基于精化锯齿理论的功能梯度夹心微板静弯曲模型

基于精化锯齿理论和新修正偶应力理论,建立了能够准确预测功能梯度夹心微板挠度、位移和应力的静弯曲模型。为了描述微板不同方向上的尺度效应,将两个正交材料尺度参数引入本文模型。以受双向正弦载荷作用的简支板为例,探究了夹心微板弯曲行为中尺度效应对结构刚度的影响。算例结果表明,当微板几何参数与材料尺度参数接近时,基于本文模型所测微板的最大弯曲挠度、局部位移和应力均小于传统精化锯齿理论给出的结果,捕捉到了尺度效应;尺度效应随着微板几何尺寸的增大而逐渐减弱,当微板几何尺寸远大于材料尺度参数时,尺度效应消失。此外,板的跨厚比和功能梯度变化指数也会对尺度效应产生一定影响。

Static bending model of functionally graded sandwich micro-plates based on the Refined Zigzag Theory

A static bending model of functionally graded sandwich micro-plates with accurate prediction on deflections,displacements and stresses was proposed based on the Refined Zigzag Theory and re-modified couple stress theory.The model can separately describe different scale effects in orthogonal directions through the two orthogonal material length scale parameters.A simply supported plate under a double sinusoidal load is taken as the illustrative example to investigate the influences of the scale effect on the mechanical behaviors.Numerical results indicate that the results given by the present model are all smaller than those given by the classical one when the material length scale parameters are comparable to the plate size,i.e.the scale effect is well depicted.The scale effect becomes weaker with the increase of the plate size and diminishes as the plate size is much larger.Additionally,the grading index and the span-to-thickness ratio also have a certain influence on the scale effect.