弹性平板的一种精确理论

本文提出一种可以精确考虑平板的横向剪切变形和法向正应力影响的平板理论。在这种新的理论中,横向剪应力的分布用含有若干个待定函数的多项式表示,这些特定函数可以用三维弹性力学基本方程和简单的线性代数运算来确定,不需解附加的微分方程,而多项式的项数则由横向载荷的分布来决定。根据这种新理论所取得的方程及其解答能够比现有理论更精确的反映不同的载荷分布对于应力分布及位移的影响。本文用例题说明了这种新理论的计算方法。

A Precise Theory of Elastic Plate

A new theory of plate which incorporates accurately the effects of lateral deformation and normal street is described in this paper. A special polynomial with a number of unknown function is used to represent the lateral shear stresses in plate at first, and then these unknown function are sim- ply determined by the fundamental equation of three dimensional elastestatics and simple linear alge- braic operation, the number of unknown function in the polynomial is dependent on lateral load dis- tribution. This new theory can reflect accurately the effects of shear deformation and load distribu- tion on stresses and displacements in plate. An example is presented for a two-opposite-edge simply supported plate to illustrate its accurately and solution method.