GENERALIZED HAMILTON VARIATIONAL PRINCIPLES FOR NON-LINEAR ANALYSES OF BEAM-COLUMN STRUCTURES

摘要

In this paper, the generalized Hamilton variational principles for non-linear analyses of Timoshenko-type and Euler-type beam-column structures are established in general case, and consequently, the corresponding mathematical models can be presented correctly, including coupling non-linear partial differential equations of motion with variable coefficients, the boundary conditions and the initial conditions. In the present work, the geometrical and material property of structures as well as the loads may be all arbitrary, except assumed that the cross-section is symmetrical about the inertia axes and the loads acting on the structure are conservation. In addition, the inertia of the neutral layer and rotation is considered as well. The generalized variational principles and mathematical models presented in the paper are the foundations for the correct theoretical analyses and numerical calculations of beam-column structures.