DYNAMIC RELAXATION METHOD FOR TRACING THE STATICAL PATH OF TRUSS STRUCTURES

  M. Rezaiee-Pajand1 , * , J. Alamatian2     1. Professor, Department Civil Engineering , Ferdowsi Univ. of Mashhad   2. Department Civil Engineering , Islamic Azad University , Mashhad Branch   * Corresponding Author: mrpajand@yahoo.com     Abstract   The load-displacement curve can be utilized for studying the structural behaviors. This curve may have two parts. In the first section, the geometrical stiffness is positive and the structure resists versus applied loads. On the other hand, the load capacity of structure reduces considerably when the geometrical stiffness becomes negative, i.e. the second part of the load-displacement curve. This behavior causes the snap-though and snap-back regions. In this paper, Dynamic Relaxation (DR) method is utilized to trace the snap-though and snap-back regions. Since the common DR method is not able to present such regions, a new formulation based on minimization of the residual force and minimization of the residual displacement will be proposed. These formulations are completely automatic and consistent with DR iterations. For numerical verification, some truss structures with elastic large deformation nonlinear behavior, are analyzed. Results show that the suggested formulation increase the efficiency of DR procedure so that DR scheme can be successfully utilized for structures with snap-though and snap-back regions.