the study permits a reliable prediction of mechanical behavior of woven fabric composites unit cells in which the weave patterns are the variables. The models are treated as a single-ply for each weave pattern embedded in a matrix pocket. The analyzed weave patterns are created by TexGen, the simulation is done with ABAQUS. At the unit cell level, effective elastic properties of the yarn were estimated from Finite Element (FE) simulations using periodic boundary conditions. An evolutionary algorithm is adopted in optimizing the elastic properties of woven fabric composites with recombination and mutation operators. We present a parameter study to investigate the effect of various geometric parameters. Those parameters include the gap length, the shape of the yarn section, the yarn thickness, the constituent materials, the fiber volume fraction and the elastic properties. By examining this optimized model through the pre-determined parameters as mentioned above, an optimal parameter set for composite's performance can be properly selected. © 2013 Elsevier Ltd. [less ▲]

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See detailNURBS-based finite element analysis of functionally graded plates: Static bending, vibration, buckling and flutter
Valizadeh, N; Natarajan, Sundarajan; González-Estrada, Octavio Andrés et al

in Composite Structures (2013), 99

In this paper, a non-uniform rational B-spline based iso-geometric finite element method is used to study the static and dynamic characteristics of functionally graded material (FGM) plates. The material ... [more ▼]

In this paper, a non-uniform rational B-spline based iso-geometric finite element method is used to study the static and dynamic characteristics of functionally graded material (FGM) plates. The material properties are assumed to be graded only in the thickness direction and the effective properties are computed either using the rule of mixtures or by Mori–Tanaka homogenization scheme. The plate kinematics is based on the first order shear deformation plate theory (FSDT). The shear correction factors are evaluated employing the energy equivalence principle and a simple modification to the shear correction factor is presented to alleviate shear locking. Static bending, mechanical and thermal buckling, linear free flexural vibration and supersonic flutter analysis of FGM plates are numerically studied. The accuracy of the present formulation is validated against available three-dimensional solutions. A detailed numerical study is carried out to examine the influence of the gradient index, the plate aspect ratio and the plate thickness on the global response of functionally graded material plates. [less ▲]

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See detailALGEBRAIC COARSE-GRAINING METHODS IN FRACTURE MECHANICS: TACKLING LOCAL LACK OF CORRELATION USING DOMAIN DECOMPOSITION
Goury, Olivier; Kerfriden, Pierre; Rabczuk, Timon et al

Scientific Conference (2012, March)

In this paper, we propose to couple model order reduction techniques with domain decomposition meth- ods for the solution to parametric problems of fracture. The nonlinear nature of the problems requires ... [more ▼]

In this paper, we propose to couple model order reduction techniques with domain decomposition meth- ods for the solution to parametric problems of fracture. The nonlinear nature of the problems requires the use of a system approximation method to speed-up the assembly of the non-linear opreators. We show that the method efficiently computes a solution faster than a full order model for a given accuracy. The speed-up increases with the problem size. [less ▲]

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See detailA cell-based smoothed finite element method for three dimensional solid structures
Nguyen-Xuan, Hung; Nguyen, Ha Manh UL; Bordas, Stéphane UL et al

in KSCE Journal of Civil Engineering (2012), 16(7), 1230-1242

This paper extends further the strain smoothing technique in finite elements to 8-noded hexahedral elements (CS-FEM-H8). The idea behind the present method is similar to the cell-based smoothed 4-noded ... [more ▼]

This paper extends further the strain smoothing technique in finite elements to 8-noded hexahedral elements (CS-FEM-H8). The idea behind the present method is similar to the cell-based smoothed 4-noded quadrilateral finite elements (CS-FEM-Q4). In CSFEM, the smoothing domains are created based on elements, and each element can be further subdivided into 1 or several smoothing cells. It is observed that: 1) The CS-FEM using a single smoothing cell can produce higher stress accuracy, but insufficient rank and poor displacement accuracy; 2) The CS-FEM using several smoothing cells has proper rank, good displacement accuracy, but lower stress accuracy, especially for nearly incompressible and bending dominant problems. We therefore propose 1) an extension of strain smoothing to 8-noded hexahedral elements and 2) an alternative CS-FEM form, which associates the single smoothing cell issue with multi-smoothing cell one via a stabilization technique. Several numerical examples are provided to show the reliability and accuracy of the present formulation. [less ▲]

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