Solution Techniques for Linear and Nonlinear Dynamics of Structures Modeled Finite Elements

Dynamic analysis is rapidly becoming a common consideration in the design of structures, especially in determining response to earthquake ground motions. Methods for linear dynamic analysis of complex structures (where the material is assumed to be linearly elastic and displacements are small) were developed during the last two decades and are now well known. However, in many cases inelastic behavior of structures must be taken into account in order to obtain an economic and safe design. Nonlinear dynamic analysis of structures is a rather new field, and many researchers are actively investigating different aspects of the subject. Some of the important applications of nonlinear analysis are found in the design of missiles, aircraft, nuclear reactors, transportation vehicles, multi-story buildings located in seismic regions, etc.

Dynamic analysis of complex structures by the finite element method is performed in two major steps. The first is to develop a finite number of equations of motion, and the second step is to solve these equations for the response at the nodes and the stresses within the elements. For large problems with several hundreds (or thousands) of degrees of freedom, the selection of an efficient algorithm for solving the equations of motion becomes a very important factor. This is especially true for nonlinear analysis, for which the cost of computations is an order of magnitude higher than that for linear analysis.