一族拉格朗日等参薄板单元  

A family of isoparameter Lagrangian elements for thin plate bending analysis

作　　者：沈冯强[1] 

机构地区：[1]合肥工业大学土木建筑工程学院,安徽合肥230009

出　　处：《合肥工业大学学报（自然科学版）》1999年第5期12-17,共6页Journal of Hefei University of Technology：Natural Science

基　　金：国家教委留学回国人员科研启动基金

摘　　要：提出用拉格朗日等参单元来模拟薄板弯曲，用拉格朗日乘子修正薄板势能泛函来强加板法线转角在单元交界处的连续性，这种拉格朗日等参薄板单元继承了平面弹性问题中拉格朗日等参单元的全部优点。它的求解过程简单，算法稳定，解答精度高，易于编制计算机程序。拉格朗日等参单元能很好地吻合曲线边界，加之节点未知量中没有广义位移（即转角），特别适合推广应用于逐步更新节点坐标的空间板、壳结构非线性问题分析。A family of isoparameter Lagrangian elements have been proposed to model the thin plate bending, where the continuity of normal rotation of a plate across element interfaces is imposed with Lagrangian multipliers. This family of thin plate bending elements inherit all advantages associated with two dimensional isoparameter Lagrargian elements used for plane stress/strain analysis. The solution procedure is simple and easy to be coded with computer languages. The algorithm is stable and the results are accurate. Compared with other thin plate bending elements available, the proposed elements are more versatile in fitting curved boundaries. These elements are suitable for geometric nonlinear analysis of 3 dimensional shells with updated Lagrangian formulation.

关 键 词：拉格朗日 等参单元 薄板 弯曲 拉格朗日乘子 

分 类 号：O343.1[理学—固体力学]