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板弯曲与平面弹性问题的多类变量变分原理
引用本文:钟万勰,姚伟岸.板弯曲与平面弹性问题的多类变量变分原理[J].力学学报,1999,31(6):717-723.
作者姓名:钟万勰  姚伟岸
作者单位:大连理工大学工程力学系
基金项目:国家自然科学基金,国家教委博士点基金
摘    要:进一步完善板弯曲与平面弹性问题的多类变量变分原理,给出了相关边界积分项的具体表达式.多类交量变分原理涵盖了平衡、应力函数、应力、位移一应变、协调和物性共五大类基本方程和所有边界条件,是一个具有更加广泛意义的变分原理.

关 键 词:板弯曲  平面弹性  变分原理  应力函数

MULTI-VARIABLE VARIATIONAL PRINCIPLES FORPLATE BENDING AND PLANE ELASTICITY
Zhong Wanxie,Yao Weian.MULTI-VARIABLE VARIATIONAL PRINCIPLES FORPLATE BENDING AND PLANE ELASTICITY[J].chinese journal of theoretical and applied mechanics,1999,31(6):717-723.
Authors:Zhong Wanxie  Yao Weian
Abstract:In this paper, the multi-variable variational principles for plate bending and plane elas-ticity are presented, which included all the boundary integral formulas. The variational principlefor plate bending covers five classes of equations of equilibrium, bending moment function-bendingmoment, curvature-deflection, compatibility, bending moment-curvature and all boundary condi-tions, in which independent variables are deflection, curvature, non-homogeneous bending moment,bending moment functions and bending moment. And the one for plane elasticity covers five classesof equations of compatibility, displacement-strain, stress function-stress, equilibrium and stress-strain, in which independent variables are stress function, stress, residual strain, displacement andstrain.The multi-variable variational principles combine the Hu-Washizu as well as Pro-HW varia-tional principles into one, it is the most general variational principle so far. Not only it can beapplied to elasticity problem with residual strain, and also multi-variable variational principle forthe shallow shell can be proposed, which is based on the analogy between plate bending and planeelasticity problems.
Keywords:plate bending  plane elasticity  variational principle  stress function
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