Topology optimization with geometrically non-linear based on the element free Galerkin method

In this article, the element free Galerkin (EFG) method is applied to carry out the topology optimization of the geometrically non-linear continuum structures. In EFG method, the moving least squares shape function is used to approximate the displacements. The 2D geometrically non-linear formulation is presented based on the EFG method. The penalty method is explored to enforce the essential boundary conditions. Considering the relative density of nodes as design variables, the minimization of compliance as an objective function, the mathematical formulation of the topology optimization is developed using the solid isotropic microstructures with penalization interpolation scheme. Sensitivity of the objective function is derived based on the adjoint method. Numerical examples show that the proposed approach is feasible and effective for the topology optimization of the geometrically non-linear continuum structures.

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