两相邻边固定两相邻边简支弹性薄板的两类变量广义变分原理

按照广义力和广义位移之间的对应关系,将弹性薄板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,进而建立两相邻边固定两相邻边简支弹性薄板的两类变量广义势能原理。通过代入另一类本构关系,再应用类似如上的方法,建立两相邻边固定两相邻边简支弹性薄板的两类变量广义余能原理。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的势能原理和余能原理。最后,应用两类变量广义余能原理求解弹性薄板的挠度。

Generalized Variational Principles of Two Kinds of Variables for Elastic Thin Plate with Two Adjacent Edges Clamped and the Other Two Adjacent Edges Simply Supported

According to the corresponding relations between generalized forces and generalized displacements, the balancing and geometrical equations of elastic thin plate 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 of two kinds of variables for elastic thin plate with two adjacent edges clamped and the other two adjacent edges simply supported are established. Through substituting another constitutive relation, using similar methods as above, the generalized complementary energy principles of two kinds of variables for elastic thin plate with two adjacent edges clamped and the other two adjacent edges simply supported are also formed. The two generalized variational principles with two kinds of variables are degenerated into potential energy principles and complementary energy principles of elastic thin plate. At last, the deflection of elastic thin plate is calculated by generalized complementary energy principles with two kinds of variables.