Home » Engineering » Mechanical & Industrial Engineering

Assess the performance of the finite element method in analyzing the bifurcations of compressible materials. The specific objective is to understand the significance of the eigenvectors of the tangential stiffness matrix by comparing them with the analytical bifurcation modes which were obtained independently in the case of the plane strain compression of compressible hypoelastic materials. Although tested for a particular example, the finite element method can be applied to analyze the instability of more complicated boundary value problems encountered in the fields of Solids Mechanics, Structural Geology, and Geomechanics.

The concepts of continuum mechanics, which are relevant to bifurcation problems, and summarizes the finite element method previously applied to surface instability (Bardet,1989). The second section analyzes the performance of the finite element method by comparing numerical and analytical results.

The constitutive equation formulated in term of nominal stress rate (Eq.5) is symmetric provided that the constitutive relation expressed in terms of Jaumann rate of Kirchhoff stress (Eq. 1) is symmetric. This last remark justifies the selection of Jaumann rate of Kirchhoff stress instead of other types of objectives stress rates. McMeeking and Rice, 1978, have shown that the major symmetry of Eq.5 leads to symmetric stiffness matrices for the large deformation formulation of finite element problems. From a computational point of view, symmetric matrices are stored and inverted more efficiently than nonsymmetric matrices. Moreover, the choice of the Jaumann rate of Kirchhoff stress does not affect the generality of the present analysis (Bardet,1989).

Since the present analysis is focused on the instability of incremental problems, the constitutive matrix Cijkl can be assumed to have constant coefficients without losing too much generality. Rate-type materials with constant constitutive moduli are referred to hereafter as hypoelastic.

Source: gees.usc.edu

Related PDF Files

Mechanical Engineering Overview

The Field - Preparation - Day in the Life - Earnings - Employment - Development - Career P

Rigid Mechanics And Its Role In Nonlinear Structural Analysis

In the nonlinear analysis of elastic structures, the displacement increments generated at

Simultaneous Design for Manufacturing Process Selection of Engineering Plastics

This paper describes a methodology that helps designers select a manufacturing process for

Piping Design: An Introduction For Non Piping Engineers

This paper attempts to explain some of the salient piping activities (along with their seq

WHATIS A MECHANICAL ENGINEER?

What is a Mechanical Engineer? Mechanical engineering plays a dominant role in enhancing s

Incoming Search: