对应不同类型变分原理的旋转薄壳轴对称单元

张社光; 陈万吉

对应不同类型变分原理的旋转薄壳轴对称单元

张社光¹,
陈万吉²

1.
上海市应用数学和力学研究所;
2.
大连工学院工程力学研究所

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出版历程
- 收稿日期: 1985-03-20
- 刊出日期: 1986-07-15

Axisymmetrical Elements of Thin Shell of Revolution Corresponding to Different Types of Variational Principles

Zhang She-guang¹,
Chen Wan-ji²

1.
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai;
2.
Institute of Engineering Mechanics, D. I. T., Dalian

摘要

摘要: 本文在一定范围内,统一考察基于不同变分原理建立的有限元模型中,泛函约束条件的不同对单元性态的影响.文中以旋转薄壳轴对称单元(简称TSR单元)为例,采用相同的曲边单元几何描述,推导了七种TSR杂交单元和二种TSR位移协调元,它们分别对应于三类杂交变分原理及最小势能原理.通过单刚列式分析和波纹壳等数值算例比较,分析了不同模型的性态异同和应用上的适应性与局限性;讨论了两类模型间的相互关系;指出了TSR杂交位移元的—个发散条件,并推荐了二种性态较理想的TSR单元.

Abstract: The purpose of this paper is to investigate, to some extent, the influnce of variational constraints on the finite element properties, which are based on different types of variational principles. Taking axisymmetrical elements of thin shell of revolution(abbreviated as TSR element) as comparative elements, and with the same geometrical description, we derive seven kinds of TSR hybrid elements and two kinds of TSR conforming elements corresponding to three types of hybrid variational principles and potential energy principle respectively. By analysing the element stiffness formulations and comparing the numerical calculations, such as corrugated shell, we discuss the differences in properties of different models, and the adaptability, limitation as well as relationship between two types of models. We also point out a divergence case of TSR hybrid displacement element, and suggest two kinds of more acceptable TSR elements.

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参考文献(15)

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