有限位移理论线弹性动力学二类和三类混合变量的最小势作用量原理和驻值余作用量原理及其应用

Abstract

2 new concepts, potential action and complementary action, were first introduced into the variational principles for linear elastodynamics. On the basis of the concept of potential action, the principle of minimum action (Hamilton’s principle) was renamed to the principle of minimum potential action. In terms of the concept of complementary action, the principle of stationary complementary action was proposed for the first time. Next, the principles of minimum potential action and stationary complementary action with dual mixed variables of displacement and stress were derived in view of the boundary condition changes by means of the reciprocal theorem. And then, through the application of the relations between the strain energy density and the complementary energy density to the above 2 principles with dual mixed variables, the principles of potential action and complementary action with triple mixed variables of displacement, stress and strain were derived. Finally, the generalized principles of potential action and complementary action were given with the Lagrange multiplier method, in the meantime, the principle of minimum potential action with dual mixed variables of large deflection beams was applied to the calculation of a bending cantilever beam under forced vibration.