Applying models of spatial interpolation for the approximation of responses in the refinement of parameters of finite element models

Anatoly Pikhalov,Anton Zabelin,P Vitaliy Vladimirovich

doi:10.1051/matecconf/201821201021

Abstract

The numerical experiment on refining the parameters of the finite element model of the beam by the method of approximating the responses is presented in the article. As mathematical models of joint-stock companies are used: linear combinations of radial-basis functions, and Kriging-models. These models are generated in the work on the basis of Latin squares and depend on the parameters to be refined (the moduli of elasticity of finite element groups of the beam). To obtain optimal values of the parameters, a genetic optimization method was used. The results of solving the optimization problem showed a high level of coincidence of the parameter values with a combination of response models obtained from dynamic and static types of calculations. It was also shown that when solving the problems of finite element models, it is sufficient to use models constructed only on the basis of radial-basis functions.

Highlights

The most important requirement for finite-element (FE) models of structures is their maximum possible correspondence to real objects by parameters of stress-strain state (SSS) and dynamic characteristics
The discrepancy between the results can be minimized by eliminating FE modeling errors, for example, in studying the accuracy-convergence of a numerical solution, as well as aspects of field trials
In order to minimize the level of discrepancy between the FE model and the real object, it is necessary to solve the problem of refinement of model parameters [2, 3]

Summary

Introduction

The most important requirement for finite-element (FE) models of structures is their maximum possible correspondence to real objects by parameters of stress-strain state (SSS) and dynamic characteristics. After constructing the matrix [Φ], it is necessary for each RBF model to calculate the weight vector {W} j, j = 1, ..., n, which determines the “weight” of each point in the parameter area, depending on the input data in the form [X] and {Yfem}j ,. This vector is calculated under the assumption that the responses of the RA models at the initial points are equal to the initial responses: W j=. The first 3 eigenfrequencies of the beam oscillations v1-v3

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Kriging models

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