Abstract
As a new formulation in structural analysis, Integrated Force Method has been successfully applied to many structures for civil, mechanical, and aerospace engineering due to the accurate estimate of forces in computation. Right now, it is being further extended to the probabilistic domain. For the assessment of uncertainty effect in system optimization and identification, the probabilistic sensitivity analysis of IFM was further investigated in this study. A set of stochastic sensitivity analysis formulation of Integrated Force Method was developed using the perturbation method. Numerical examples are presented to illustrate its application. Its efficiency and accuracy were also substantiated with direct Monte Carlo simulations and the reliability-based sensitivity method. The numerical algorithm was shown to be readily adaptable to the existing program since the models of stochastic finite element and stochastic design sensitivity are almost identical.
Highlights
As an alternative of the classical stiffness method, the force method 1–3 was popular in structural analysis of civil, mechanical, and aerospace engineering because of its accurate estimates of forces in structural analysis
Under the assumption of the spatial homogonous random fields, two approximate formulas of the stochastic sensitivity analysis were implemented for IFM
The further development of the methodology for providing more accurate calculations in stochastic sensitivity analysis of IFM would be desirable for larger coefficient of variation of randomness
Summary
As an alternative of the classical stiffness method, the force method 1–3 was popular in structural analysis of civil, mechanical, and aerospace engineering because of its accurate estimates of forces in structural analysis. The sensitivity analysis of structural systems to variations in their parameters is one of the ways to evaluate the performance of structures It is very important for system optimization, parameter identification, reliability assessment, and so forth in engineering analysis. There is a necessity to estimate the effect of uncertainty in stochastic sensitivity derivatives with respect to random design variables on structural responses. Based on the first-order perturbation method, Ghosh et al 13 illustrated that the stochastic structural response sensitivity is quite satisfactory compared to Monte Carlo simulation results under small variation of input random parameters. Under the assumption of the spatial homogonous random fields, two approximate formulas of the stochastic sensitivity analysis were implemented for IFM Another stochastic sensitivity analysis from the reliability-based method was evaluated for comparisons according to the inverse cumulative distribution function of design variables. The numerical algorithm was shown to be readily adaptable to the existing program since the models of stochastic finite element and stochastic design sensitivity are almost identical
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