Topic
Linear elasticity
About: Linear elasticity is a research topic. Over the lifetime, 9080 publications have been published within this topic receiving 258684 citations.
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01 Oct 1992
TL;DR: In this paper, the authors present guidelines for Element Meshes and Global Nodal Numbering, as well as a selection of approximate functions for the FE-method - Scalar Problems and Weight Function - Weighted Residual Methods.
Abstract: * Introduction. * Matrix Algebra. * Direct Approach. * Strong and Weak Formulations - One-dimensional Heat Flow. * Gradient - Gauss' Divergence Theorem - Green Theorem. * Strong and Weak Forms - Two-and Three-Dimensional Heat Flow. * Choice of Approximating Functions for the FE-method - Scalar Problems. * Choice of Weight Function - Weighted Residual Methods. * FE-formulation of One-Dimensional Heat Flow. * FE-formulation of Two-and-Three Dimensional Heat Flow. * Guidelines for Element Meshes and Global Nodal Numbering. * Stresses and Strains. * Linear Elasticity. * FE-formulation of Torsion and Non-circular Shafts. * Approximating Functions for the FE-method - Vector Problems. * FE-formulation of Three-and-Two Dimensional Elasticity. * FE-formulation of Beams. * FE-formulation of Plates. * Isoparametric Finite Elements. * Numerical Integration.
267 citations
TL;DR: In this article, a linear elastic contact between a rigid plane and a halfspace whose surface height is described by a bandwidth-limited Fourier series is considered, and the surface normal displacements and contact pressures are found by a numerical technique that exploits the structure of the Fast Fourier Transform (FFT) and an exact result in linear elasticity.
Abstract: Elastic contact between a rigid plane and a halfspace whose surface height is described by a bandwidth-limited Fourier series is considered The surface normal displacements and contact pressures are found by a numerical technique that exploits the structure of the Fast Fourier Transform (FFT) and an exact result in linear elasticity The multiscale nature of rough surface contact is implicit to the method, and features such as contact agglomeration and asperity interaction-a source of difficulty for asperity-based models-evolve naturally Both two-dimensional (2-D) and three-dimensional ( 3-D ) contact are handled with equal ease Finally, the implementation is simple, compact, and fast
265 citations
TL;DR: In this paper, a circular fillet patch is introduced through the appropriate degeneration of a control mesh in order to address the problem of modeling small features in finite element models and is tested with two problems of linear elasticity and is shown to be accurate.
264 citations
TL;DR: In this article, an effective numerical implementation of the three-dimensional dual boundary element method, for linear elastic crack problems, is presented, where displacement and traction integral equations are used independently on crack surfaces to overcome the numerical difficulties associated with co-planar crack surfaces in boundary element analysis.
Abstract: In this paper, an effective numerical implementation of the three-dimensional dual boundary element method, for linear elastic crack problems, is presented. Displacement and traction integral equations which constitute the dual boundary formulation are used independently on crack surfaces to overcome the numerical difficulties associated with co-planar crack surfaces in boundary element analysis. The crack surfaces are modelled with discontinous quadrilateral quadratic elements. The use of discontinous elements allow for accurate integration of finite part integrals. The accuracy of the proposed method is demonstrated by solving a number of problems including edge and embedded cracks.
263 citations
TL;DR: This work calculates the local elastic moduli in a weakly polydispersed two-dimensional Lennard-Jones glass undergoing a quasistatic shear deformation at zero temperature and shows that zones of low shear modulus concentrate most of the strain in the form of plastic rearrangements.
Abstract: In this work we calculate the local elastic moduli in a weakly polydispersed two-dimensional Lennard-Jones glass undergoing a quasistatic shear deformation at zero temperature. The numerical method uses coarse-grained microscopic expressions for the strain, displacement, and stress fields. This method allows us to calculate the local elasticity tensor and to quantify the deviation from linear elasticity (local Hooke's law) at different coarse-graining scales. From the results a clear picture emerges of an amorphous material with strongly spatially heterogeneous elastic moduli that simultaneously satisfies Hooke's law at scales larger than a characteristic length scale of the order of five interatomic distances. At this scale, the glass appears as a composite material composed of a rigid scaffolding and of soft zones. Only recently calculated in nonhomogeneous materials, the local elastic structure plays a crucial role in the elastoplastic response of the amorphous material. For a small macroscopic shear strain, the structures associated with the nonaffine displacement field appear directly related to the spatial structure of the elastic moduli. Moreover, for a larger macroscopic shear strain we show that zones of low shear modulus concentrate most of the strain in the form of plastic rearrangements. The spatiotemporal evolution of this local elasticity map and its connection with long term dynamical heterogeneity as well as with the plasticity in the material is quantified. The possibility to use this local parameter as a predictor of subsequent local plastic activity is also discussed.
262 citations