A treatise on nonlinear finite element analysis

Abstract

The use of the finite element method of structural analysis in geometrically and materially nonlinear applications is described in this work. The basic equations of continuum mechanics required for the use of this analysis procedure are documented and, in many instances, explicitly derived. The matrix displacement method of finite element analysis is considered, first of all, as applied using linear theory. The extension of this technique to nonlinear applications follows for both static and dynamic behavior. It is this emphasis on nonlinear phenomena which contains the primary contributions of this endeavor. Consistent presentations of the general equations of equilibrium are in each case, followed by specialization of these complex compressions to physically understandable problems. Extensive consideration is given the numerical procedures which may be employed to determine solutions to the structural equations of motion. The relative advantages and disadvantages of using each available procedure are documented along with the classes of problems in which each technique has proven efficient. Applications of the finite element method in studies of nonlinear phenomena are described for both static and dynamic responses. This work is characterized by an emphasis upon understanding the assumptions and limitations imposed upon structural analyses by the basic equations, computational procedure and the solution procedure employed in computer codes for nonlinear analyses. In this respect, this treatise represents, at the present time, the only readily usable, extensive treatment of nonlinear finite element analysis procedures.