NONLINEAR DYNAMIC RESPONSE OF HARDENING, SOFTENING AND ELASTOPLASTIC SDOF SYSTEMS USING GENERALIZED SINGLE STEP ALGORITHMS WITH NEWTON - RAPHSON ITERATIONS

Abstract eng:
The dynamic equation of motion of a SDOF system with a nonlinear elastic hardening spring, a SDOF system with a nonlinear elastic softening spring and a SDOF system with a nonlinear elastic-plastic spring is integrated numerically using a family of linear generalized single step-single solve algorithms. For this purpose, these algorithms are extended by using a Newton-Raphson type iterative procedure in each time step to ensure dynamic equilibrium. After a literature review of the available time integration schemes used for nonlinear problems, the linear family of algorithms is presented along with several common time integration algorithms as special cases of the generalized algorithm. An explicit flowchart is given showing the integration procedure used in the present study. The modified algorithm is applied to the aforementioned three types of SDOF systems and results concerning phase portraits, (relative) energy decrease, iterations needed for equilibrium and internal force - displacement curves are presented. It is shown that the algorithms with optimal numerical dissipation and dispersion perform in general better than others, and that from the algorithms with optimal numerical dissipation and dispersion, only the one with zero-displacement and zero-velocity overshooting behavior can capture efficiently the elastoplastic dynamic response.

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