Topology design optimization of geometrically non-linear structures using meshfree method

A topology optimization method using meshfree methods is developed for geometrically non-linearly structures. A density approach is used to optimally distribute the bulk material densities in a continuum design domain. The reproducing kernel (RK) shape function is employed to discretize both displacement and bulk density fields. Thus, the points can be located at any part of the design domain and be easily included in or excluded from the response analysis. The well-known convergence difficulty, which normally occurs in the sub-domain of low bulk density, can be avoided by excluding the sub-domain. The numerical instability of bulk density solution due to the rank deficiency of system matrix is effectively prevented by properly selecting the number of independent design variables. Through numerous numerical examples, we confirm that the developed method works very well even in the large deformation problems. The sub-domain exclusion scheme is found to be greatly beneficial in terms of computational costs compared with the results without the scheme.