弹性力学广义变分原理的应用条件

研究了在弹性力学的三类变量广义变分原理中 ,变量σij,εij和ui 是否独立 ,是否包含了应力应变关系 .指出了在应用广义变分原理时应满足下列条件 :泛函中的应变能用应变表示 ,应变余能用应力表示 ;在用广义变分原理求实际问题的近似解时 ,三类变量的试探函数可以独立选择 ,但各类变量之间应不违背力学基本关系 .

具有约束条件的变分不等式的可行的增广拉格朗日方法

采用增广拉格朗日方法求解了具有约束条件的变分不等式问题,并证明了这一方法的全局收敛性.运用增广拉格朗日方法和非精确的半光滑牛顿法求解了具有约束条件的变分不等式的一类子问题.我们给出了四个数值算例以说明这一方法的可行性.

Variational Approach of Timoshenko Beams with Internal Elastic Restraints

An exact approach for free transverse vibrations of a Timoshenko beam with ends elastically restrained against rotation and translation and arbitrarily located internal restraints is presented. The calculus of variations is used to obtain the equations of motion, the boundary conditions and the transitions conditions which correspond to the described mechanical system. The derived differential equations are solved individually for each segment of the beam with the corresponding boundary and transitions conditions. The derived mathematical formulation generates as particular cases, and several mathematical models are used to simulate the presence of cracks. Some cases available in the literature and the presence of some errors are discussed. New results are presented for different end conditions and restraint conditions in the intermediate elastic constraints with their corresponding modal shapes.