Elastic Constitutive Laws and Stability Analyses

Abstract

In this paper, the influence of several elastic constitutive laws upon the stability analyses of plane trusses is discussed. The chosen laws are connected to the engineering strain, Green’s strain and logarithmic strain concepts. A geometrically exact nonlinear formulation for a truss bar element is developed for each of them and the correspondent tangent stiffness matrices are obtained. The stability analyses of some sample plane trusses are performed by finding the conditions when the determinant of their respective global tangent stiffness matrices is found to be zero. The first example is a symmetric two-bar structure and both limit loads and buckling loads are plotted for the full range of possible initial inclination angles of the bars for the three chosen constitutive laws. A similar truss with an extra vertical bar is studied to discuss possible material instability if Green’s strain concept is adopted.