| Popis: |
In traditional topology optimization formulation the external load are deterministic and the uncertainties are not considered. The convex modeling based topology optimization method for solving topology optimization problems under external load uncertainties is presented in this dissertation. The load uncertainties are formulated using the non-probabilistic based unknown-but-bounded convex model. The sensitivities are derived and the problem is solved using gradient based algorithm. The proposed convex modeling based method yields the material distribution which would optimize the worst structure response under the uncertain loads. Comparing to the deterministic based topology optimization formulation, the proposed method provided more reliable solutions when load uncertainties were involved. The proposed method can work with other method to solved complicated design problems. A protective structure design problem involving load uncertainties, multiple design objectives and unconstrained structure is solved by integrating the convex modeling based topology optimization method with regional strain energy formulation and inertial relief method. The simplicity, efficiency and versatility of the proposed convex modeling based method can be considered as a supplement to the sophisticated probabilistic based topology optimization methods. |
