含参数辛元与热弹性复合材料层合板分析
Parametered symplectic element and analysis of thermoelastic composite laminates

为了提高计算热弹性复合材料层合板应力的精度，基于相关文献的非协调辛元理论，将弹性材料的广义H-R变分原理扩展为热弹性材料的广义H-R变分原理，并提出了相应的修正原理。建立了含参数非协调辛元。该单元的主要优点之一是避免了传统混合元中系数矩阵主对角线上存在零元素的问题，因而保证了有限元线性方程组数值结果的稳定性。同时，该单元关于广义的位移变量和应力变量对称，因此其对应的有限元线性方程组对称保辛。实例结果表明：与精确解对比，该单元的广义位移和广义应力的数值结果不仅精度一致，而且精度高；与位移有限元法的结果比较，收敛速度快。 In order to improve the stress accuracy of thermal elastic composite laminates, the generalized H-R variational principle of elastic material was extended to the generalized H-R variational principle of thermal elastic material based on the symplectic element theory of related references, and the corresponding modified principle was proposed. The parametered symplectic element was established. One of the main advantages of this element is that there is no zeros in the leading diagonal of coefficient matrix compared to the traditional mixed element. Consequently, the stability of the numerical results of finite element linear system of equations is guaranteed. At the same time, the element is symmetric for both the displacement variable and the stress variable, so its corresponding finite element linear system of equations is symmetric and symplectic conservation. Compared with the exact solution, the numerical results show that the accurate order of the generalized displacements and stresses are consistent, and hold high accuracy. 国家自然科学基金（11502286