A truly meshless method based on partition of unity quadrature for shape optimization of continua

A numerical method for shape design optimization using a truly meshless method based on partition of unity(PU) is presented in this paper. This method does not rely on a partition of the integration domain into small cells as a background mesh, but rather on a PU by a set of overlapping patches covering the domain. The quadrature points distributed can move automatically as the nodes move, and the density of quatrature points will scale with the density of nodes spontaneously. This unique feature makes the method very suitable for shape optimization, in which the nodes are randomly distributed and the spacings between the nodes are fluctuant. Two linear elastic shape optimization problems are solved by using the proposed method. Higher convergence rates and better optimization efficiencies obtained as compared with classical RKPM method demonstrate that this method is effective and versatile for shape optimization problems.