Research on a Systematic Methodology for Theory of Elasticity
-
摘要: 证明了弹性力学求解体系的微分形式与积分形式的等价关系,建立了统一求解体系构架.新体系包括微分形式、积分形式及混合形式.利用微分形式与积分形式的等价关系,导出了各种变分原理.提出了广义虚功方程和广义虚函数的概念.Abstract: The equivalence between differential form and integral form of a systematic methodology for theory of elasticity is proved.A uniform framework of the systematic methodology is established.New system includes differential form,integral form and mixed form.All kinds of variational principles are proved by the equivalence between differential form and integral form.The idea for generalized virtual work and virtual function is presented.
-
Key words:
- theory of elasticity /
- variational principle /
- equation of virtual work
-
[1] 钱伟长,叶开沅.弹性力学[M].北京:科学出版社,1956. [2] 徐芝纶.弹性力学[M].北京:高等教育出版社,1990. [3] 武际可,王敏中.弹性力学引论[M].北京:北京大学出版社,1981. [4] Timoshenko S P.Theory of Elasticity[M].(Third Edition).New York:McGraw-Hill,1970. [5] 钱伟长.变分法及有限元[M].北京:科学出版社,1980. [6] 胡海昌.弹性力学中的变分原理[M].北京:科学出版社,1981. [7] Zienkiewicz O C.The Finite Element Method[M].(Third Edition).New York:McGraw-Hill,1977. [8] Kyuichiro Washizu.Variational Methods in Elasticity and Plasticity[M].(Second edition).Pergamon Press,1975. [9] 王勖成,邵敏.有限单元法基本原理与数值方法[M].北京:清华大学出版社,1988. [10] 冯康,石钟慈.弹性结构的数学理论[M].北京:科学出版社,1981. [11] 龙驭球.变分原理 有限元 壳体分析[M].沈阳:辽宁科学技术出版社,1987. [12] 龙驭球.有限元法概论[M].北京:人民教育出版社,1978. [13] 钟万勰.弹性力学求解新体系[M].大连:大连理工大学出版社,1995. [14] 钟万勰.条形域平面弹性问题与哈密尔顿体系[J].大连理工大学学报,1991,31(4):373-384. [15] 钟万勰.分离变量法与哈密顿体系[J].计算结构力学及其应用,1991,8(3):229-240. [16] 钟万勰.互等定理与共轭辛正交关系[J].力学学报,1992,24(4):432-437. [17] 钟万勰.哈密尔顿阵本征向量辛正交的物理意义[J].大连理工大学学报,1993,33(4):110-111. [18] ZHONG Wan-xie,Williams F W.Physical interpretation of the symplectic orthogonality of the eigensolutions of a Hamiltonian or symplectic matrix[J].Computers & Structures,1993,49(4):749-750. [19] ZHONG Wan-xie,Williams F W.On the direct solution of wave propagation for repetitive structures[J].J Sound & Vib,1995,181(3):485-501. [20] 钟万勰,徐新生,张洪武.Hamilton体系与弹性力学Saint-Venant问题[J].应用数学和力学,1996,17(9):781-789. [21] ZHONG Wan-xie,Williams F W.The eigensolutions of wave propagation for repetitive structures[J].Structural Engineering and Mechanics,1993,1(1):47-60. [22] 钟万勰.弹性平面扇形域问题及哈密顿体系[J].应用数学和力学,1994,15(12):1057-1066.
点击查看大图
计量
- 文章访问数: 2423
- HTML全文浏览量: 89
- PDF下载量: 894
- 被引次数: 0