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Equilibrium and displacement elements for the design of plates and shells

机译:板壳设计的平衡和位移元件

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This paper reconsiders the finite-element modelling of the linear elastic behaviour of plates and shells as governedby the Reissner–Mindlin first-order shear deformation theory. Particular attention is given to the problems associatedwith the locking of thin forms of structure when modelled with isoparametric conforming elements. As a meansof ameliorating or removing these problems, three recent alternative types of elements are studied. Two aredisplacement elements which include different approaches to the definition of assumed strains, and the third isbased on a hybrid equilibrium formulation of a flat shell element. The purpose of the paper is to compare andexplain their performances and outputs in the context of two benchmark problems: a trapezoidal plate and theScordelis−Lo cylindrical shell. Numerical examples are used to illustrate the convergence of stress-resultant contoursas well as global quantities such as strain energy. The main conclusion is that while all three alternative typesof element overcome locking with regard to displacements, the hybrid models are generally more efficient atproviding good quality stress resultants. This is particularly so for those which contribute little to the total strainenergy but yet may be significant in design.
机译:本文重新考虑了由Reissner-Mindlin一阶剪切变形理论控制的板壳的线性弹性行为的有限元建模。当用等参适形元建模时,应特别注意与薄型结构锁定有关的问题。作为改善或消除这些问题的一种方法,研究了三种最新的替代类型的元素。两种是位移元素,包括采用不同方法定义假定的应变,第三种是基于扁平壳单元的混合平衡公式。本文的目的是在两个基准问题的范围内比较和解释它们的性能和输出:梯形板和Scordelis-Lo圆柱壳。数值例子用来说明应力等值线的收敛以及整体量,例如应变能。主要结论是,尽管所有三种替代类型的单元都克服了关于位移的锁定,但混合模型通常在提供高质量应力结果方面更为有效。对于那些对总应变能贡献很小但在设计上可能很重要的人来说尤其如此。

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