基于基本解和径向基函数插值的热弹性无网格分析

Thermoelastic meshless analysis based on method of fundamental solutions with radial basis functions approximation

采用基于基本解方法和径向基函数插值的无网格算法(MFS-RBF)分析了广义的热弹性问题．位移分为齐次解和特解两部分,径向基函数被用来插值任意温度变化和体力分布,对应于径向基函数的特解集被用来构造位移特解部分,而基本解方法用来计算相应的位移齐次解．最后,常见的重力荷载、惯性荷载和温度荷载算例验证了算法的有效性和简单性．

The method of fundamental solutions (MFS) with radial basis functions (RBF) approximation was developed for general thermoelastic analysis. Radial basis functions were used to approximate arbitrary body forces and temperature changes, and then the particular solutions induced by body forces and temperature change were constructed by means of a set of approximated particular solutions related to the chosen RBF, while the MFS was used to compute the corresponding homogeneous solutions. Finally, three examples involving gravity, inertial force and temperature change respectively are tested and results demonstrate the advantages of good accuracy and simple process of the MFS-RBF.