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

Abstract

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.

Một chương trình phân tích kết cấu mờ ứng dụng dựa trên xấp xỉ Taylor bậc nhất

“…Các mô hình xấp xỉ yêu cầu khối lượng tính toán ít hơn mô hình tính phức tạp ban đầu. Một số nghiên cứu gần đây theo hướng sử dụng mô hình thay thế trong phân tích mờ có thể tìm thấy trong các tài liệu [7][8][9][10][11][12][13][14][15]. Cần lưu ý rằng, độ chính xác của các phương pháp này hoàn toàn phụ thuộc độ chính xác của mô hình thay thế.…”

A fast fuzzy finite element approach for laterally loaded pile in layered soils

“…(2) can be numerical demanding. In order to reduce the computational burden, researchers have focused on efficient procedures to reduce the number of function evaluations in performing these optimization problems [8,10,11].…”

“…In recent years, non-probabilistic FE methods based on fuzzy set theory have been introduced to the analysis of uncertain structural systems. The fuzzy FE methods have been applied for both static and dynamic analysis of various structures [8][9][10][11]. In this paper, an efficient fuzzy FE approach is developed to analyze the response of laterally loaded pile in multi-layer soils.…”

Fuzzy Finite Element Analysis for Static Responses of Plane Structures

“…In recent years, a large number of FFEM have been proposed, from static analysis to extension in dynamic analysis of structures. Fundamental strategies of FFEM can be categorized into main groups as follows: the interval arithmetic approach for static analysis of structures [2-8], 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]. In which, applying the response surface method (RSM) [29] is presented by [16,17] based on optimization techniques is extremely valuable in the fuzzy analysis of structures.…”

“…Besides that, 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. The publication [30] used this notion for the stability problem of steel frame with fixity factor modeled as a symmetric triangular fuzzy number.…”