The Earthquake Engineering Online Archive

Static and dynamic analysis of nonlinear structures

Mondkar, Digambar P.; Powell, Graham H.

UCB/EERC-75/10, Earthquake Engineering Research Center, University of California, Berkeley, 1975-03, 152 pages (530/M642/1975)

This report presents the theoretical and computational procedures which have been applied in the design of a general purpose nonlinear computer code for static and dynamic analysis of nonlinear structures. Using the principle of virtual displacements, incremental equations of motion for structures undergoing large displacements and strains are first derived, using the Lagrangian description of deformation. These equations of motion are then discretized using the finite element displacement formulation, and the element characteristics, including "linear" and "nonlinear" stiffness matrices, are derived for the particular case of a two-dimensional isoparametric finite element. Physical nonlinearity due to material behavior is introduced for elasto-plastic materials, and the constitutive laws for commonly used elasto-plastic models are described. A computational algorithm for state determination of such path dependent materials is presented. Various procedures for solution of the nonlinear equations are reviewed. An integration procedure for dynamic analysis, based on step-by-step methods with optional iteration, is described. Control parameters suitable for setting up a flexible solution strategy, as implemented in the general purpose computer code, are outlined. Results for a series of example analyses are presented to demonstrate the capabilities of the computer code and to investigate the stability and accuracy of various solution strategies.

Available online: http://nisee.berkeley.edu/documents/EERC/EERC-75-10.pdf (5 MB)