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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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TL;DR: In this paper, an alternative formulation based on the enhanced assumed strain (EAS) method of Simo and Rifai is proposed directed towards the transverse shear terms of the strain field.
Abstract: The degenerated approach for shell elements of Ahmad and co-workers is revisited in this paper. To avoid transverse shear locking effects in four-node bilinear elements, an alternative formulation based on the enhanced assumed strain (EAS) method of Simo and Rifai is proposed directed towards the transverse shear terms of the strain field. In the first part of the work the analysis of the null transverse shear strain subspace for the degenerated element and also for the selective reduced integration (SRI) and assumed natural strain (ANS) formulations is carried out. Locking effects are then justified by the inability of the null transverse shear strain subspace, implicitly defined by a given finite element, to properly reproduce the required displacement patterns. Illustrating the proposed approach, a remarkably simple single-element test is described where ANS formulation fails to converge to the correct results, being characterized by the same performance as the degenerated shell element. The adequate enhancement of the null transverse shear strain subspace is provided by the EAS method, enforcing Kirchhoff hypothesis for low thickness values and leading to a framework for the development of shear-locking-free shell elements. Numerical linear elastic tests show improved results obtained with the proposed formulation.
95 citations
01 Jan 2000
TL;DR: In this thesis, an alternative real-time solution without compromising the mass matrix in the FEM system is presented, instead of decoupling the system by diagonalizing the mass and damping matrix, which improves the sparsity of the system.
Abstract: In this thesis, we model and simulate large global deformations of linear viscous materials. Furthermore, we simulate the dynamic behaviors of such deformations using finite element methods (FEM).
Real-time simulation and animation of global deformation of 3D objects, using the finite element method, is difficult due to the following 3 fundamental problems: (1) The linear elastic model is inappropriate for simulating large motions and large deformations (unacceptable distortion will occur); (2) The time step for dynamic integration has to be drastically reduced to simulate collisions, if the traditional penalty methods are applied; (3) The size of the problem (the number of elements in the FEM mesh) is in n magnitude larger than that of a 2D problem.
In this thesis, we counter these 3 difficulties as following: (1) using quadratic strain instead of the popular linear strain to simulate arbitrarily large motions and global deformations of a 3D object; (2) applying an efficient collision constraint to a decoupled system, which makes an integration step for collision as cheap as a regular dynamic integration step; (3) using a graded mesh instead of a uniform mesh, which reduces the asymptotic complexity of a 3D problem to that, of a 2D problem.
In order to preserve some of the subtle material properties such as viscous elasticity, we also present an alternative real-time solution without compromising the mass matrix in the FEM system. Instead of decoupling the system by diagonalizing the mass and damping matrix, we preprocess the system using modified nested dissection, which improves the sparsity of the system.
In this thesis, we also present how we can apply the same FEM model to simulate haptic feedback to a human operation in the virtual environment.
94 citations
TL;DR: In this article, a finite volume based method for modeling of incompressible linear elastic body problems is described, which is based on the solution of the integral form of conservation equations governing momentum balance and the introduction of pressure as an additional variable.
94 citations
TL;DR: A finite-element- in-space, and quadrature-in-time-discretization of a compressible linear quasistatic viscoelasticity problem and a reduction of the problem to standard linear elasticity where similarly optimal a priori error estimates are derived for the DG(r) approximation are considered.
Abstract: We consider a finite-element-in-space, and quadrature-in-time-discretization of a compressible linear quasistatic viscoelasticity problem. The spatial discretization uses a discontinous Galerkin finite element method based on polynomials of degree r--termed DG(r)--and the time discretization uses a trapezoidal-rectangle rule approximation to the Volterra (history) integral. Both semi- and fully-discrete a priori error estimates are derived without recourse to Gronwall's inequality, and therefore the error bounds do not show exponential growth in time. Moreover, the convergence rates are optimal in both h and r providing that the finite element space contains a globally continuous interpolant to the exact solution (e.g. when using the standard ? k polynomial basis on simplicies, or tensor product polynomials, ? k , on quadrilaterals). When this is not the case (e.g. using ? k on quadri-laterals) the convergence rate is suboptimal in r but remains optimal in h. We also consider a reduction of the problem to standard linear elasticity where similarly optimal a priori error estimates are derived for the DG(r) approximation.
94 citations
TL;DR: In this article, the uniqueness of the solutions of a class of initial-boundary value problems in linear, isotropic, homogeneous, nonlocal elasticity was proved based on the positive definiteness of total strain energy.
94 citations