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Isogeometric analysis of functionally graded plates using a refined plate theory ; ; et al in Composites. Part B, Engineering (2014), 64 We present in this paper a simple and effective approach that incorporates isogeometric finite element analysis (IGA) with a refined plate theory (RPT) for static, free vibration and buckling analysis of ... [more ▼] We present in this paper a simple and effective approach that incorporates isogeometric finite element analysis (IGA) with a refined plate theory (RPT) for static, free vibration and buckling analysis of functionally graded material (FGM) plates. A new inverse tangent distributed function through the plate thickness is proposed. The RPT enables us to describe the non-linear distribution of shear stresses through the plate thickness without any requirement of shear correction factors (SCF). IGA utilizes basis functions namely B-splines or non-uniform rational B-splines (NURBS) which reach easily the smoothness of any arbitrary order. It hence satisfies the C1 requirement of the RPT model. The present method approximates the displacement field with four degrees of freedom per each control point allowing an efficient solution process. [less ▲] Detailed reference viewed: 126 (4 UL)Gradient Smoothing for Nearly Incompressible Hyperelasticity ; ; et al Poster (2014) Detailed reference viewed: 98 (4 UL)Gradient Smoothing for Nearly Incompressible Hyperealsticity ; ; et al Poster (2014) Detailed reference viewed: 117 (7 UL)Efficient modeling of random heterogeneous materials with an uniform probability density function (slides) ; ; et al Scientific Conference (2014) Homogenised constitutive laws are largely used to predict the behaviour of composite structures. Assessing the validity of such homogenised models can be done by making use of the concept of “modelling ... [more ▼] Homogenised constitutive laws are largely used to predict the behaviour of composite structures. Assessing the validity of such homogenised models can be done by making use of the concept of “modelling error”. First, a microscopic “faithful” -and potentially intractable- model of the structure is defined. Then, one tries to quantify the effect of the homogenisation procedure on a result that would be obtained by directly using the “faithful” model. Such an approach requires (a) the “faithful” model to be more representative of the physical phenomena of interest than the homogenised model and (b) a reliable approximation of the result obtained using the ”faithful” and intractable model to be available at cheap costs. We focus here on point (b), and more precisely on the extension of the techniques devel- oped in [3] [2] to estimate the error due to the homogenisation of linear, spatially random composite materials. Particularly, we will approximate the unknown probability density function by bounding its first moment. In this paper, we will present this idea in more detail, displaying the numerical efficiencies and computational costs related to the error estimation. The fact that the probability density function is uniform is exploited to greatly reduce the computational cost. We will also show some first attempts to correct the homogenised model using non-conforming, weakly intrusive microscopic patches. [less ▲] Detailed reference viewed: 269 (1 UL)IMPROVING THE CONVERGENCE OF BOUNDS FOR EFFECTIVE ELASTIC PARAMETERS OF HETEROGENEOUS MATERIALS ; ; Bordas, Stéphane Scientific Conference (2014) Detailed reference viewed: 247 (0 UL)Model order reduction for speeding up computational homogenisation methods of type FE2 ; ; Bordas, Stéphane Presentation (2014) Detailed reference viewed: 118 (2 UL)Fundamental Solutions and Dual Boundary Element Method for Crack Problems in Plane Cosserat Elasticity ; Bordas, Stéphane in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (2014) In this paper, both singular and hypersingular fundamental solutions of plane Cosserat elasticity are derived and given in a ready-to-use form. The hypersingular fundamental solutions allow to formulate ... [more ▼] In this paper, both singular and hypersingular fundamental solutions of plane Cosserat elasticity are derived and given in a ready-to-use form. The hypersingular fundamental solutions allow to formulate the analogue of Somigliana stress identity, which can be used to obtain the stress and couple stress fields inside the domain from the boundary values of the displacements, microrotation and stress and couple stress tractions. Using these newly derived fundamental solutions, the boundary integral equations of both types are formulated and solved by the boundary element method. Simultaneous use of both types of the equations (approach known as the dual BEM) allows to treat problems where parts of the boundary are overlapping, such as crack problems, and to do this for general geometry and loading conditions. The high accuracy of the boundary element method for both types of equations is demonstrated for a number of benchmark problems, including a Griffith crack problem and a plate with an edge crack. The detailed comparison of the BEM-results and the analytical solution for a Griffith crack is given, particularly, in terms of stress and couple stress intensity factors, as well as the crack opening displacements and microrotations on the crack faces. A modified method for computing the couple stress intensity factors is also proposed and evaluated. Finally, the asymptotic behavior of the solution to the Cosserat crack problems, in the vicinity of the crack tip is analyzed. [less ▲] Detailed reference viewed: 677 (13 UL)Strain smoothing technique in 3D for nearly incompressible neo-Hookean material ; ; et al Report (2014) Detailed reference viewed: 208 (12 UL)Global energy minimization for multiple fracture growth ; Bordas, Stéphane Report (2013) Detailed reference viewed: 226 (5 UL)Space-time reduced basis approximation and goal-oriented a posteriori error estimation for wave equation ; ; Bordas, Stéphane in Theory and Application of Model Order Reduction (2013, December) We study numerically the linear second order wave equation with an output quantity of interest which is a linear functional of the field variable using reduced basis approximation methods in the space ... [more ▼] We study numerically the linear second order wave equation with an output quantity of interest which is a linear functional of the field variable using reduced basis approximation methods in the space-time domain. The essential new ingredient is the a posteriori error estimation of the output quantity of interest. The technique, which is based on the well-known dual-weighted residual (DWR) method is deployed within a reduced basis approximation context. First, we introduce the reduced basis recipe - Galerkin projection onto a space spanned by the reduced basis functions which are constructed from the solutions of the governing PDE at several selected points in the parameter space. Second, in order to construct these basis functions we propose a new “goal-oriented” Proper Orthogonal Decomposition (POD)-Greedy sampling procedure, which is based on these new a posteriori error estimations. Finally, this a posteriori error estimation is also used to evaluate approximately the quality of many output computations in the online stage within the reduced basis procedure. [less ▲] Detailed reference viewed: 312 (3 UL)Advances in Applied Mechanics Bordas, Stéphane Book published by Elsevier (2013) Advances in Applied Mechanics draws together recent significant advances in various topics in applied mechanics. Published since 1948, Advances in Applied Mechanics aims to provide authoritative review ... [more ▼] Advances in Applied Mechanics draws together recent significant advances in various topics in applied mechanics. Published since 1948, Advances in Applied Mechanics aims to provide authoritative review articles on topics in the mechanical sciences, primarily of interest to scientists and engineers working in the various branches of mechanics, but also of interest to the many who use the results of investigations in mechanics in various application areas, such as aerospace, chemical, civil, environmental, mechanical and nuclear engineering. [less ▲] Detailed reference viewed: 221 (5 UL)smooth nodal stress in the XFEM for crack propagation simulations ; Bordas, Stéphane ; Scientific Conference (2013, September) In this paper, we present a method to achive smooth nodal stresses in the XFEM without post-processing. This method was developed by borrowing ideas from ``twice interpolating approximations'' (TFEM) [1 ... [more ▼] In this paper, we present a method to achive smooth nodal stresses in the XFEM without post-processing. This method was developed by borrowing ideas from ``twice interpolating approximations'' (TFEM) [1]. The salient feature of the method is to introduce an ``average'' gradient into the construction of the approximation, resulting in improved solution accuracy, both in the vicinity of the crack tip and in the far field. Due to the high order polynomial basis provided by the interpolants, the new approximation enhances the smoothness of the solution without requiring an increased number of degrees of freedom. This is particularly advantageous for low-order elements and in fracture mechanics, where smooth stresses are important for certain crack propagation criteria, e.g. based on maximum principal stresses. Since the new approach adopts the same mesh discretization, i.e. simplex meshes, it can be easily extended into various problems and is easily implemented. We discuss the increase in the bandwidth which is the major drawback of the present method and can be somewhat alleviated by using an element-by-element solution strategy. Numerical tests show that the new method is as robust as XFEM, considering precision, model size and post-processing time. By comparing in detail the behaviour of the method on crack propagation examples, we can conclude that for two-dimensional problems, the proposed method tends to be an efficient alternative to the classical XFEM [2][3] especially when local, stress-based propagation criteria are used. [less ▲] Detailed reference viewed: 387 (4 UL)Analysis using higher-order XFEM: Implicit representation of geometrical features from a given parametric representation ; Bordas, Stéphane ; et al in Mécanique & Industries (2013, August 30) We present a promising approach to reduce the difficulties associated with meshing complex curved domain boundaries for higher-order finite elements. In this work, higher-order XFEM analyses for strong ... [more ▼] We present a promising approach to reduce the difficulties associated with meshing complex curved domain boundaries for higher-order finite elements. In this work, higher-order XFEM analyses for strong discontinuity in the case of linear elasticity problems are presented. Curved implicit boundaries are approximated inside an unstructured coarse mesh by using parametric information extracted from the parametric representation (the most common in Computer Aided Design CAD). This approximation provides local graded sub-mesh (GSM) inside boundary elements (i.e. an element split by the curved boundary) which will be used for integration purpose. Sample geometries and numerical experiments illustrate the accuracy and robustness of the proposed approach. [less ▲] Detailed reference viewed: 370 (1 UL)Isogeometric analysis: an overview and computer implementation aspects ; ; Bordas, Stéphane 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 ▲] Detailed reference viewed: 1051 (11 UL)A multiscale partitioned reduced order model applied to damage simulation ; ; Bordas, Stéphane Scientific Conference (2013, July) Simulating fracture in realistic engineering components is computationally expensive. In the context of early-stage design, or reverse engineering, such simulations might need to be performed for a large ... [more ▼] Simulating fracture in realistic engineering components is computationally expensive. In the context of early-stage design, or reverse engineering, such simulations might need to be performed for a large range of material and geometric parameters, which makes the solution to the parametric problem of fracture unaffordable. Model order reduction, such as the proper orthogonal decomposition (POD), is one way to reduce significantly the computational time by reducing the number of spatial unknowns. The solution is searched for in a reduced space spanned by a few well-chosen basis vectors only. In the context of solid mechanics involving structural softening, the strong topological changes in the zone where damage localises are extremely sensitive to variations of the parameters, which requires reduced spaces of prohibitively large dimensions in order to approximate the solution with a sufficiently high degree of accuracy. Introduced in [1], partitioned model order reduction is an alternative to global model order reduction that essentially divides up the problem into smaller regions. Each region can then be tackled using a reduced model of appropriate size, if at all, depending on the local material non-linearities in the region. In the context of multiscale homogenization, simulations of representative volume elements (RVE) have to be performed to obtain the material properties in the different elements of a coarse mesh. When considering a nonlinear material, those multiple RVE simulations can be com- putationally very expensive. They however only differ by the history of boundary conditions applied. This contribution proposes to apply partitioned model order reduction to those RVEs with reduced bases parametrized by the boundary conditions. REFERENCES [1] P. Kerfriden, O. Goury, T. Rabczuk, S. Bordas, A partitioned model order reduction approach to rationalise computational expenses in nonlinear fracture mechanics, Computer Methods in Applied Mechanics and Engineering, 256:169–188, 2013. [less ▲] Detailed reference viewed: 304 (5 UL)The Node-Based Smoothed Finite Element Method in nonlinear elasticity ; ; Bordas, Stéphane Report (2013) Detailed reference viewed: 188 (12 UL)An adaptive multiscale strategy to simulate fracture of composite structures ; ; Bordas, Stéphane Scientific Conference (2013, June 05) Detailed reference viewed: 400 (11 UL)Relaxing the compatibility condition in (extended) finite element methods: applications to fracture and nano-mechanics Bordas, Stéphane ; ; et al in Actes du CSMA, Giens, 2013 (2013, June 01) Recently, novel nite element methods were proposed from the coupling of stabilized conforming nodal integration with the standard nite element method [1]. An overarching theory has been devel- oped in the ... [more ▼] Recently, novel nite element methods were proposed from the coupling of stabilized conforming nodal integration with the standard nite element method [1]. An overarching theory has been devel- oped in the recent paper [2]. The main premise of this theory is the wish to achieve reliable results using lower order elements, i.e. simple meshes (triangles, tetrahedra). SFEM retains the accuracy and inherit the advantages of triangular and tetrahedral meshes to represent complex geometries and can bene t directly from any advance in automatic remeshing. Furthermore, smoothed FEMs are a lot less sensitive to locking (volumetric and shear) as well as mesh distortion (because Jacobians are not required since no isoparametric mapping is used. In this sense, SFEMs are a way to improve the quality of the results obtained by simplex elements, thereby signi cantly reducing the need for human-intervention in the generation of hexahedral meshes. http://csma2013.csma.fr/resumes/r_6ATKU0V3.pdf [less ▲] Detailed reference viewed: 262 (3 UL)Optimization of elastic properties and weaving patterns of woven composites ; ; Bordas, Stéphane 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 ▲] Detailed reference viewed: 386 (7 UL)NURBS-based finite element analysis of functionally graded plates: Static bending, vibration, buckling and flutter ; ; 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 ▲] Detailed reference viewed: 515 (8 UL) |
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