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A fuzzy finite element algorithm based on response surface method for free vibration analysis of structure

This paper introduces an improved response surface-based fuzzy finite element analysis of structural dynamics. The free vibration of structure is established using superposition method, so that fuzzy displacement responses can be presented as functions of fuzzy mode shapes and fuzzy natural frequencies. Instead of direct determination of these fuzzy quantities by modal analysis which will involve the calculation of the whole finite element model, the paper proposes a felicitous approach to design the response surface as surrogate model for the problem. | Vietnam Journal of Mechanics, VAST, Vol. 37, No. 1 (2015), pp. 17 – 27 DOI:10.15625/0866-7136/37/1/3923 A FUZZY FINITE ELEMENT ALGORITHM BASED ON RESPONSE SURFACE METHOD FOR FREE VIBRATION ANALYSIS OF STRUCTURE Nguyen Hung Tuan1,∗ , Le Xuan Huynh2 , Pham Hoang Anh2 1 Hanoi Community College, Vietnam 2 National University of Civil Engineering, Hanoi, Vietnam ∗ E-mail: hungtuan161@gmail.com Received April 22, 2014 Abstract. This paper introduces an improved response surface-based fuzzy finite element analysis of structural dynamics. The free vibration of structure is established using superposition method, so that fuzzy displacement responses can be presented as functions of fuzzy mode shapes and fuzzy natural frequencies. Instead of direct determination of these fuzzy quantities by modal analysis which will involve the calculation of the whole finite element model, the paper proposes a felicitous approach to design the response surface as surrogate model for the problem. In the design of the surrogate model, complete quadratic polynomials are selected with all fuzzy variables are transformed to standardized fuzzy variables. This methodology allows accurate determination of the fuzzy dynamic outputs, which is the major issue in response surface based techniques. The effectiveness of the proposed fuzzy finite element algorithm is illustrated through a numerical analysis of a linear two-storey shear frame structure. Keywords: Fuzzy finite element method, response surface method, surrogate model, free vibration analysis. 1. INTRODUCTION Fuzzy finite element method (FFEM) is an extension of finite element method (FEM) in the case that the input quantities in the finite element model such as load, material properties, stiffness of supports, connections, contain incomplete, none-clear parameters, which are described in the form of fuzzy numbers. In recent years, there is an increasing focus on the development of FFEM, first for static analysis and then extended in .