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.
ABSTRACT. Based on the results of A. D. Rzanitsin and V. D . Raizer in the referencesof [l] and [2], this paper gives other definitions of the confidence level of subjected loads f3s and the confidence level of the strength of materials f3R, then studies the relationship between the load factor k, the material factor m and the safety factor n in the traditional models with the factors of f3s, f3R and (3 in the random models in the structural design. The research results show that physical meaning of two factors of f3s, f3R is the same as the factors of k and m, however it gives more clearly assessements on effects of the over load state and the material inhomogeneous state of the safety working state of the structures. Since the reliability -safety set is also determined from the research results. Some numerical examples are carried out to show the relationship between these above factors.
This article presents an approach to assess safety levels of structures. A new formula for determining the fuzzy reliability of structures is proposed for the case where the set of loading effect and set of structural durability are general fuzzy sets. Illustration example concerning the bending strength evaluation of a simple-beam structure, is presented with the choice of triangular fuzzy sets for loading effect and structural durability.
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