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Figure from:Structural optimization based on meshless element free Galerkin and level set methods

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Figure 4: Optimization history, for problem 1 using the EFG based optimization method (black dot: void material, red dot : solid material).

Figure 4 Optimization history, for problem 1 using the EFG based optimization method (black dot: void material, red dot : solid material).

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where n represents nodal points in the local support domain, B; is the strain matrix and u; and v; are the nodal displacements for j** node. In Fig. 1, a graphical representation of nodal points, virtual background cell structure, support domain or domain of influence for a computational point and 4 x 4 Gauss quadrature points are shown. Consequently, the stress vector can be
where n represents nodal points in the local support domain, B; is the strain matrix and u; and v; are the nodal displacements for j** node. In Fig. 1, a graphical representation of nodal points, virtual background cell structure, support domain or domain of influence for a computational point and 4 x 4 Gauss quadrature points are shown. Consequently, the stress vector can be
In this paper, we use the following cubic spline weight function:
In this paper, we use the following cubic spline weight function:
Figure 3: Flow chart of proposed method. 6 Numerical experiments and discussions
Figure 3: Flow chart of proposed method. 6 Numerical experiments and discussions
Figure 5: Optimization history, for problem 1 using the FEM based optimization method.
Figure 5: Optimization history, for problem 1 using the FEM based optimization method.
Figure 6: Volume and objective function convergence for test problem 1.
Figure 6: Volume and objective function convergence for test problem 1.
Figure 8: Volume and objective function convergence for test problem 2.
Figure 8: Volume and objective function convergence for test problem 2.
Figure 9: Optimization history, for problem 3 using the EFG based optimization method (black dot: void material, red dot : solid material).
Figure 9: Optimization history, for problem 3 using the EFG based optimization method (black dot: void material, red dot : solid material).
Figure 10: Volume and objective function convergence for test problem 3.
Figure 10: Volume and objective function convergence for test problem 3.
Figure 11: Optimization history, for problem 4 using the EFG based optimization method (black dot: void material, red dot : solid material).
Figure 11: Optimization history, for problem 4 using the EFG based optimization method (black dot: void material, red dot : solid material).
Figure 12: Volume and objective function convergence for test problem 4.
Figure 12: Volume and objective function convergence for test problem 4.
Figure 13: Optimization history, for problem 5 ing the EFG based optimization method (black dot: void material, red dot : solid material).
Figure 13: Optimization history, for problem 5 ing the EFG based optimization method (black dot: void material, red dot : solid material).