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

580

4

= [ ( , ( 1 )) 1 ( , ( 1 )) 2 … … ( , ( )) 1 ( , ( )) 2 ]

(5)

In the elastic case, it is sufficient to know only the initial and final value of the applied load. Thus, as a result of the optimization problem solution, an optimal set of material constants can be found for use in the finite element model. In this algorithm, the finite-element calculation must be performed only once, to obtain the values of for the initial parameters. 3. Results of the algorithm implementation To illustrate this approach, we considered a test problem for a composite sample with a concentrator (notches) consisting of 14 isotropic fiberglass plies (Fig. 1). For convenience of calculations it was assumed that 5 control points are located along axis 1 (coaxial with the direction of the applied load) between the 7th and 8th layer, as shown in Fig. 1c. To test the workability of the algorithm, the deformations obtained in the experiment described in the work of Anoshkin et al. (2016) were used. The initial values of the constants of the model are presented in Table 1.

Young’s modulus , GPa Poisson’s ratio 0.12

Table 1. Isotropic ply propreties.

Initial value 20.0668

c

b

a

Fig. 1. (a) scheme of the sample with a notch; (b) per-layer FE model of the sample; (c) location of the control points in the mesh.

Tensile displacements of 1 mm at the end of the specimen were specified as boundary conditions. With different material properties, loads of different values are required to induce the specified displacements. Since a variable in the optimization problem is the value of the load, in order to make the values ( ) correspond the values ( , ) , it is necessary to interpolate the experimental and calculated "force-deformation" data. In the elastic case, this dependence is linear, therefore, interpolation is not difficult. Such a transformation can also be used in