Reissner板的哈密尔顿体系及其辛正交解析法

基于Ｒｅｉｓｓｎｅｒ板理论，通过对混合能变分的修正，建立了更一般的哈密尔顿型广义变分原理，并给出了Ｒｅｉｓｓｎｅｒ板问题的哈密尔顿正则方程及其共轭辛正交解析法。     

Reisner板的哈密尔顿体系及其辛正交解析法

基于Ｒｅｉｓｎｅｒ板理论，通过对混合能变分原理的修正，建立了更一般的哈密尔顿型广义变分原理，并给出了Ｒｅｉｓｎｅｒ板问题的哈密尔顿正则方程及其共轭辛正交解析法     

非线性拟协调元与杂交／混合元：：I.关于Hellinger—Rei…

给出了非线性拟协调有限元列式方法，将非线性拟协调有限元与基于Ｈｅｌｌｉｎｇｅｒ－Ｒｅｉｓｓｎｅｒ变分原理的杂交／混合有限元进行了比较。     

非线性拟协调元与杂交／混合元：Ⅰ．关于Hellinger－Reissner变分原理

给出了非线性拟协调有限元列式方法，将非线性拟协调有限元与基于Ｈｅｌｌｉｎｇｅｒ－Ｒｅｉｓｓｎｅｒ变分原理的杂交／混合有限元进行了比较。     

位移模式对Cross—PLY矩形板热弹性响应的影响

本文建立了以Ｒｅｉｓｓｎｅｒ混合变分原理为基础的迭层板剪切变形理论来求解Ｃｒｏｓｓ－ＰＬＹ矩形板的热弯曲问题，用二种方式来模拟平面位移沿厚度的变化：将一阶剪切变形理论的平面位移叠加一项交错线性函数；设平面位移是分线性连续函数。为保证层间应力的连续性，将横向剪切应力处理成厚度坐标的二次函数，温度沿厚度线性变化。通过对称及反对称Ｃｒｏｓｓ－ＰＬＹ矩形板的热应力及挠度分析比较，指出了位移模式对热弹性响应     

位移模式对Cross－PLY矩形板热弹性响应的影响

本文建立了以Ｒｅｉｓｓｎｅｒ混合变分原理为基础的迭层板剪切变形理论来求解Ｃｒｏｓｓ－ＰＬＹ矩形板的热弯曲问题，用二种方式来模拟平面位移沿厚度的变化：将一阶剪切变形理论的平面位移叠加一项交错线性函数；设平面住移是分段线性连续函数。为保证层间应力的连续性，将横向剪切应力处理成厚度坐标的二次函数，温度沿厚度线性变化。通过对称及反对称Ｃｒｏｓｓ－ＰＬＹ矩形板的热应力及挠度分析比较，指出了位移模式对热弹性响应的影响。     

厚板弹塑性混合状态Hamiltonian元的半解析法

采用初应力法并通过对增量形式Ｈｅｌｌｉｎｇｅｒ－Ｒｅｉｓｓｎｅｒ变分原理的修正，给出了厚板弹塑性分析的Ｈａｍｉｌｔｏｎ正则方程及其相应的半解析法。此法在厚板平面内采用通常的有限元离散，而沿板厚方向采用状态空间法给出半解析解答。     

层合圆柱厚壳热应力分析的状态方程及其半解析法

通过对Ｈｅｌｌｉｎｇｅｒ－Ｒｅｉｓｓｎｅｒ变分原理的修正，导出了变温作用下层合圆柱厚壳的状态方程及其半解析法，该方法在ｚ－θ曲面内采用通常的有限元离散，而沿壳厚（ｒ）方向采用状态空间法给出解析解答，且通过采用状态转移矩阵，建立了层合圆柱壳内外表面应力和位移之间的关系式，然后利用打靶法进行求解，从而大大降低了计算中的未知量数目。     

有关复合材料迭层板平面响应的理论

为了准确地分析迭层板的平面响应，本文建立了一种以Ｒｅｉｓｓｎｅｒ的新的混合变分原理为基础的迭层板剪切变形理论。将一阶剪切变形理论的平面位移叠加一项交错线性数函数平模拟平面位移沿厚度的变化，为保证层间应力的连续性，将横向剪切应力处理成厚度从标的二次函数。将该理论具体实施到迭层的柱形弯曲问题中，理论解与Ｐａｇａｎｏ的精确解比较的结果说明了本文的迭层板理论对于分析平面响应是非常有效的。     

各向异性弹性力学问题Hamilton正则方程的一般形式

本文从修正后的Ｈｅｌｌｉｎｇｅｒ－Ｒｅｉｓｓｎｅｒ变分原理出发，导出了由２１个弹性常数组成的各向异性材料的混合方程，井证明它们即是Ｈａｍｉｌｔｏｎ正则方程。由该统一形式还给出了角铺设材料和正交各向异性材料的Ｈａｎｉｌｔｏｎ正则形式。     

薄板有限元广义混合法及克服病态问题研究

以薄板理论的广义混合变分原理为基础,建立了一种适用于薄板弯曲分析的有限元广义混合模式,给出了较实用的选择分裂因子的方法,算例表明有限元广义混合法比常规位移模式的精度高,同时还能克服常规有限元中的某些病态问题。本文还讨论了该法克服常规有限元中某些病态问题的机理。     

用有限元广义混合法分析不可压缩或几乎不可压缩弹性体

不可压缩或几乎不可压缩问题在数学上表现为最小 势能原理中的某些项趋于无穷大,使得有限元方程产生病态。本文给出了不可压缩或几乎不可压缩弹性分析的广义混合变分原理,以此为基础建立了该类问题的有限元广义混合法。该变分原理的泛函中不含有上面这种奇异项,故其有限元方程不会产生病态。算例表明该有限元法可以同时进行可压缩、不可压缩或几乎不可压缩弹性分析,且精度良好;有限元常规位移法及Hermann法是该法的特例。     

A new kind of mixed elements for shells of revolution subjected to arbitrary loads

In this paper a generalized variational principle with two-field variables is derived from the Reissner principle of elasticity in the curvilinear coordinates of a revolution shell, based on which, a new kind of mixed elements with independent transverse rotations is formulated for revolution shells subjected to harmonic external loads. The resultant-stress interpolations are carefully selected so that the shear part of the element stiffness contains the Kirchhoff hypothesis for thin shells and element stiffness matrices have correct ranks. The elements are free from shear locking and spurious kinematic modes. Numerical examples show that the new elements have good generality and high accuracy for thin and moderately-thick revolution shells.     

Construction of rectangular displacement-based element for thick/thin plates

In this paper, a method of constructing displacement-based element for thick/thin plates is developed by using the technique of generalized compatibility, and a rectangular displacement based element with 12 degrees of freedom for thick/thin plates is presented. This method enjoys a good accuracy with simple formulation and is free of shear locking as the thickness of the plate approaches zero. The project supported by National Natural Science Foundation of China through Grant No. 59208075     

Generalized mixed finite element method for 3D elasticity problems

Without applying any stable element techniques in the mixed methods, two simple generalized mixed element(GME) formulations were derived by combining the minimum potential energy principle and Hellinger–Reissner(H–R) variational principle. The main features of the GME formulations are that the common C0-continuous polynomial shape functions for displacement methods are used to express both displacement and stress variables, and the coefficient matrix of these formulations is not only automatically symmetric but also invertible. Hence, the numerical results of the generalized mixed methods based on the GME formulations are stable. Displacement as well as stress results can be obtained directly from the algebraic system for finite element analysis after introducing stress and displacement boundary conditions simultaneously. Numerical examples show that displacement and stress results retain the same accuracy. The results of the noncompatible generalized mixed method proposed herein are more accurate than those of the standard noncompatible displacement method. The noncompatible generalized mixed element is less sensitive to element geometric distortions.     

Bilevel generalized mixed equilibrium problems involving generalized mixed variational-like inequality problems in reflexive Banach spaces

A new bilevel generalized mixed equilibrium problem(BGMEP) involving generalized mixed variational-like inequality problems(GMVLIPs) is introduced and studied in the reflexive Banach spaces.First,an auxiliary generalized mixed equilibrium problem(AGMEP) is introduced to compute the approximate solutions of the BGMEP involving the GMVLIPs.By using a minimax inequality,the existence and the uniqueness of solutions of the AGMEP are proved under mild conditions without any coercive assumptions.By using an au...     

A new twelve DOF quadrilateral element for analysis of thick and thin plates

A simple quadrilateral 12 DOF plate bending element based on Reissner–Mindlin theory for analysis of thick and thin plates is presented in this paper. This element is constructed by the following procedure:

• 1.the variation functions of the rotation and shear strain along each side of the element are determined using Timoshenko's beam theory; and
• 2.the rotation, curvature and shear strain fields in the domain of the element are then determined using the technique of improved interpolation.

The proposed element, denoted by ARS-Q12, is robust and free of shear locking and, thus, it can be employed to analyze very thin plate. Numerical examples show that the proposed element is a high performance element for thick and thin plates.     

On the refined first-order shear deformation plate theory of Kármán type

A new refined first-order shear-deformation plate theory of the Kármán type is presented for engineering applications and a new version of the generalized Kármán large deflection equations with deflection and stress functions as two unknown variables is formulated for nonlinear analysis of shear-deformable plates of composite material and construction, based on the Mindlin/Reissner theory. In this refined plate theory two rotations that are constrained out in the formulation are imposed upon overall displacements of the plates in an implicit role. Linear and nonlinear investigations may be made by the engineering theory to a class of shear-deformation plates such as moderately thick composite plates, orthotropic sandwich plates, densely stiffened plates, and laminated shear-deformable plates. Reduced forms of the generalized Kármán equations are derived consequently, which are found identical to those existe in the literature. Foundation item: the National Natural Science Foundation of China (59675027) Biography: Zhang Jianwu (1954-)     

偶应力问题的杂交／混合元分析

将弹性力学中Hellinger—Reissner交分原理推广到偶应力理论中，并以罚函数的形式引入其约束条件，提出了一种有效的杂交／混合单元。文中分别分析了带中心小孔平板在轴向均匀加载时的应力集中情况，以及含中问裂纹的无限平板单轴拉伸时的位移场和应力场。算例表明，该单元计算效率高，精度好，即使在材料本征长度很小时，仍然能够得到相当理想的结果。     

一类新型受任意载荷的杂交旋转壳单元

本文从弹性力学Reissner变分原理出发推导旋转壳曲线坐标系下内分，位移的二类变量广义变分原理，依据这个原理推导一类旋转壳坐标系中具有独立横向转角的受谐和外载荷下的杂交旋转壳单元，内力模式的选用使刚度矩阵的剪切部份在薄壳情况下能反映Kirchhoff假设，并使单元刚度矩阵满秩，从而保证单元无剪切自锁和零能模式，数例证明这类单元对中厚和薄旋转壳具有良好的通用性和较高的精度。