This paper presents a practical approach based on High Dimensional Model Representation (HDMR) for analysing the response of structures with fuzzy parameters. The proposed methodology involves integrated finite element modelling, HDMR based response surface generation, and explicit fuzzy analysis procedures. The uncertainties in the material, geometric, loading and structural parameters are represented using fuzzy sets. To facilitate efficient computation, a HDMR based response surface generation is employed for the approximation of the fuzzy finite element response quantity. © 2011 Indian Academy of Sciences.

B. N. Rao

Department Of Civil Engineering

EXPLICIT FORMULATION

Finite element

Fuzzy analysis

HIGH DIMENSIONAL MODEL REPRESENTATION

Response surface

Fuzzy sets

Structural analysis

Surface Properties

Surfaces

Uncertainty analysis

finite element method

Fulltext

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Sadhana - Academy Proceedings in Engineering Sciences

This paper presents an efficient probabilistic analysis method for predicting component reliability of structural/mechanical systems subject to random loads, material properties, and geometry. The proposed method involves High Dimensional Model Representation (HDMR) for the limit state/performance function approximation and fast Fourier transform for solving the convolution integral. The limit state/performance function approximation is obtained by linear and quadratic approximations of the first-order HDMR component functions at most probable point. In the proposed method, efforts are required in evaluating conditional responses at a selected input determined by sample points, as compared to full-scale simulation methods. Therefore, the proposed technique estimates the failure probability accurately with significantly less computational effort compared to the direct Monte Carlo simulation. The methodology developed is applicable for structural reliability estimation involving any number of random variables with any kind of distribution. The accuracy and efficiency of the proposed method is demonstrated through five examples involving explicit/implicit performance functions.

International Journal of Computational Methods in Engineering Science and Mechanics

Probabilistic analysis using high dimensional model representation and fast fourier transform

High dimensional model representation (HDMR) approximates multivariate functions in such a way that the component functions of the approximation are ordered starting from a constant and gradually approaching to multivariance as we proceed along the terms like first-order, second-order and so on. Until now HDMR applications include construction of a computational model directly from laboratory/field data, creating an efficient fully equivalent operational model to replace an existing time-consuming mathematical model, identification of key model variables, global uncertainty assessments, efficient quantitative risk assessments, etc. In this paper, the potential of HDMR for tackling univariate and multivariate piece-wise continuous functions is explored. Eight numerical examples are presented to illustrate the performance of HDMR for approximating a univariate or a multivariate piece-wise continuous function with an equivalent continuous function. Copyright © 2007 John Wiley & Sons, Ltd.

Communications in Numerical Methods in Engineering

High dimensional model representation for piece-wise continuous function approximation

Mathematical Models and Computer Simulations

On derivative-based global sensitivity criteria

International Journal for Numerical Methods in Engineering

Nonparametric probabilistic approach of uncertainties for elliptic boundary value problem

Computers & Structures

Application of fuzzy numerical techniques for product performance analysis in the conceptual and preliminary design stage

Efficient explicit formulation for practical fuzzy structural analysis

Journal	Sadhana - Academy Proceedings in Engineering Sciences
ISSN	02562499
Open Access	Yes