最小功耗原理的有限元法  

Finite Element Method of Least Work Consumption Principle

作　　者：唐松花[1] 罗迎社[1] 周筑宝[2] 王智超[1] 

机构地区：[1]湘潭大学基础力学与材料工程研究所,湖南湘潭411105 [2]中南大学土木建筑学院,湖南长沙410075

出　　处：《湘潭大学自然科学学报》2006年第3期40-44,共5页Natural Science Journal of Xiangtan University

基　　金：湖南省自科基金重点资助项目(03JJY3007);湖南省优秀博士论文专项奖励配套资助项目(湘大研发[2004]6号)

摘　　要：固体力学的有限元法几乎都以变分原理为基础,但这些变分原理常常对材料的应力、应变关系有所限制.最小功耗原理的变分原理未对材料的应力、应变关系附加任何限制.以此为理论基础,提出了一种新的有限元方法,给出了计算公式.算例结果正确,表明该方法是有效的.最小功耗原理的有限元法可求解不同应力、应变关系的结构分析问题,求解范围扩大,从而将弹性、塑性及流变理论问题统一起来.Finite clement method（ FEM） in solid mechanics are almost based on variational principles, yet which often restrict the stress.strain relation of materials. The variational pritwiple of least work consumption principle attaches no restrictions to the stress.strain relations.This paper puts forward a new finite element method based on that variational principle, anti gives the calculation formula.The results of calculating example are correct, which indicate the method is effeclive. FEM of least work consumption principle can solvc structure analysis problem with different the stress.strain relations. The solving range is brosden, and then this mcthod unifies elastic.plastic and rheological problems.

关 键 词：最小功耗原理 变分原理 有限元法 LAGRANGE乘子 

分 类 号：O302[理学—力学]