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大变形对称弹性理论的广义变分原理 总被引:1,自引:1,他引:0
本文以陈至达提出的变形几何非线性理论 ̄[1]为基础,应用Lagrange乘子法,对大变形对称弹性力学问题进行了研究,给出了相应的位能广义变分原理、余能广义变分原理,以及动力学问题的广义变分原理;同时,文中还证明了位能广义变分原理和余能广义变分原理的等价性。 相似文献
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本文除了给出三个弹性体系的泛函以外,重点在于建立以变分式形式出现的九个似变分原理,并将弹性理论问题中的各种变分原理,按其独立未知数的种类分成五种类型。从文中可以看到建立似变分原理要比构造泛函来得方便和广泛。最后,本文从似变分原理出发,求解弹性力学问题,从例题中可看到,直接从似变分原理出发求弹性力学问题的近似解,其运算十分方便明了。 相似文献
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In selecting rational types of underground structures resisting explosion, in order to improve stress states of the structural section and make full use of material strength of each part of the section, the research method of composite structures is presented.Adopting the analysis method of micro-section free body, equilibrium equations, constraint equations and deformation coordination equations are given. Making use of the concept of generalized work and directly introducing Lagrange multiplier specific in physical meaning,the validity of the constructed generalized functional is proved by using variation method.The rational rigidity matching relationship of composite structure section is presentedthrough example calculations. 相似文献
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GENERALIZEDVARIATIONALPRINCIPLESOFSYMMETRICALELASTICITYPROBLEMOFLARGEDEFORMATIONSZhaoYu-xiang(赵玉祥)GuXiang-zhen(顾祥珍)LiHuan-qiu... 相似文献
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In this paper,based on the mathematical theory of classical mechanics and Chen‘s theorem,the variational method is used in the study of large deformation symmetrical elasticity problems.The generalized variational principles of potential energy and complementary energy,based on the instantaneous configuration are obtained,and the equivalence between the two principles is proved.Besides,the generalized variational principles of dynamical problems based on the instantaneous configuration are also given. 相似文献
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文中以经典力学的数学理论和陈氏定理为基础,用变分的方法求解大变形对称弹性力学问题,得出了以瞬时位形为基准的位能广义变分原理和余能广义变分原理,以及两个变分原理的等价性;此外,还给出了以瞬时位形为基准的动力学问题的广义变分原理. 相似文献
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