基于混合Trefftz有限梯度元法的功能梯度材料热传导数值模拟

A hybrid Trefftz graded finite element method to steady-state heat conduction in functionally graded material

针对功能梯度材料物性参数随坐标变化的特点,基于Trefftz完备解提出了求解功能梯度材料热传导问题的有限梯度元方法。首先,利用变量代换推导出指数型、二次型和三角型功能梯度材料稳态热传导问题的Trefftz完备解;然后,利用Trefftz完备解对单元内部的温度场进行插值,构造出可自然模拟材料梯度属性的梯度单元,在该基础上建立混合Trefftz有限梯度元法求解功能梯度材料的稳态热传导方程;最后,采用混合Trefftz有限梯度元法对典型功能梯度材料板的温度分布进行数值模拟,以验证该方法的正确性和有效性。

A hybrid Trefftz graded finite element method is built for heat conduction problem in functionally graded materials(FGMs).First,the Trefftz complete solutions of heat conduction equation for exponential,trigonometrical and quadratical FGMs are derived.Then,the graded element is constructed by linear combination of Trefftz complete solutions which are applied to build the hybrid Trefftz graded finite element method.The performance of the proposed method is assessed by several benchmark examples.The results demonstrate that the proposed method is effective and can achieve high accuracy.