有限位移理论的功的互等定理及其应用  

The Reciprocal Theorem for the Finite Displacement Theory and Its Applications

作　　者：付宝连[1] 

机构地区：[1]燕山大学建筑工程与力学学院,河北秦皇岛066004

出　　处：《应用数学和力学》2015年第10期1019-1034,共16页Applied Mathematics and Mechanics

摘　　要：提出了有限位移理论三维线弹性力学的功的互等定理.基于这一定理,导出了大挠度弯曲矩形板的功的互等定理.同时,应用简化矩形板的定理,直接得到了大挠度板条的功的互等定理.作为应用,计算了在均载作用下两端固定大挠度板条的弯曲和在均载作用下4边固定大挠度矩形板的弯曲.计算表明,根据弯曲薄板大挠度功的互等定理,大挠度弯曲矩形板可应用小挠度的相应基本解得以简单地解决.The reciprocal theorem of 3D linear elasticity for the finite displacement theory was proposed. On the basis of the theorem, the reciprocal theorem of rectangular plates of large de- fection was derived. Meanwhile, the reciprocal theorem of plate strips of large deflection was directly obtained through simplification of the theorem of the rectangular plates. For applica- tions, the bending of a plate strip of large deflection with 2 ends fixed under uniformly distribu- ted load and the bending of a rectangular plate of large deflection with 4 edges fLxed under uni- formly distributed load were calculated. The calculation shows, on the basis of the reciprocal theorem of bending thin plates of large deflection, the bending rectangular plates of large de- flection can easily be sovled with the aid of the basic solution corresponding to the small-deflec- tion case.

关 键 词：线弹性力学 有限位移理论 大挠度 功的互等定理 

分 类 号：TU311[建筑科学—结构工程] O343.2[理学—固体力学]