Dynamic Analysis of Structures Using the Finite Element Method

Abstract

In the preceding chapters, we considered the dynamic analysis of structures modeled as beams, frames, or trusses. The elements of all these types of structures are described by a single coordinate along their longitudinal axis; that is, these are structures with unidirectional elements, called, “skeletal structures.” They, in general, consist of individual members or elements connected at points designated as “nodal points” or “joints.” For these types of structures, the behavior of each element is first considered independently through the calculation of the element stiffness matrix and the element mass matrix. These matrices are then assembled into the system stiffness matrix and the system mass matrix in such a way that the equilibrium of forces and the compatibility of displacements are satisfied at each nodal point. The analysis of such structures is commonly known as the Matrix Structural Method and could be applied equally to static and dynamic problems.