Abstract
Abstract In this paper, a fuzzy finite element algorithm is investigated to determine static responses of plane structures. This algorithm concerns finite element method, fuzzy sets theory, and response surface method. Firstly, the notion of a standardized triangular fuzzy number is developed and utilized to replace original fuzzy numbers in the surrogate models. Then, the error estimations between the training and the test sets are performed to select the suitable response surface model amongst the regression models. Lastly, a good performance combination of complete and non-complete quadratic polynomial regression models is proposed to define the responses of structures. The merits of the proposed algorithm are illustrated via numerical examples.
Highlights
A good performance combination of complete and non-complete quadratic polynomial regression models is proposed to define the responses of structures
Fuzzy finite element method (FFEM) is the combination of finite element method (FEM) and fuzzy sets theory [1] to define the responses of structures in the case that the input quantities such as loads, material and geometry properties, stiffness of supports, contain incomplete information, which is described in the form of fuzzy numbers
Fundamental strategies of FFEM can be categorized into main groups as follows: the interval arithmetic approach for static analysis of structures [2,3,4,5,6,7,8], the optimization strategy for static and dynamic analysis of structures [9,10,11,12,13,14,15,16,17,18,19,20], the combination of interval arithmetic and optimization strategy for dynamic analysis of structures [21,22,23], applying perturbation method [24] in the stochastic finite element methods [25] for fuzzy analysis of structures [26,27,28]
Summary
Fuzzy finite element method (FFEM) is the combination of finite element method (FEM) and fuzzy sets theory [1] to define the responses of structures in the case that the input quantities such as loads, material and geometry properties, stiffness of supports, contain incomplete information, which is described in the form of fuzzy numbers. The publications [16, 17] applied RSM to define fuzzy displacement for static analysis and fuzzy natural frequency [16], fuzzy envelope frequency functions for dynamic analysis [17] In those works, all original fuzzy variables are presented in the surrogate model. Co-linearity can occur as the fuzzy variables are correlated to each other To overcome these drawbacks, the study [19] presented a notion for the standardized fuzzy variable of symmetric triangular fuzzy numbers and an algorithm for calculating fuzzy displacements of free vibration analysis. Based on the response surface method, this paper proposes a fuzzy finite element algorithm to determine both fuzzy displacements and fuzzy internal forces for static analysis of plane structures when the input quantities are general triangular fuzzy numbers.
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