梯度功能材料薄壳动态热挠度的Laplace变换有限元分析

采用Laplace变换有限元法分析了梯度功能材料薄壳结构的热冲击挠度。首先从控制方程出发,推导出梯度功能材料热冲击问题的泛函及变分原理;然后对梯度功能材料薄壳的热冲击问题推导出有限元方程;利用Laplace变换引入初值条件后推导出拉氏域上的有限元计算公式,经求解后再通过Laplace数值逆变换求得时间域上各给定时刻的解答。计算实例证明了该方法的有效性,其计算结果可供工程设计参考。

The Laplace Transform Finite Element Method for Thermal Shock Problems of Functionally Gradient Material Thin Cabinet

In this paper, the thermal shock problems of thin cabinet made of Functionally Gradient Materials (FGM) are analyzed by Laplace transform finite element method. Firstly, based on the governing equations, the functional and variational principle of the FGM thermal shock problems are derived. And then, the finite element equations of thermal shock problems of FGM thin cabinet are founded. With the initial condition added by Laplace transform, the finite element equations in the Laplace domain are founded. Finally, the responses at given moments in the time domain are obtained by numerical inversion of Laplace transforms. The calculation examples show that the method is effective,and the numerical results can be used for engineering design references.