A new orthogonality relationship for orthotropic thin plate theory and its variational principle  

作　　者：LUO Jianhui 1 , LONG Yuqiu 2 & LIU Guangdong 1 1. College of Civil Engineering, Hunan University, Changsha 410082, China 2. Department of Civil Engineering, Tsinghua University, Beijing 100084, China 

出　　处：《Science China(Physics,Mechanics & Astronomy)》2005年第3期371-380,共10页中国科学：物理学、力学、天文学（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.10272063);the Basic Science Research Foundation of Tsinghua University(JC2002003);the Special Scientific Foundation for Chinese Doctoral Education(20020003044);the Foundation for the Author of National Excellent Doctoral Dissertation of China(200242).

摘　　要：The thought how dual vectors are constructed in a new orthogonality relationship for theory of elasticity is generalized into orthotropic thin plate bending problems by using the analogy theory between plane elasticity problems and plate bending problems. Dual differential equations are directly obtained by using a mixed variables method. A dual differential matrix to be derived possesses a peculiarity of which principal diagonal sub-matrixes are zero matrixes. Two independently and symmetrically orthogonality sub-relationships are discovered. By using the integral form for elastic bending theory of orthotropic thin plate the orthogonality relationship is demonstrated. By selecting felicitous dual vectors a new orthogonality relationship for theory of elasticity can be generalized into elastic bending theory of orthotropic thin plate. By using the integral form a variational principle which is relative to differential form and a whole function expression are proposed.The thought how dual vectors are constructed in a new orthogonality relationship for theory of elasticity is generalized into orthotropic thin plate bending problems by using the analogy theory between plane elasticity problems and plate bending problems. Dual differential equations are directly obtained by using a mixed variables method. A dual differential matrix to be derived possesses a peculiarity of which principal diagonal sub-matrixes are zero matrixes. Two independently and symmetrically orthogonality sub-relationships are discovered. By using the integral form for elastic bending theory of orthotropic thin plate the orthogonality relationship is demonstrated. By selecting felicitous dual vectors a new orthogonality relationship for theory of elasticity can be generalized into elastic bending theory of orthotropic thin plate. By using the integral form a variational principle which is relative to differential form and a whole function expression are proposed.

关 键 词：THEORY of elasticity  thin plate theory  dual vectors  ORTHOGONALITY relationship  orthotropic  VARIATIONAL principle. 

分 类 号：O343[理学—固体力学]