NONLINEAR WAVE EQUATIONS ARISING IN MODELLING OF SOME STRAIN-HARDENING STRUCTURES

摘要

A class of nonlinear wave equations of p-Laplacian type are presented based on a generalized Hooke's law derived in the framework of small plastic deformation theory of Hencky. These equations can be used for modelling vibration of rods, beams, and plates made of heat treated metals that have strain-hardening properties, in particular, for vibration of stainless steel fibre of the hybrid stainless steel assembly used in transportation industry for lighter and more crashworthy vehicles. These metals are special cases of a class of nonlinear elastic-plastic materials, also referred to as Ludwick materials. Some finite element and finite difference schemes are proposed to fully discretize the wave equations and obtain numerical solutions,and a graphic numerical example is given.