层合厚板静动态问题的精确解

EXACT SOLUTION FOR THE STATICS AND DYNAMICS OF LAMINATED ORTHOTROPIC THICK PLATE

本文在文献(5)的基础上,对任意层正交各向异性材料层合厚板在局部座标系下建立其三维弹性力学的状态方程。由于状态方程所涉及的物理量满足层间协调条件,这使得建立整个板的状态方程极为方便,且定解方程阶数和板的层数无关。文中给出四边简支三层层合板在法向均载作用下弯曲问题和自由振动问题的精确解。采用文献(5)所介绍的方法,不难推广至其它边界条件下的静、动力分析。

In this study, three-dimensional state equation for the j-th ply of a laminated orthotropic thick plate is established in the local co-ordinate system according to the knowledge wnich has been introdnced in reference 5. Fecause all the physical quantities appearing in state equation satisfy the compability conditions of the interfaces,it is extremely convenient to develop the state equation of the whole plate. Furthermore, the number of the unknowns included in the final equations has no relationship with that of plies of the plate. Exact Solutions are presented for the statics and dynamics of a three-ply orthotropic thick plate with simply supported-edges.The approach developed in the present study can also be applied to the analysis of a laminated orthotropic plate with other boundary conditions when the conclusion introduced in (5) is employed.