Large Displacement Matrix Analysis of Elastic/Viscoplastic, Plane Frame Structures

Abstract

Within the framework of lumped mass/elementary beam theory, a large displacement matrix analysis of elastic/perfectly viscoplastic plane frame structures undergoing primarily flexural deformations and following a constitutive power law is first formulated. A general purpose computer program based on the step-by-step computational procedure in conjunction with the fourth order Runge-Kutta integration technique is then developed. The computerized study is then used in an analytical/experimental correlation study of the dynamic response of a laboratory impact test problem of a mild steel plane frame dropped into a narrow rigid pole obstacle at 20 mph (32.2 km/hr); good analytical and experimental correlation results are obtained up to 2 percent of strain. An example problem of inelastic response of an automobile bumper (beam) subjected to impact loading is also given. Discussion of the results with regard to strain rate sensitivity effects on dynamic plastic behavior and comparison of the “exact” solution with those obtained under certain simplified approximations are made.