Linear elasticity

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

Shear stiffness of a solid–solid multicontact interface

Abstract: The macroscopic multicontact between two rough nominally flat surfaces is a common object whose physics is only partially understood. This paper is aimed at giving experimental evidence for the linear elastic response of a multicontact interface to a moderate shear force, i.e. below the threshold for incipient sliding. Non–intuitive properties of the interfacial shear stiffness are exhibited, in the spirit of macroscopic friction laws, which should be of practical interest when evaluating the performances of a built–up system. These are explained qualitively within the random surface framework prevailing in multicontact mechanics, and a numerical treatement of the three–dimensional profile of a real rough surface is proposed, which enables a direct quantitative simulation of the elastic stiffness. This is found to be compatible with experimental data on a polymer glass and an aluminium alloy. The sensitivity of interfacial stiffness measurements is discussed, and illustrated by the experimental evidence of the plastic deformation of aluminium alloy asperities under light nominal pressure. This emphasizes the need for an elastoplastic description of asperity deformation within a multicontact.

Towards an acoustoelastic theory for measurement of residual stress

Abstract: The rudiments of an acoustoelastic theory is developed within the framework of linear elasticity with initial stress. Since no assumption is made about the origin of the initial stress, our acoustoelastic theory will be applicable to evaluation of stress in plastically deformed bodies, provided that the superimposed ultrasonic waves be hyperelastic. New universal relations are deduced. An approach to evaluation of stress which does not use calibration specimens and makes full use of universal relations in our acoustoelastic theory is advocated. Examples are given which illustrate application of our theory to evaluate residual stress in plates. Preliminary corroborations of our theory are provided by the recent experiments of King & Fortunko and Thompson et al.

Behavior of Corrugated Web I-Girders under In-Plane Loads

Abstract: A theoretical formulation of the linear elastic in-plane and torsional behavior of corrugated web I-girders under in-plane loads is presented. A typical corrugated web steel I-girder consists of two steel flanges welded to a corrugated steel web. Under a set of simplifying assumptions, the equilibrium of an infinitesimal length of a corrugated web I-girder is studied, and the cross-sectional stresses and stress resultants due to primary bending moment and shear are deduced. The analysis shows that a corrugated web I-girder will twist out-of-plane simultaneously as it deflects in-plane under the action of in-plane loads. In the paper, the in-plane bending behavior is analyzed using conventional beam theory, whereas the out-of-plane torsional behavior is analyzed as a flange transverse bending problem. The results for a simply supported span subjected to a uniformly distributed load are presented. Finally, finite element analysis results are presented and compared to the theoretical results for validation.

A hybridizable discontinuous Galerkin method for linear elasticity

Abstract: This paper describes the application of the so-called hybridizable discontinuous Galerkin (HDG) method to linear elasticity problems. The method has three significant features. The first is that the only globally coupled degrees of freedom are those of an approximation of the displacement defined solely on the faces of the elements. The corresponding stiffness matrix is symmetric, positive definite, and possesses a block-wise sparse structure that allows for a very efficient implementation of the method. The second feature is that, when polynomials of degree k are used to approximate the displacement and the stress, both variables converge with the optimal order of k+1 for any k⩾0. The third feature is that, by using an element-by-element post-processing, a new approximate displacement can be obtained that converges at the order of k+2, whenever k⩾2. Numerical experiments are provided to compare the performance of the HDG method with that of the continuous Galerkin (CG) method for problems with smooth solutions, and to assess its performance in situations where the CG method is not adequate, that is, when the material is nearly incompressible and when there is a crack. Copyright © 2009 John Wiley & Sons, Ltd.