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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: 693 (13 UL)Gradient Smoothing for Nearly Incompressible Hyperealsticity ; ; et al Poster (2014) Detailed reference viewed: 119 (7 UL)Isogeometric analysis of laminated composite and sandwich plates using a new inverse trigonometric shear deformation theory ; Bordas, Stéphane ; et al in European Journal of Mechanics. A, Solids (2014), 43 This paper presents a new inverse tangent shear deformation theory (ITSDT) for the static, free vibration and buckling analysis of laminated composite and sandwich plates. In the present theory, shear ... [more ▼] This paper presents a new inverse tangent shear deformation theory (ITSDT) for the static, free vibration and buckling analysis of laminated composite and sandwich plates. In the present theory, shear stresses are vanished at the top and bottom surfaces of the plates and shear correction factors are no longer required. A weak form of the static, free vibration and buckling models for laminated composite and sandwich plates based on ITSDT is then derived and is numerically solved using an isogeometric analysis (IGA). The proposed formulation requires C1-continuity generalized displacements and hence basis functions used in IGA fulfill this requirement. Numerical examples are provided to show high efficiency of the present method compared with other published solutions. © 2013 Elsevier Ltd. All rights reserved. [less ▲] Detailed reference viewed: 363 (5 UL)Analysis of composite plates through cell-based smoothed finite element and 4-noded mixed interpolation of tensorial components techniques ; ; Ferreira, Ana et al in Computers and Structures (2014), 135 The static bending and the free vibration analysis of composite plates are performed with Carrera's Unified Formulation (CUF). We combine the cell-based smoothed finite element method (CSFEM) and the 4 ... [more ▼] The static bending and the free vibration analysis of composite plates are performed with Carrera's Unified Formulation (CUF). We combine the cell-based smoothed finite element method (CSFEM) and the 4-noded mixed interpolation of tensorial components approach (MITC4). The smoothing method is used for the approximation of the bending strains, whilst the mixed interpolation allows the calculation of the shear transverse stress in a different manner. With a few numerical examples, the accuracy and the efficiency of the approach is demonstrated. The insensitiveness to shear locking is also demonstrated. © 2014 Elsevier Ltd. All rights reserved. [less ▲] Detailed reference viewed: 665 (36 UL)Gradient Smoothing for Nearly Incompressible Hyperelasticity ; ; et al Poster (2014) Detailed reference viewed: 105 (4 UL)Strain smoothing technique in 3D for nearly incompressible neo-Hookean material ; ; et al Report (2014) Detailed reference viewed: 226 (12 UL)Analysis using higher-order XFEM: implicit representation of geometrical features from a given parametric representation ; Bordas, Stéphane ; et al in Mechanics and Industry (2014), 15(05), 443-448 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: 283 (6 UL)Explicit finite deformation analysis of isogeometric membranes ; ; et al in Computer Methods in Applied Mechanics and 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 ▲] Detailed reference viewed: 613 (7 UL)An efficient goal-oriented sampling strategy using reduced basis method for parametrized elastodynamic problems ; ; Bordas, Stéphane et al in Numerical Methods for Partial Differential Equations (2014) In this paper, we study the class of linear elastodynamic problems with a ne parameter dependence using a goal-oriented approach by finite element (FE) and reduced basis (RB) methods. The main ... [more ▼] In this paper, we study the class of linear elastodynamic problems with a ne parameter dependence using a goal-oriented approach by finite element (FE) and reduced basis (RB) methods. The main contribution of this paper is the "goal-oriented" proper orthogonal decomposition (POD)-Greedy sampling strategy within the RB approximation context. The proposed sampling strategy looks for the parameter points such that the output error approximation will be minimized by Greedy iterations. In estimating such output error approximation, the standard POD-Greedy algorithm is invoked to provide enriched RB approximations for the FE outputs. We propose a so-called "cross-validation" process to choose adaptively the dimension of the enriched RB space corresponding with the dimension of the RB space under consideration. Numerical results show that the new goal-oriented POD-Greedy sampling procedure with the cross-validation process improves signi ficantly the space-time output computations in comparison with the ones computed by the standard POD-Greedy algorithm. The method is thus ideally suited for repeated, rapid and reliable evaluations of input-output relationships in the space-time setting. [less ▲] Detailed reference viewed: 304 (3 UL)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: 136 (4 UL)Model order reduction for speeding up computational homogenisation methods of type FE2 ; ; Bordas, Stéphane Presentation (2014) Detailed reference viewed: 124 (2 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: 274 (1 UL)An integrated design-analysis framework for three dimensional composite panels ; ; Bordas, Stéphane 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 ▲] Detailed reference viewed: 313 (6 UL)Boundary Element Method with NURBS-geometry and independent field approximations in plane elasticity ; ; et al Scientific Conference (2014) Detailed reference viewed: 348 (2 UL)Global energy minimization for multiple fracture growth ; Bordas, Stéphane Report (2013) Detailed reference viewed: 233 (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: 322 (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: 231 (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: 394 (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: 376 (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: 1065 (11 UL) |
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