Dynamic Analysis of Elastoplastic Softening Discretized Structures

Abstract

Associative, elastic‐plastic constitutive laws with linear kinematic hardening or softening are attributed to the discrete structures or structural models considered herein for their dynamic analysis in the range of small deformations. Discretizations are carried out in space by finite element consistent modeling and in time by various finite difference, implicit time‐integration schemes. In this context sufficient conditions are established for: (1) Uniqueness (nonbifurcation) of the time‐step solution; (2) a kinematic extremum property of this solution; and (3) convergence on it of modified Newton‐Raphson iterative procedure. The sufficient criteria proposed materialize in correlated upper bounds on a measure of the constitutive softening and on the time‐step amplitude. The stabilizing effects of inertia are expressed in these bounds through the maximum eigenfrequency of the structural model supposed linear elastic. Time‐integration techniques differ significantly in implications of softening: e.g., the average acceleration method permits larger steps for convergence than the backward‐difference method.