Theoretical framework and engineering applications of Hamiltonian Structural Analysis Method

摘要

The theoretical framework and engineering applications of the Hamiltonian Structural Analysis Method are presented. The proposed method, which allows to solve the structural elastic problem, is based on the solution of a Hamiltonian system made of 1st order differential equations. This method, which is a new way to approach a classical variational problem, leads to the definition of the Hamiltonian system for any elastic problem, by introducing the degrees of freedom and the corresponding compatibility equations, founding equilibrium equations in variational form. In the frame of the General Beam Theory, beam on elastic soil, thin-walled structures with non-uniform torsion, distortion and shear lag as well as temperature distributions inside the sections and other problems can be solved directly, by founding the expression of the Hamiltonian function and by approaching the variational formulation. This fact allows engineers to find the exact solution, based on the system of differential equations of the elastic problem, for straight and curved beams. Numerical applications and validation examples compared to literature data are given in order to show the wide range of applicability of the proposed method.