角点悬空弯曲厚矩形板的边界积分法

在边界积分法中引用了拟基本系统矩形板,在该拟基本系统与实际系统之间应用功的互等定理,得到一挠曲面方程的积分表达式,只要对此表达式进行极简单的积分便可得到该挠曲面方程,这比直接求解Reissner挠度控制方程要简单,边界积分法的求解过程概念清晰,计算伊始便给出了挠曲面方程的总体表达式.以Reissner厚板理论为基础,应用边界积分法研究了角点悬空厚矩形板的弯曲问题,给出了在集中荷载作用下两邻边固定另两邻边自由且角点悬空弯曲厚矩形板的封闭解析解,并给出了相应的数据和图表以供工程上的应用和参考.

Boundary integration method of bending of thick rectangular plate with the corner paint hang in the air

Introducing basic system rectangular plate, and applying reciprocal theorem of works between the actual system and the basic system, it obtain a deflection equation integral expression. Carried on the simple integral to the expression,it can obtain the deflection equation, it is easier than to solve Reissner`s deflection governing equation. Boundary integration method solution process concept is clear, the computation beginning has then given the deflection equation overall expression. This article take the Reissner`s theory of thick plates as a foundation, the closed analytical solution of bending of thick rectangular plate with two border edges fixed two border edges free corner paint hang in the air under a concentrated load is found by use of boundary integration method, and the corresponding numerical date, figures and tables are provided for the engineering applications. For any complex boundary conditions. including corner paint hang in the air of the complex boundary conditions the closed analytical solution of bending of thick rectangular plate can be given.