Metamodeling for the Identification of Composite Material Properties

Abstract

The problem of identification of elastic properties E=·E ^x,·E ^y,·E ^xy,μ× of composite structural elements from vibration tests is considered. The metamodels built on basis of FEM computer experiments and natural measurements of eigenfrequencies are used for the identification [1], [2]. Two methods are compared. First - the minimization of the discrepancy between calculated and measured frequencies. The numerical frequencies are calculated by finite element model using numerical experiment - a set of trial values for the unknown material parameters. The numerical frequencies are compared with the measured frequencies, and material properties are found by minimizing the relative discrepancy

$$ \mathop {\min }\limits_E \sum\limits_{i = 1}^m {\left( {\frac{{f_i^{\exp } - f_i^{calc} }} {{f_i^{\exp } }}} \right)} ^2 $$

Second - the direct creating of the inverse metamodel

$$ E = E\left( {f_1 ,f_2 , \ldots ,f_m } \right) $$

In this case the calculated frequencies are taken as inputs, and material parameters as outputs of the metamodel. For the second case the input variables are highly correlated [3], but the analysis of significance gives the possibility of the best choice of eigenmode numbers for the first method. The combination of both methods is demonstrated on the layered curved carbon/epoxy panel example. Identification of elastic properties of a panel has been carried out with satisfactory results. However the errors of frequency determinations, caused by manufacturing errors (the dimensions, density and others differ from it’s nominal values) and measurement errors (caused e.g. by discretization of frequency band using fast Fourier transformation) can produce unacceptable error of identification, therefore all parameters, not only frequencies, must be measured with split-hair accuracy. In the case of simultaneous identification of elastic and density parameters the result can be indefinite.