%0 Journal Article
%T MULTI-VARIABLE VARIATIONAL PRINCIPLES FORPLATE BENDING AND PLANE ELASTICITY<br>板弯曲与平面弹性问题的多类变量变分原理
%A Zhong Wanxie
%A Yao Weian
%A <br>钟万勰
%A 姚伟岸
%J 力学学报
%D 1999
%I 
%X 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.
%K plate bending
%K plane elasticity
%K variational principle
%K stress function<br>板弯曲
%K 平面弹性
%K 变分原理
%K 应力函数
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=5D344E2AD54D14F8&jid=4100DA4A1A3BA1B0CE5AD99AE1DFB420&aid=3E84A6CDC4692D012FEEC9EA6C638E20&yid=B914830F5B1D1078&vid=4AD960B5AD2D111A&iid=B31275AF3241DB2D&sid=E5ED9059DE792E50&eid=19402779123D7C0E&journal_id=0459-1879&journal_name=力学学报&referenced_num=3&reference_num=8