proportional topology optimization under ‎reliability-based constraints

Topology optimization is a methodology widely used in the design phase that has gained space in engineering. on the other hand, uncertainty is present in material properties, loads, and boundary conditions in practically any design. the main goal for this paper lies in the coupling of the two subjects to account for uncertainties in the topology optimization. the proportional topology optimization method renders the possibility of treating the stress constraints in a unified way. this allows topologies that at the same time preserve structural reliability and optimize costs. the proportional topology optimization method under the reliability constraint is presented for isostatic and hyperstatic beam examples with stress and displacement lsf.