PSI - Issue 33

Boris Fedulov et al. / Procedia Structural Integrity 33 (2021) 843–849 Fedulov B.N., Fedorenko A.N. / Structural Integrity Procedia 00 (2019) 000–000

845

3

� � � �� �� 0 � � � � One can see that there are no any restrictions on angle parameters, what can be explained by a periodic nature of the material orientation. 2.1. Sensitivity For compliance problem, using adjoint method, it is possible to obtain relations for gradients of objective function [4-5]: � ��� � �� �� � � � �� �� �� � �

� ��� � �� �� � � � 0 � � �� �� � � � ��� � �� �� � � � 0 � � �� �� � �

(2)

This is worth noting that all gradients are essentially local and can be calculated fast during optimization procedure. Gradient descent method was implemented into ABAQUS software by means special user subroutine. The exact algorithm for update optimization parameters can be found in [4-7] 3. Numerical example Let us consider bridge-like structure for optimization in 2D and 3D problem statement. The optimization volume is a brick with 80x30 mm for 2D problem and 80x30x40 mm for 3D one. Elastic constants of anisotropic material are shown in Table 1.

Table 1. Mechanical properties.

E 11 (Pa) E 22 (Pa) E 33 (Pa) G 12 (Pa) G 13 (Pa) G 23 (Pa)

1.45E+11 8.34E+09 8.34E+09 4.71E+09 4.71E+09 3.02E+09 2.33E-01 2.33E-01 3.79E-01

ν 12 ν 13 ν 23

3.1. 2D example Two-dimensional finite element model consists of 5000 reduced integrated 4 nodes elements with plane strain formulation. Initial orientation coincides with longitudinal (horizontal) direction. Boundary conditions have both