对带有微结构的弹性固体理论的再研究

基金项目: 国家自然科学基金资助项目(10072024);国家自然科学基金委员会(1001130235);德意志研究联合会(51520001)资助的国际合作项目;辽宁省教育委员会A类科研项目(990111001)

Restudy of Theories for Elastic Solids With Microstructure

Department of Mathematics and Center for the Application of Mathematics, Liaoning University, Shenyang 110036, P.R.China

摘要: 对现有的带有微结构的弹性固体理论进行了再研究,并指出由于引进许多记号而使诸基本方程的推导过程复杂化的原因。针对该理论中存在的问题,提出更为普遍的功率能率原理,并借助此原理和广义Piola定理即可自然地推导出局部和非局部理论的运动方程、能率和能量的均衡方程、本构方程和边界条件。这些基本方程和边界条件连同初始条件一起即可用来解决带有微结构的弹性固体动力学理论的混合问题。
- 弹性固体 /
- 微结构 /
- 功率能率原理 /
- 混合问题
Abstract: The dynamical theories of elastic solids with microstructure are restudied and the reason why so many notations have been introduced for derivation of basic equations for such theories is given.In view of the existing problems in those theories the rather general principle of power and energy rate is postulated and the equations of motion,the balance equations of energy rate and energy and the boundary conditions for local and nonlocal theories are naturally derived with help of that principle and the generalized Piola.s theorem.These basic equations and the boundary conditions together with the initial conditions may be used to solve the mixed problems of the dynamical theory of elastic solids with microstructure.
- elastic solid /
- microstructure /
- principle of power and energy rate /
- mixed problem

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