Linear elasticity

About: Linear elasticity is a research topic. Over the lifetime, 9080 publications have been published within this topic receiving 258684 citations.

Earthquake-Induced Soil Pressures on Structures

Abstract: The earthquake-induced pressures on soil-retaining structures are investigated. The study was motivated by the lack of suitable earthquake design data for relatively rigid structures on firm foundations in situations where the foundation, structure and retained soil remain essentially elastic. Pressures and forces on the walls of a number of idealized wall-soil problems are analyzed. The solutions obtained are evaluated for a range of the important parameters to give results useful for design. In the idealized problems the soil is represented by an elastic layer of finite length bonded to a rigid foundation or rock layer. The wall or structure is represented by a rigid element resting on the rock layer and is permitted to undergo rotational deformation about the base. The mass or moment of inertia of the structure and its rotational stiffness are included as parameters in the idealization. Static and dynamic solutions are obtained using both analytical and finite element methods. Solutions are evaluated for the assumption of perfectly rigid behavior of the wall. The general solution for the deformable wall case was developed by superposition of the solution for the perfectly rigid case and solutions derived for displacement forcing of the wall structure. The assumption of linear elastic behavior of the wall- soil system is likely to be approximately satisfied in situations where a building or other large civil engineering structure is founded on firm soil or rock strata. In contrast to the linearly elastic assumption made in this study, the commonly used Mononobe-Okabe method employs the assumption of sufficiently large wall deformations to induce a fully plastic stress condition in the soil. It was concluded that both the elastic theory and the Mononobe-Okabe method have valid applications in the design of wall structures subjected to earthquake motions, but that because of significant differences in the solutions obtained from each method, care is required in selecting the most appropriate method for a particular situation.

A fast solution method for three‐dimensional many‐particle problems of linear elasticity

Abstract: A boundary element method for solving three-dimensional linear elasticity problems that involve a large number of particles embedded in a binder is introduced. The proposed method relies on an iterative solution strategy in which matrix—vector multiplication is performed with the fast multipole method. As a result the method is capable of solving problems with N unknowns using only O(N) memory and O(N) operations. Results are given for problems with hundreds of particles in which N"O(105). ( 1998 John Wiley & Sons, Ltd.

An analysis of thep-version of the finite element method for nearly incompressible materials

Abstract: In this paper we analyze the behavior of the so-calledp-version of the finite element method when applied to the equations of plane strain linear elasticity. We establish optimal rate error estimates that are uniformly valid, independent of the value of the Poisson ratio,v, in the interval ]0, 1/2[. This shows that thep-versiondoes not exhibit the degeneracy phenomenon which has led to the use of various, only partially justified techniques of reduced integration or mixed formulations for more standard finite element schemes and the case of a nearly incompressible material.

Discontinuous Galerkin and the Crouzeix–Raviart element : application to elasticity

Abstract: We propose a discontinuous Galerkin method for linear elasticity, based on discontinuous piecewise linear approximation of the displacements. We show optimal order a priori error estimates, uniform in the incompressible limit, and thus locking is avoided. The discontinuous Galerkin method is closely related to the non-conforming Crouzeix-Raviart (CR) element, which in fact is obtained when one of the stabilizing parameters tends to infinity. In the case of the elasticity operator, for which the CR element is not stable in that it does not fulfill a discrete Korn's inequality, the discontinuous framework naturally suggests the appearance of (weakly consistent) stabilization terms. Thus, a stabilized version of the CR element, which does not lock, can be used for both compressible and (nearly) incompressible elasticity. Numerical results supporting these assertions are included. The analysis directly extends to higher order elements and three spatial dimensions.