Design Sensitivity Analysis and Topology Optimization of Displacement-Loaded Structures

초록

A continuum-based material property design sensitivity analysis method for the systems having non-homogeneous boundary condition is developed to be used in the displacement-loaded topology design optimization problems. The non-homogeneous Dirichlet problem is transformed into the homogeneous one. An adjoint variable method is selected to efficiently compute the design sensitivity of the problems. For the topology optimization, the density method that uses the relative material density to distribute the material properties is employed. The design sensitivity expressions for the performance measures of displacement and rigidity functional are derived to be used in the topology optimization. It is shown that, in adjoint systems, the solution space requires just homogeneous boundary conditions. Numerical tests for the developed method are performed by comparing the analytical sensitivity with the finite difference one, which shows excellent agreement. The result of topology optimization for the displacement-loaded systems is shown to be equivalent to that for the force-loaded systems.

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