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In this research a new approach is proposed for elasto-plastic analysis of structures with truss elements. This method covers both perfectly plastic and hardening properties. The Proposed technique uses substituting virtual loads instead of modifying the stiffness matrix. To solve this kind of problems, complementary programming is utilized. Numerical examples demonstrate that elastoplastic analysis by this approach has very good convergence, rapidity, and accuracy.

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In this paper, a new enhanced version of the Particle Swarm Optimization (PSO) is presented. An important modification is made by adding probabilistic functions into PSO, and it is named Probabilistic Particle Swarm Optimization (PPSO). Since the variation of the velocity of particles in PSO constitutes its search engine, it should provide two phases of optimization process which are: exploration and exploitation. However, this aim is unachievable due to the lack of balanced particles’ velocity formula in the PSO. The main feature presented in the study is the introduction of a probabilistic scheme for updating the velocity of each particle. The Probabilistic Particle Swarm Optimization (PPSO) formulation thus developed allows us to find the best sequence of the exploration and exploitation phases entailed by the optimization search process. The validity of the present approach is demonstrated by solving three classical sizing optimization problems of spatial truss structures.

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The purpose of this study is to determine the effect of vierendeel panel width and vertical truss spacing ratio in an inelastic behavior of the STF system due to earthquake loads. The STF system is applied to a six-storey building that serves as apartments [2]. The STF system is used in the building in the transverse direction (N-S direction), while in the longitudinal direction (W-E direction) the building system uses the special moment resisting frame. The structural behavior was evaluated using nonlinear pushover and time history analyses. The results showed that by increasing the ratio of vierendeel panel width and vertical truss spacing, the ductility of the structure was increased. Based on the performance evaluation, the ratio of the vierendeel panel width and vertical truss spacing on the STF buildings that provided satisfactory performance was more or equal to 1.6. The ultimate drift obtained from non-linear time history analysis was smaller than the pushover analysis. This result showed that the static nonlinear pushover analysis was quite conservative in predicting the behavior of the six-storey building in an inelastic condition.