(A) nodal-density-based model for reliability-based topology optimization under geometric uncertainty

Abstract

A geometric uncertainty model for the reliability-based topology optimization is proposed. Proposed model is capable of optimizing topology with spatially known uncertainty data directly. Densities of predefined design points are design variables for topology optimization. A density field is constructed from the densities using Shepard interpolation and structural finite element analysis is performed based on the field. A random field is discretized by Karhunen-Loève expansion or expansion optimal linear estimation method. The geometric uncertainty is represented by the shift of each design points whose magnitudes and directions are computed from the discretized random field and a predefined function. Analytic sensitivities are derived for reliability-based topology optimization. Finally, proposed method is validated by numerical examples.