考虑温度梯度影响的偶应力理论的无网格方法

Meshfree method for couple stress theory considering the effect of temperature gradient

采用偶应力理论描述温度梯度影响下薄板结构复杂热力耦合特征,利用移动最小二乘近似构造的形函数高阶连续特征,将温度梯度、结构的应变和旋转曲率直接用节点的温度或位移进行插值,建立了考虑温度梯度影响的偶应力理论的无网格数值计算框架。对温度梯度影响下的薄板弯曲效应进行数值模拟,分析了温度梯度对结构变形的影响。结果表明:考虑温度梯度影响时薄板有显著的变形,且变形值随着温度梯度的增大而增大。

In this paper,the couple stress theory considering the effect of temperature gradient is adopted to describe the complex thermal coupling characteristics of structure.Based on the high-order continuty of shape function constructed by moving least squares approximation,the couple stress theory is used to describe the temperature gradient,the strain and the rotational curvature of structure under the influence of temperature gradient.The meshfree computing framwork of couple stress theory considering the effect of temperature gradient is established.The bending deformations of thin plates under temperature gradient are numerically simulated by using the established meshfree method,the effects of temperature gradient on structural deformations are studied.The results show that there are significant displacement changes when the temperature gradient are considered,and the displacement increase is increased with the increase of the temperature gradient.