弹性薄板大挠度问题两类变量的广义变分原理

Generalized Variational Principles for Two Kinds of Variables of Elastic Thin Plate with Large Deflection

应用变积方法,按照广义力和广义位移之间的对应关系,将弹性薄板大挠度问题的平衡方程和几何方程乘上相应的虚量,然后积分,代数相加,代入本构关系,建立弹性薄板大挠度问题两类变量的广义势能原理。通过代入另一类本构关系,再应用类似如上的方法,建立弹性薄板大挠度问题两类变量的广义余能原理。再将这两种两类变量的广义变分原理分别退化到弹性薄板大挠度问题的势能原理和余能原理。

According to the corresponding relations between generalized forces and generalized displacements, the balancing and geometrical equations of elastic thin plate with large deflection are multiplied by corresponding virtual quantities, integrated and then added algebraically. Proceeding to the next step, by substituting constitutive relation, the generalized potential energy principles for two kinds of variables of elastic thin plate with large deflection are established by the variational integral method. Through substituting another constitutive relation and using the similar methods as above, the generalized complementary energy principles are also given. The two generalized variational principles with two kinds of variables are degenerated into potential energy principles and complementary energy principles for elastic thin plate with large deflection.