A Study on the Random Elastic Behaviour of Bar Structures

ABSTRACT

Elastic response of bar structures is governed by input parameters of random nature; two of these variables are loading and material properties. To account for the uncertainty of selected parameters in any general structural analysis, probabilistic modelling is necessary. This paper develops a Monte Carlo method of analysis for predicting elastic response of bar structures due to random loading, and the uncertainty of the elastic moduli and section properties. Each random variable is modelled by a symmetric beta distribution. An example is included to illustrate this method.

INTRODUCTION

The application of probabilistic techniques to modelling various uncertainty aspects in structural analysis has become relatively frequent in recent years. Examples of such approaches can be found in works by Cambou (1975), Spanos (1988) and Melerski (1988, 1992). The design data parameters that may exhibit significant randomness are loading and material properties of structural elements. Incorporating these random variables in modelling the elastic response of any bar structure results in output predictions (deflections, moments, reactions, etc.) being of a probabilistic format. Based on these and the assumed probability density functions, upper and lower limits of the considered structural response fields can then be evaluated for design purposes.

Following on from the work by Koutsoukis and Melerski (1996), this paper sets out to further develop probabilistic techniques for predicting the elastic response of bar structures. A linear first-order structural analysis is employed as the basic deterministic method and coupled with a Monte Carlo simulation to account for the probabilistic nature of the problem. Each random parameter is modelled by a symmetric beta distribution. The Monte Carlo method is then modified by employing a variance reduction technique which allows for more reliable predictions whilst using a smaller sample space (i.e. simulation analysis times are reduced). An example is included to illustrate results from the modified Monte Carlo method. These results are then compared with those obtained by a standard Monte Carlo approach in Koutsoukis and Melerski (1996).

Although in the present work only two random quantities are being dealt with, the method can easily be extended to include more data parameters of distinct probabilistic properties. It must, however, be borne in mind that this could lead to significant computation time requirements.

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A Study on the Random Elastic Behaviour of Bar Structures