A force analogy method (FAM) assessment on different static condensation procedures for frames with full Rayleigh damping

Abstract

In this paper, influence of different static condensation methods on nonlinear time history response of structures in presence of full Rayleigh damping matrix has been studied. Equation of motion is derived in details for 2 newly introduced cases; Full Static Condensation Model and Reduced Static Condensation Model (RSCM or RSCM-1). Nonlinear analyses are performed with state-space form of equation of motion along with force analogy method. A novel aspect of this study in comparison with previous researches is to consider full Rayleigh damping in formulations for static condensation in nonlinear structural analysis. Numerical examples are presented for the proposed methods. In addition, the same structure was modeled in finite element method and analyzed by the OpenSEES program. Comparisons demonstrate that results, which are obtained from introduced methods in this article, are in good agreement with the finite element method results. In addition to explaining the equation derivations in main article, proofs for some equations have been demonstrated in appendices. The comparisons show that both RSCM and Full Static Condensation Model lead to almost the same results but in case of using RSCM-1, the responses have some deviation from other condensation methods. KEYWORDS force analogy method (FAM), FSCM, RSCM, static condensation, nonlinear dynamic analysis, Rayleigh damping 1 | INTRODUCTIONAt the beginning of using computers in structural analysis, dynamic and time history analyses were performed only in linear elastic fields. By improvements in computer abilities, the possibility of nonlinear structural analysis in computer programs became more applicable. Finite element method (FEM) was widely used for this purpose, and many researches and developments have been introduced for this method during past years.Lin [1] proposed another method almost at the same time of introduction of FEM. It was called force analogy method (FAM). FAM has not become as popular as FEM, [2] although it has many advantages and abilities. In recent years, FAM took attention again and has been used for nonlinear dynamic analysis of frames in some researches. [2][3][4] FAM is also used for solving other kinds of nonlinear problems. Collapse of structures with nonlinear modal analysis, [5] concrete shear walls, [6] energy in structures and damage indexes, [7] structural control, [8] and modeling the influence of corrosion on structural behavior through pushover analysis [9] are some examples for using it recent studies.Different from nonlinear FEM, stiffness matrices remain unchanged during nonlinear analysis process of FAM. This is one of the greatest advantages of FAM in comparison with equivalent calculations in FEM. [4] Stiffness matrices must be recalculated in each time step during nonlinear stage in FEM. Therefore, using FAM instead of FEM can greatly reduce the costs of nonlinear analysis.The importance of Rayleigh damping was investigated by Erduran. [10] He found out that "mass-proportional" damping will lead to high damping force...

Instability load analysis of a telescopic boom for an all-terrain crane

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A study on the accuracy of force analogy method in nonlinear static analysis

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