Nonlinear dynamic analysis of frames with isotropic and kinematic hardening/softening. (1st June 2020) - Mohammadzadeh, S.; Moharrami, H.
Highlights: The solution time is much (about 100 times) less than other classical methods. The method is not iterative and does not have convergence criterion to meet. The accuracy is improved marginally compared to the time integration-based methods. Linear yield surface and constant time steps are the only approximations. The method is able to model the hardening and softening properties of materials. Longer time steps have less effect on the accuracy compared to the other methods. Abstract: Static nonlinear analysis of frames and plane stress/strain structures via mathematical programming algorithms has been addressed by many researchers. It has been shown that the method of Dissipated Energy Maximization (DEM) is an efficient algorithm for nonlinear static analysis. This study extends the application of DEM method to the nonlinear dynamic analysis of frames considering bending moment-axial force interaction. The nonlinear static analysis algorithm that is the basis of nonlinear dynamic analysis, and corresponding assumptions including linear-kinematics, lumped-plasticity, piecewise-linear yield function, and the associated flow rule are briefly explained. The dynamic analysis that is carried out by Duhamel integral method is fully formulated. The proposed method traces the nonlinear equilibrium path through a linear mathematical programming process and makes modifications on response of Duhamel's integral to yield the nonlinear response. In addition, the Bauschinger effect (kinematic hardening) is included in the formulations to get more realistic responses. Several examples illustrate the efficiency and accuracy of the proposed method. It has been shown that the method is the most accurate and fastest algorithm compared to conventional methods of nonlinear dynamic analyses.