考虑横向拉伸影响的FGM板的静态分析

Static analysis of FGM double curved shallow shell with transverse stretching

在三阶剪切变形理论的基础上,添加关于厚度坐标z的幂函数项,并假设板结构的上下表面剪切力为0,提出了一种考虑横向拉伸影响的高阶剪切变形理论。并且研究了简支边界条件下受静态载荷作用的功能梯度材料矩形板的静态弯曲行为。基于虚功原理推导出了功能梯度矩形板的基本方程,利用Navier双三角级数法计算了功能梯度材料矩形板在静态载荷作用下沿厚度方向的位移及应力分布的数值结果。计算结果与三维精确解理论、其他高阶剪切变形理论得到的数值结果进行了比较。对比结果表明,改进的考虑横向拉伸影响的高阶剪切变形理论的正确性和优越性。

The static analysis of simply supported functionally graded material rectangular plates is presented under the static loading by using an improved higher-order shear deformation theory by considering the effect of transverse stretching. The thickness coordinate z is added to the power functions to account for the effect of transverse stretching based on the third-order shear deformation theory with the assumption of zero shear stress on the top and bottom surfaces. The basic equations of FGM plate have been derived from the principle of virtual work and Navier method is employed to obtain the numerical results of displacements and stresses distributions of FGM rectangular plate along thickness direction under the static loading. The results are compared with those obtained by the 3 D exact solution theory and other higher-order shear deformation theories. The correctness and superiority of the improved higher-order shear deformation theory have been shown by considering the effect of transverse stretching.