孔隙热弹性体有限变形动力学的若干变分原理  

SEVERAL VARIATIONAL PRINCIPLES FOR FINITE DEFORMATION DYNAMICS OF THERMOELASTIC VOIDS BODIES

作　　者：李莹[1] 程昌钧[1] 

机构地区：[1]上海市应用数学和力学研究所,上海大学力学系,上海200072

出　　处：《固体力学学报》2010年第1期74-79,共6页Chinese Journal of Solid Mechanics

基　　金：上海市重点学科建设项目(S30106);上海大学研究生创新基金项目资助

摘　　要：首先通过对熵均衡方程积分,将其变换为无一阶时间导数项的等价方程,再将Hamilton变分原理运用和推广于各向异性孔隙热弹性体有限变形动力学中,建立了相应的非线性控制微分方程、力的边界条件和初始条件.同时,引入孔隙百分比变化和温度变化引起的力矩,将Hamilton变分原理推广到孔隙热弹性结构中,提出了以Kirchhoff-Love假设为基础的孔隙热弹性Karman-型薄板的完全的非线性数学模型,该模型考虑了中面力、中面惯性和转动惯性影响.In this paper, the equation for entropy balance is firstly converted to an equivalent form without the first-order time-derivative by integral. The Hamilton variational principle is extended to the fi- nite deformation dynamics of anisotropic thermoelastic voids bodies to present the all nonlinear governing differential equations, force boundary conditions and initial conditions. The Hamilton variational principle is also extended to the thermoelastic voids structures after introducing the moments caused by the change of porosity and temperature, a complete nonlinear model of theomoelastic Karman-type voids plates, based on the Kirchhoff-Love assumption, is presented, in which, the influences of middle plane force, middle plane inertia and rotation inertia have been included.

关 键 词：Hamilton变分原理 各向异性孔隙热弹性体 有限变形 孔隙热弹性结构 Karman-型薄板 

分 类 号：O343.6[理学—固体力学]