一般边界条件下压电层合厚板的精确解

从三维弹性理论和压电学理论出发,通过假设边界函数,导出一般边界条件下压电层合板的状态方程,并运用传递矩阵求解方法,给出了满足周边和上、下表面所有边界条件的精确解析解.此解计及了正交异性压电弹性体的所有弹性常数和压电学常数,满足层合板所有基本方程和层间连续条件,适合任意厚跨比.本文所述的方法原理对于验证、比较其他简化模型和各种数值计算模型都有十分重要的指导意义,在工程中也有着广泛的应用前景.

EXACT SOLUTIONS OF THICK LAMINATED PIEZOELECTRIC PLATES UNDER GENERAL BOUNDARY CONDITIONS

Based on the theories of 3\|D elasticity and piezoelectricity and by assuming appropriate boundary functions,state equations for piezoelectric laminates under general boundary conditions are established.By using transfer matrix method,exact analytical solutions that satisfy all the boundary conditions at four edges,as well as upper and bottom surfaces,are presented.The solution given, which is suitable for all the thickness to span ratios, has taken into account all the independent elastic and piezoelectric constants for an orthotropic piezoelectric body and satisfied the continuity conditions between piles of the laminates.The principle of the present method and corresponding results are not only of great guiding significence to testify and compare with varies approximate models and numerical calculating models ,but also have the prospect of widespread applications in engineering.