用三角形广义协调元分析任意形状板的大挠度问题

本文分别用广义协调三角形板单元ＧＣＩＩ－Ｔ９及ＧＣⅢ－Ｔ９对固支圆板及斜板进行了大挠度分析，验证了非线性广义协调三角形板单元的精度及收敛性。     

几何非线性广义协调四边形板单元

本文将广义协调四边形板单元ＬＧＣ－Ｑ１２及ＬＳＬ－Ｑ１２的弯曲位移模式引入板的大挠度分析中，构造了几何非线性广义协调四边形板单元，并分别对固支圆板、固支椭圆板及固支斜板进行了大挠度分析     

基于共旋三角形厚薄通用壳元的几何非线性分析

基于共旋列式方法发展了一种用于复合材料层合板结构几何非线性分析的简单高效的三结点三角形平板壳元。该壳元由具有面内转动自由度的广义协调膜元GT9与假设剪切应变场和假设单元转角场的广义协调厚薄通用板元TMT组合而成。为避免薄膜闭锁而采用单点积分计算与薄膜应变有关的项, 同时增加一个稳定化矩阵以消除单点积分导致的零能模式。基于层合板一阶剪切变形理论, 给出了考虑层合板具体铺层顺序的修正的横向剪切刚度, 使该壳元可用于中厚层合板结构的分析。由于共旋列式大转动小应变的假设, 共旋列式内核的几何线性的单元刚阵可仅计算一次而保存下来用于整个几何非线性求解的过程以提高计算效率。数值算例表明提出的壳元进行包括复合材料层合板结构的厚薄壳结构的几何非线性分析的精度高且效率高。     

薄板大挠度广义协调有限元分析

将广义协调元用于求解薄板大挠度问题。编写了专用程序GCEP并计算了四边简支、四边铰支和四边固定方形薄板在横向均布荷载作用下的跨中挠度。计算结果表明,广义协调元对于求解结构几何非线性问题同样具有精度高、收敛快等优点。     

GSQ24壳体单元用于板壳结构的几何非线性分析

在考虑剪切变形的Von Karman大变形小应变假设下,基于全Lagrange描述方法,将平面内带有旋转自由度的GSQ24壳体单元用于板壳结构的几何非线性分析,给出了板壳结构大变形下的小位移刚度矩阵、初应力刚度矩阵、初位移刚度矩阵有限元列式。同时,文中也给出了既考虑材料非线性,又考虑几何非线性的强非线性问题的板壳结构分析时的有限元列式。数值算例与变分法和级数解结果比较,表明本文方法的可行性。     

一个三角形广义协调薄板弯曲元

本文采用一点边协调方案^[1,2]构造了一个三角形广义协调薄板弯曲单元。此三角形单元具有自由度少,推导简明,列式简单等优点,且通过分片检验。数值算例表明本文单元是一个较高的精度、并保证收敛的新型薄板弯曲三角形元。可适用于实际工程计算。     

板片空间结构地震反应的双重非线性时程分析

本文推导了三维桁元，梁元和三角形板壳元（ＤＫＴ元）在Ｕ．Ｌ．描述下的双重非线性切线刚度矩阵，通过对增量形式虚功方程作线性处理来减少计算量，对一个单层板片空间结构进行了地震反应的时程分析，文中着重分析了几何非线性和材料非线性对板片空间结构地震反应的影响，以及水平和竖向地震作用的影响。     

采用面积坐标的四边形板弯曲单元

本文采用四边形面积坐标，并应用广义协调法构造出一个具有１２个自由度的四边形板弯曲单元。单元的挠度场以面积坐标多项式表示，对应于直角坐标ｘ，ｙ的完全三次式和部分四次式，因而单元是完备的广义协调的板单元。应用的１２个协调条件为挠度的四个点协调条件和四个边协调条件，以及法向转角的四个边协调条件。由于面积坐标和直角坐标之间为线性变换关系，因此单元刚度矩阵的推导相当简单。数值算例表明：本文单元具有高精度、收敛性、可靠性和对网格畸变不敏感的优点     

冲击荷载下弹粘塑性矩形薄板的动力响应

本文用空间有限元、时间差分法分析了受冲击荷载的矩形固支板的动力响应。分析中考虑了大位移引起的几何非线性;塑性、应变强化及应变率效应引起的材料非线性的影响。     

采用广义协调条件构造具有旋转自由度的三角形膜元

本文根据广义协调的概念,通过引进单元结点刚体转角,构造出了两种具有平面内旋转自由度的三角形膜元。单元列式简单,并能通过分片检验,数值算例表明,它们是一类高精度的收敛单元。     

Linear and Geometrically nonlinear analysis of plates and shells by a new refined non-conforming triangular plate/shell element

A refined non-conforming triangular plate/shell element for linear and geometrically nonlinear analysis of plates and shells is developed in this paper based on the refined non-conforming element method (RNEM). A conforming triangle membrane element with drilling degrees of freedom in Cartesian coordinates and the refined non-conforming triangular plate-bending element RT9, in which Kirchhoff kinematic assumption was adopted, are used to construct the present element. The displacement continuity condition along the interelement boundary is satisfied in an average sense for plate analysis, and the coupled displacement continuity requirement at the interelement is satisfied in an average sense, thereby improving the performance of the element for shell analysis. Selectively reduced integration with stabilization scheme is employed in this paper to avoid membrane locking. Numerical examples demonstrate that the present element behaves quite satisfactorily either for the linear analysis of plate bending problems and plane problems or for the geometrically nonlinear analysis of thin plates and shells with large displacement, moderate rotation but small strain.     

采用SemiLoof型约束条件的薄板矩形广义协调元

本文采用SemiLoof型约束条件,建立一个十二自由度的薄板矩形广义协调元。单元自由度只含角点位移,不含Loof结点位移、单元间的协调条件全部采用点型协调条件,不采用积分型协调条件。此单元吸取广义协调元和SemiLoof元的双重优点,消除其缺点,成为同类低阶薄板单元中的最优单元。     

Triangular and rectangular plate elements based on generalized compatibility conditions

Three generalized conforming elements for thin plate bending based on generalized compatibility conditions are derived: a triangular element with 9 d.o.f. (LT element) and two rectangular elements with 12 d.o.f. (LR-1 and LR-2). Their formulation is as simple as the conventional non-conforming element and they can be implemented in routine manner. By satisfying the generalized compatibility condition under constant moments, these new elements can always pass the patch test. Numerical examples show that high accurate result is obtained with fewer degrees of freedom by using these new elements of thin plate.     

Material and Geometric Nonlinear Analysis of Functionally Graded Plate-Shell Type Structures

A nonlinear formulation for general Functionally Graded Material plate-shell type structures is presented. The formulation accounts for geometric and material nonlinear behaviour of these structures. Using the Newton–Raphson incremental-iterative method, the incremental equilibrium path is obtained, and in case of snap-through occurrence the automatic arc-length method is used. This simple and fast element model is a non-conforming triangular flat plate/shell element with 24 degrees of freedom for the generalized displacements. It is benchmarked in the solution of some illustrative plate- shell examples and the results are presented and discussed with numerical alternative models. Benchmark tests with material and geometrically nonlinear behaviour are also proposed.     

A family of simple and robust finite elements for linear and geometrically nonlinear analysis of laminated composite plates

A family of simple, displacement-based and shear-flexible triangular and quadrilateral flat plate/shell elements for linear and geometrically nonlinear analysis of thin to moderately thick laminate composite plates are introduced and summarized in this paper.

The developed elements are based on the first-order shear deformation theory (FSDT) and von-Karman’s large deflection theory, and total Lagrangian approach is employed to formulate the element for geometrically nonlinear analysis. The deflection and rotation functions of the element boundary are obtained from Timoshenko’s laminated composite beam functions, thus convergence can be ensured theoretically for very thin laminates and shear-locking problem is avoided naturally.

The flat triangular plate/shell element is of 3-node, 18-degree-of-freedom, and the plane displacement interpolation functions of the Allman’s triangular membrane element with drilling degrees of freedom are taken as the in-plane displacements of the element. The flat quadrilateral plate/shell element is of 4-node, 24-degree-of-freedom, and the linear displacement interpolation functions of a quadrilateral plane element with drilling degrees of freedom are taken as the in-plane displacements.

The developed elements are simple in formulation, free from shear-locking, and include conventional engineering degrees of freedom. Numerical examples demonstrate that the elements are convergent, not sensitive to mesh distortion, accurate and efficient for linear and geometric nonlinear analysis of thin to moderately thick laminates.     

用简单高效的矩形广义协调元分析薄板的振动

本文介绍一种在薄板振动分析中很简单,而且很实用的广义协调矩形元,将其应用于薄板固有振动分析中,求解前几阶的固有频率。文中算例表明,该单元简易,程序通用,且精度高。同时,它还可以与平面应力单元组合,构成平板型壳单元,用以分析某些壳体(如柱壳、折板等)的振动,同样简单实用。