Implementation of a unified library of solvers for nonlinear structural analysis

Abstract

The nonlinear analysis of structural systems is a well known field among structural engineers and researchers. A large variety of solution schemes exists nowadays in literature each one with their advantages and disadvantages but none is suitable for all nonlinear problems and for different types of nonlinearities. Analysis tools have to be able to trace the full equilibrium path in order to so they have to include more than one solution scheme. As most of the control schemes can be written under the form of a constraint equation a unified framework allows the implementation of several control methods with the same algorithm enabling the user to choose the method that bests suits their nonlinear problem. In this work a unified library of nonlinear solver schemes developed by other authors is implemented in a finite element environment. The library has the ability to introduce different nonlinear solution schemes with the same algorithm by means of a unified framework. Four control methods: load, displacement work and arc-length are presented and their limitations and capabilities are announced. Finally the library is tested through simple application examples and conclusions are presented.