弹性厚板的分区广义变分原理
Subregion Generalized Variational Principles for Elastic Thick Plates
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摘要: 本文提出弹性厚板分区广义变分原理,其要点如下:1.各分区可任意定为势能区或余能区.分区势能、分区余能、分区混合变分原理是它的三种特殊形式.2.每个分区中独立变分变量的个数可任意规定.每个分区可定为单类变量区、二类变量区或三类变量区.3.每个交界线上的位移和力的连接条件可以放宽.这个原理为非协调元的厚板有限元法提供理论基础.各种厚板有限元模型可看作这个原理的特殊应用.特别是弹性厚板分区混合变分原理的提出为分区混合有限元法应用于厚板问题打下了基础.Abstract: In this paper, the subregion generalized variational principle for elastic thick plates is proposed. Its main points may be stated as follows:1. Each subregion may be assigned arbitrarily as a potential region or complementary region. The subregion variational principles of potential energy, complementary energy and mixed energy represent three special forms of this principle.2. The number of independent variational variables in each sub-region may be assigned arbitrarily. Any one of the subregions may be assigned as a one-variable-region, two-variable-region or three-variable-region.3. The conjunction conditions of displacements and stresses on each interline of neighbouring subregions may be relaxed. On the basis of this principle the finite element analysis of non-conforming elements for thick plates can be formulated.Different finite element models for thick plates can be obtained by different applications of this principle. In particular,the subregion mixed variational principle for thick plates may be applied to formulating the subregion mixed finite element method for thick plates.
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[1] 钱伟长,《变分法及有限元》(上册),科学出版社,(1980). [2] 胡海昌,《弹性力学的变分原理及其应用》,科学出版社,(1981). [3] Washizu,K.,Varsattonal材ethod s:,Elasticity and Plasticity,Pergamon Press,(1975). [4] 钱伟长,非协调元和广义变分原理,合肥有限元邀请学术报告会论文,(1981), [5] 龙驭球,弹性力学中的分区厂义变分原理,上海力学,2,2(1981),1-9. [6] 龙驭球,弹性薄板的分区广义变分原理,《应用数学和力学论文集》,(待出版). [7] 龙驭球,支秉垛,匡文起,单建,分区混合有限元法计算应力强度因子,力学学报,4(1982).
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