A novel hybrid-Trefftz finite element (HTFE) has been developed for the static analysis of thick and thin antisymmetric cross-ply and angle-ply laminated composite plates. For the first time a high order shear deformation theory is used for both the internal and auxiliary displacement fields for constructing the Trefftz functions. The usual tedious approach of converting the system of governing partial differential equations into a single governing equation has been avoided in the present development. The Trefftz functions have been derived from the exact solutions of the homogeneous governing equations of equlibrium. The current HTFE formulation does not need to find the particular solutions of the system of governing partial differential equations. Comparison with exact and analytical solutions reveals that the HTFE developed here is excellently capable of predicting the responses of the antisymmetric laminated composite plates. The Trefftz functions developed here can be used for deriving the polygonal HTFE with any number of sides.

已经开发出一种新颖的混合-Trefftz有限元（HTFE），用于对厚和薄的非对称交叉层和角层层合复合板进行静态分析。首次将高阶剪切变形理论用于内部和辅助位移场，以构建Trefftz函数。在当前的发展中，避免了将控制偏微分方程组的系统转换为单个控制方程组的通常乏味的方法。Trefftz函数已从均衡的齐次控制方程的精确解中得出。当前的HTFE公式不需要找到控制偏微分方程组的特定解决方案。与精确和分析解决方案的比较表明，此处开发的HTFE具有出色的预测非对称层压复合板响应的能力。此处开发的Trefftz函数可用于推导具有任意多个边的多边形HTFE。