弹性力学变分原理间的等价和变量独立性问题的探讨

Discussion on Equivalance and Indpendence of Variables between Variational Principles in Elasticity

本文通过对位能原理泛函的变分，使平衡方程和应力应变关系以欧拉方程形式出现，再用拉氏乘子法解除其它所有约束，最后得到胡－鹫原理的泛函；用同样的方法，从余能原理的泛函推得Ｈ－Ｒ原理泛函的过程中，了解到驻值方程的出现和约束条件的存在，在有条件的变分原理中具有灵活性。

In this paper, the functional of potential energy principle is variated to obtain equilibrium equations and constitutive relations which appear as Euler's equations. Then, alll other constrains are introduced by means of Lagrange multiplier, and the fundamental of Hu-Washizu principle which satisfies all the fundamental equations in elasticity is obtained. After that, the functional of Hellinge-Reissuer principle is obtained from complementary energy principle using the same method. In the end, discussion on equivalance and indepence of variables between H-W and H-R variational principles is carried out. In the above procedure, we can understand that appearance of stationary equations and the existance of constrant in variational principle with constraints.