摘要:
本文对即将形成的一门新的学科——离散型固体力学的基本假设,微分形式的方程,及其间断型变分原理进行了论述.离散型固体力学是离散介质力学的一个分支,是近期以来力学的一个发展方向.它是基于固体体系具有离散性、可分性,待解函数在定义城内具有各种不同的间断性,以及定义域的边界可动性的基础上,为解决种种情况下的固体的应力,位移、应变所形成的力学系统.当待解函数在整个定义域内为充分光滑的函数类和略去边界可动性的影响时,则离散型固体力学就退化为连续介质力学范畴的古典固体力学.它所属的变分原理,在相应的情况下,也就退化为古典与非占典变分原理.
Abstract:
This paper discusses the fundamental assumptions, the differential equations, and the variational principles of discontinuous form belonging to a new developing branch of science-the solid mechanics of discrete form.The solid mechanics of discrete form belongs to the branch of science of discrete medium mechanics which is the developing direction of the mechanics for the present. Based on the solid system with discretization and separability, the unknown functions with discontinuity in defined regions and the defined regions with variable boundaries, the mechanics systems to solve the solid displacements,strains and stresses in various cases are called the solid mechanics of discrete form.When the unknown functions are sufficiently smooth functions in the whole defined region and the effects of the variable boundaries are disregarded,the solid mechanics of discrete form will degenerate into the classical solid mechanics belonging to continuum.mechanics: Its variational principles will degenerate into the classical variational principles with the same cases.
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