The Experts below are selected from a list of 93 Experts worldwide ranked by ideXlab platform
Gerhard Starke - One of the best experts on this subject based on the ideXlab platform.
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a posteriori error estimation for planar linear elasticity by stress reconstruction
arXiv: Numerical Analysis, 2017Co-Authors: Fleurianne Bertrand, Marcel Moldenhauer, Gerhard StarkeAbstract:The nonconforming triangular piecewise quadratic finite element space by Fortin and Soulie can be used for the Displacement Approximation and its combination with discontinuous piecewise linear pressure elements is known to constitute a stable combination for incompressible linear elasticity computations. In this contribution, we extend the stress reconstruction procedure and resulting guaranteed a posteriori error estimator developed by Ainsworth, Allendes, Barrenechea and Rankin \cite{AinAllBarRan:12} and by Kim \cite{Kim:12a} to linear elasticity. In order to get a guaranteed reliability bound with respect to the energy norm involving only known constants, two modifications are carried out: (i) the stress reconstruction in next-to-lowest order Raviart-Thomas spaces is modified in such way that its anti-symmetric part vanishes in average on each element; (ii) the auxiliary conforming Approximation is constructed under the constraint that its divergence coincides with the one for the nonconforming Approximation. An important aspect of our construction is that all results hold uniformly in the incompressible limit. Local efficiency is also shown and the effectiveness is illustrated by adaptive computations involving different Lame parameters including the incompressible limit case.
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first order system least squares for the signorini contact problem in linear elasticity
SIAM Journal on Numerical Analysis, 2009Co-Authors: Frank S Attia, Zhiqiang Cai, Gerhard StarkeAbstract:A first-order system least squares formulation for the Signorini problem modeling frictionless contact in linear elasticity is studied. In addition to the Displacement field, the stress tensor is used as an independent process variable. A contact boundary term is added to the usual least squares functional in order to achieve coercivity and continuity in appropriate norms. The discrete functional is shown to constitute an a posteriori error estimator on which an adaptive refinement strategy may be based. As finite element spaces, standard conforming piecewise polynomials for the Displacement Approximation are combined with Raviart-Thomas elements for the rows in the stress tensor. Computational results for a test problem of Hertzian contact illustrate the effectiveness of our least squares approach.
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an adaptive least squares mixed finite element method for the stress Displacement formulation of linear elasticity
Numerical Methods for Partial Differential Equations, 2005Co-Authors: Johannes Korsawe, Gerhard StarkeAbstract:A least-squares mixed finite element method for linear elasticity, based on a stress-Displacement formulation, is investigated in terms of computational efficiency. For the stress Approximation quadratic Raviart-Thomas elements are used and these are coupled with the quadratic nonconforming finite element spaces of Fortin and Soulie for approximating the Displacement. The local evaluation of the least-squares functional serves as an a posteriori error estimator to be used in an adaptive refinement algorithm. We present computational results for a benchmark test problem of planar elasticity including nearly incompressible material parameters in order to verify the effectiveness of our adaptive strategy. For comparison, conforming quadratic finite elements are also used for the Displacement Approximation showing convergence orders similar to the nonconforming case, which are, however, not independent of the Lame parameters. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005
Volker Ulbricht - One of the best experts on this subject based on the ideXlab platform.
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xfem modeling of interface failure in adhesively bonded fiber reinforced polymers
Advanced Engineering Materials, 2016Co-Authors: Markus Kastner, Irene Jansen, Franz Hirsch, Sebastian Müller, Volker UlbrichtAbstract:This paper addresses the multi-scale simulation of heterogeneous materials with a special emphasis on the modeling of internal discontinuities. In a homogenization context the local material structure is discretized by the extended finite element method which uses an enriched Displacement Approximation in combination with a cohesive zone model. This approach is applied to predict the effective material behavior of a fiber reinforced polymer and is then used to investigate the interaction of the fiber-matrix interface with an adhesive layer. All simulations are validated by corresponding experimental data.
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development of a quadratic finite element formulation based on the xfem and nurbs
International Journal for Numerical Methods in Engineering, 2011Co-Authors: Georg Haasemann, Markus Kastner, Stefan Pruger, Volker UlbrichtAbstract:The FE-simulation of inhomogeneous structures, such as composite materials, biological tissues or foams, requires the generation of respective finite element meshes. With increasing complexity of the inner architecture of such structures, this becomes a time-consuming and laborious task. Additionally, the risk of forming bad-shaped elements that may lead to ill-conditioned numerical problems grows significantly. A solution to this problem provides the extended finite element method (XFEM). Thereby, the interface between different materials is represented by a local enrichment of the Displacement Approximation. As a consequence of this, the element boundary need not be aligned to the interface. In order to improve the accuracy of the interface Approximation, the development of a plane element based on the XFEM and quadratic shape functions will be presented. This element allows for the description of curved material interfaces. The computation of the element stiffness matrix requires a numerical integration process that accounts for discontinuous fields. Regarding a linear element formulation, this can be achieved by an adapted triangulation of the element domain. However, in the case of a curved interface this solution is not applicable. Hence, non-uniform rational B-Spline (NURBS) surfaces are used to evaluate the integrals numerically. Finally, the results of different examples will show the general properties such as the accuracy of the numerical integration procedure and the convergence behavior of this element formulation. Copyright © 2011 John Wiley & Sons, Ltd.
Karan S. Surana - One of the best experts on this subject based on the ideXlab platform.
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A p-version curved shell element based on piecewise hierarchical Displacement Approximation for laminated composite plates and shells
Computers & Structures, 1995Co-Authors: Karan S. SuranaAbstract:This paper presents a piecewise hierarchical p-version three-dimensional nine-node curved shell element formulation with interlamina continuity of Displacements for laminated composite plates and shells. The Displacement field Approximation for each lamina can be of arbitrary polynomial order in the plane of the lamina as well as in the transverse direction, and is based on p-version. The p-version hierarchical Approximation functions and the corresponding nodal variable operators for each lamina are derived directly from the Lagrange family of interpolation functions by first constructing the one-dimensional p-version hierarchical Approximation functions and the corresponding nodal variable operators for three- and one-node equivalent configurations in the ξ, η and ζ directions and then taking their products. The lamina stiffness matrix and the equivalent load vectors are derived using the principle of virtual work and the p-version lamina Displacement Approximation. The interlamina continuity conditions of Displacements are imposed at the lamina interfaces. The interlamina continuity conditions are conveniently arranged in the form of transformation matrices, which allow the transformation of the lamina degrees of freedom to the laminate degrees of freedom. These transformation matrices are used to transform the lamina stiffness matrices and equivalent load vectors to the laminate stiffness matrix and equivalent load vector. The transformed lamina stiffness matrices and load vectors are summed to obtain the laminate stiffness matrix and equivalent load vectors. The interlamina continuity conditions of Displacements permit condensation of [3(pξ + 1)(p)η + 1)] degrees of freedom (where ζ is the direction of lamina lay up) for all laminae except the first. Numerical examples are presented to demonstrate the accuracy, efficiency and convergence characteristics of the present formulation.
E V Iarve - One of the best experts on this subject based on the ideXlab platform.
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three dimensional stress analysis of textile composites part ii asymptotic analysis
International Journal of Solids and Structures, 2004Co-Authors: Sangwook Sihn, E V IarveAbstract:Abstract An asymptotic singular stress analysis was performed in the unit-cell of the plain–woven composite in the vicinity of the yarn–yarn–matrix interface intersection with and without the inter-yarn delamination. The problem was reduced to a three-material wedge singularity type by introducing several curvilinear coordinate systems and systematic expansions in power series of the distance from the contour of the stress singularity. The power of stress singularity at the inter-yarn and yarn–matrix interface junction was investigated as a function of crimp angle and matrix-to-yarn stiffness ratio. In the case of perfect bonding between the yarns and the matrix with small crimp angles near 9°, the power of singularity is weak (∼0.02) and insensitive to the stiffness ratio of the axial yarn to the matrix material. For increased crimp angles, however, small variations in the stiffness of the matrix material can significantly affect the power of singularity. In the case of the inter-yarn delamination, two singular roots––one crack type (∼0.5) and one weak (∼0.01)––were obtained for all crimp angles and delamination opening modes. Coefficients of the asymptotic expansion were obtained by comparing the full-field three-dimensional numerical solution based on B-spline Displacement Approximation method with multi-term asymptotic expansions in the vicinity of the singular point. Good agreement between the two solutions was observed in all examples considered.
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mesh independent modelling of cracks by using higher order shape functions
International Journal for Numerical Methods in Engineering, 2003Co-Authors: E V IarveAbstract:A mesh independent crack modelling approach based on Displacement Approximation with higher order shape functions is proposed. The Heaviside step function based local enrichment method, known as eXtended Finite Element Method, is modified by replacing the step function with a higher order shape functions Approximation. Polynomial B-spline Approximation functions are used in the present paper. An advantage of the proposed method is that its implementation only involves integration of the products of original shape functions and their derivatives and does not require modification of the integration domains. A volume integral based expression is proposed to calculate the effective surface area of the crack modelled by using an approximate step function. It is shown to give the actual crack surface area in the limit of the approximate step function approaching the Heaviside function. The convergence and accuracy of the method is illustrated in examples of transverse and oblique (with respect to loading direction) crack problems in rectangular plates. Uniaxial tension of a unidirectional composite with an open hole is considered. Hoop stress relaxation due to longitudinal splitting is successfully modelled by the method proposed and compared to direct modelling by using ANSYS software. Published in 2002 by John Wiley & Sons, Ltd.
C Y Dong - One of the best experts on this subject based on the ideXlab platform.
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adaptive extended isogeometric analysis based on pht splines for thin cracked plates and shells with kirchhoff love theory
Applied Mathematical Modelling, 2019Co-Authors: H S Yang, C Y DongAbstract:Abstract In this paper, a posteriori error estimation and mesh adaptation approach for thin plate and shell structures of through-the-thickness crack is presented. This method uses the extended isogeometric analysis (XIGA) based on PHT-splines (Polynomial splines over Hierarchical T-meshes), which is abbreviated as XIGA-PHT. In XIGA-PHT, the isogeometric Displacement Approximation is locally enriched with enrichment functions, which efficiently capture the Displacement discontinuity across the crack face as well as the stress singularity in the vicinity of the crack tip. On the one hand, the rotational degrees of freedom (RDOFs) are not required in Kirchhoff-Love theory, which drastically reduces the complexity of enrichment mode and computational scale for crack analysis. On the other hand, the PHT-splines basis functions can automatically satisfy the requirement of C 1 -continuity for the Kirchhoff-Love theory. Moreover, the PHT-splines facilitate the local refinement, which is the deficiency of NURBS-based isogeometric formulations. The local refinement is highly suitable for adaptive analysis. The stress recovery-based posteriori error estimator combined with the superconvergent patch recovery (SPR) technique is used to evaluate the approximate local discretization error. A new strategy for selecting enriched recovered functions in the enriched areas was proposed. Special functions extracted from the asymptotic stress solutions are applied to obtain the recovered stress field in the enriched area. The results of stress intensity factors or J-integral values obtained by the adaptive XIGA-PHT are compared with reference solutions. Several thin plate and shell illustrative examples demonstrate the effectiveness and accuracy of the proposed adaptive XIGA-PHT.