The Earthquake Engineering Online Archive

Solution strategies for statically loaded nonlinear structures

Simons, Jeffrey W.; Powell, Graham H.

UCB/EERC-82/22, Earthquake Engineering Research Center, University of California, Berkeley, 1982-11, 110 pages (510/S56/1982)

This investigation aims at developing a reliable and substantially automatic solution strategy for a wide variety of statically loaded nonlinear structures. A framework for nonlinear static solution strategies, based on Newton-Raphson iteration, is developed. The framework consists of four computational tasks: linearization, displacement prediction, state determination, and convergence checking. These tasks are performed in an advancing phase and a correcting phase. Currently available solution strategies are shown to differ in the way particular tasks are performed. The strategies considered include modified Newton methods, quasi-Newton methods, displacement-controlled iteration, techniques for variable load step selection, and event-to-event strategies. Finally, a general solution strategy is described that includes as options most existing schemes as well as certain new schemes. This strategy permits analysis by either loadcontrolled or displacement-controlled methods, with flexibility in the choice of controlling parameters. The general solution strategy has been incorporated into the ANSR-III computer program and tested on a series of four example problems. Three of the examples involve buckling of truss structures, and the fourth involves crushing of a pipe between two platens. It is concluded that the solution strategy is reliable and efficient for a wide variety of strongly nonlinear problems.

Available online: http://nisee.berkeley.edu/documents/EERC/EERC-82-22.pdf (2 MB)