ON THE ANALOGY BETWEEN TWO-DIMENSIONAL NON-LINEAR RESTORING FORCE CHARACTERISTICS OF STRUCTURES AND THE THEORY OF PLASTICITY

Abstract

Two model structures are presented. One model structure consists of a rigid plate and two springs. Each spring has the same tri-linear P-δ relation. Relation between two dimensional forces M_x, N_z and two dimensional deformations Φ_x, δ_z is examined. To formulate the restoring force-deformation relation, the concept of plastic potential and Prager's kinematic hardening rule are used. Using the theory of plasticity, two-dimensional non-linear behavior of the model structure can be perfectly described. The other model is a square section. The meterial of the section doesn't transfer tensile stress, and is rigid-perfectly plastic in the compressive strain region. Relation between forces M_x, N_o and deformation φ_x, ε_o is examined. Some part of restoring force-deformation relation of the model structure is far different from the rigid-perfectly plastic theory. Possibilities and difficulties to describe the multi-dimensional non-linear restoring force characteristic of structures by using the theory of plasticity are shown.