将哈密顿求解体系推广应用于Reissner-Mindlin厚板问题。首先导出了厚板哈密顿对偶微分方程，然后采用换元乘子法导出了厚板哈密顿变分原理的泛函表示式，最后提出并证明了厚板理论的两个正交关系。厚板哈密顿体系的理论成果将为研究厚板解析解和有限元解提供新的有效工具。

Two 4-node quadrilateral membrane elements, denoted as AGQ6-I and AGQ6-II, have been developed in this paper. Instead of the traditional isoparametric coordinate, the quadrilateral area coordinates were used to establish the formulations of the new elements. And several generalized conforming conditions were then introduced to determine all unknown parameters. Numerical examples showed that the presented elements exhibit excellent performances in both regular and distorted mesh divisions. They could even yield exact solutions for pure bending problems under distorted meshes and provide lock-free solutions for the MacNeal's test problem of trapezoidal locking. Besides, the weak patch test was conducted to guarantee the convergence of both new elements. It has also been demonstrated that the area coordinate method is an efficient tool for developing simple, effective and reliable serendipity plane membrane elements.

The singularity of stress and strain at the tip of three-dintensional notch is analysed by the power expansion method. The eigenequation of the notch is gained through the boundary conditions of the notch, the eigenvalues under different inner angles of the notch are obtained. the expression of stress at the tip of the notch is finally derived.

基于分区混合能量原理的分区混合元法是一种高精度有限元方法，可用于分析含裂纹、孔洞、切口等缺陷的问题。本文推导了分区混合元法中应力元的刚度矩阵；分析了应力元的多余零能模式，并证明了整体分析中对多余零能模式的消弭；文中还对分区混合元法中应力元的应力项数与应力单元尺寸对分析结果的影响进行了系统的讨论。

A simple displacement-based, quadrilateral 20 DOF(5 DOFper node) bending element based on the first-order shear deformation theory for analysis of arbitrary laminated composite plates is presented in this paper. This element is constructed by the following procedure: (i) the variation functions of the rotation and the shear strain along each side of the element are determined using Timoshenko's beam theory; and (ii) the shear strain, rotation and in-plane displacement fields in the domain of the element are then determined using the technique of improved interpolation. Furthermore, a simple hybrid procedure is also proposed to improve the stress solutions. The proposed element, denoted as CTMQ20, possesses the advantages of both the displacement-based and hybrid elements. Thus, excellent results for both displacements and stresses, especially for the transverse shear stresses, can be obtained.