PSI - Issue 5

Mikhail Tashkinov et al. / Procedia Structural Integrity 5 (2017) 577–583 Mikhail Tashkinov et al. / Structural Integrity Procedia 00 (2017) 000 – 000

581

5

practical applications where it is not possible to estimate the load applied on real structures, but the displacements can be measured. Fig. 2 shows the field of values of the component 11 of the strain tensor at given boundary conditions in layer 7 which contains control nodes. The properties of the layer corresponded to the initial values. Calculations were carried out in the Abaqus package. Regression sampling was formed by comparing the values of deformations in control nodes with the experimental ones.

Fig. 2. The strain field in the layer with the initial properties.

The implementation of the optimization task was performed in the Wolfram Mathematica environment. Fig. 3 shows a contour representation of the value of the functional (3) for the test problem with a step-by-step refinement of the Young's modulus and the Poisson's ratio of the layer included in the parameter vector. Green points indicate the steps of the optimization algorithm. The following refined values of the constants were obtained after the algorithm run: = 23,623 GPa and = 0.138879 .

Fig. 3. Contour plot of the error estimate.

To compare the results and analyze the convergence of the L-M optimization algorithm for a particular case, a step by-step search for constants was carried out using the Newton's method, a description of which can be found, for