| Title |
Analytical Solutions for The Maximum and Limit States of The Elementary Dynamic Elastoplastic Systems Subjected to Step Forces |
| Keywords |
analytical solutions ; maximum state ; limit state ; dynamic elastoplastic system ; step force ; |
| Abstract |
Analytical solutions for the maximum and limit states of the elementary dynamic multi-axial elastoplastic system subjected to step forces are presented. These are the extension to the full analytical solutions, given by the author, for the single-degree-of-freedom (SDOF) uniaxial elastoplastic system. In this paper we introduce new dynamic MDOF elastoplastic system having one multi-axial slider. The maximum and limit states of this system are derived directly using the analytical solutions of the dynamic SDOF uniaxial system and the evolution of the system subjected to step forces. The behavior of the assembly composed of elementary dynamic elastoplastic systems having one- or multi-axial slider is studied. A new approach to the direct evaluation for the maximum and limit states is then proposed. This allows generalizing the direct method, which was proposed by Lee and Zarka and is applicable only to structures locally uniaxial, for general structures. Only two or three static elastic analyses allow to obtain the residual stresses, plastic strains, and inelastic displacements of the maximum and limit states of the structures, resulting in a drastic saving in computation times and costs during inelastic dynamic analysis. |