Chien Wei-zang. Classification of Variational Principles in Elasticity[J]. Applied Mathematics and Mechanics, 1984, 5(6): 765-770.
 Citation: Chien Wei-zang. Classification of Variational Principles in Elasticity[J]. Applied Mathematics and Mechanics, 1984, 5(6): 765-770.

# Classification of Variational Principles in Elasticity

• Publish Date: 1984-12-15
• In this paper, variational principles in elasticity are classified accordiag to the differences is the constraints used in these principles, It is shown in a previous paper[4] that the stress-strain relations are the constraint conditions in all these variational principles, and can not be removed by the method of liaear Lagrange multiplier.The other possible constraats are four of them:(1)equations of equilibrium,(2)Strain-displacement relations,(3)boundary conditions of given external forces and boundary conditions of given boundary displacements. In variational principles of elasticity, some of them have only one kind of such constraints, some have two kinds or three kinds of constraints and at the most four kinds of constraints. Thus, we have altogether 15 kinds of possible variational principles, However, for every possible variatioaal prineiple, either the strain energy density,or the complementary energy density may be used, Hence, there are altogether 3p classes of functionals of variational principles in elasticity. In this paper, all these functionals are tabulated in detail.
•  [1] 胡海昌,《弹性力学中的变分原理及其应用》,科学出版社(1981). [2] 胡海昌,弹性力学变分原理简介,北京力学学会印(1982年10月). [3] 钱伟长,高阶拉氏乘子法和弹性理论中更一般的广义变分原理,应用数学和力学.,2(1983),137-150. [4] 钱伟长,再论弹性力学中的广义变分原理—就等价定理问题和胡海昌先生商榷.力学学报.4(1983).325-340.

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