Study On A Topological Optimization Method Based On Quadratic Programming And Its Application Of Continuum Structure

Structure topology optimization is the most challenging research in structural optimization technology, which is an innovative design developed in recent years. After the combination of structural discrete topology variable condition and the original objective, a new topological optimization method of continuum structures based on quadratic programming has been presented in this thesis, and how do this mothod use in displacement or stress constraint continuum structures optimization is researched. In the Optimization problem with the displacement constraint, the capacity of the final optimal solution, that the method starting from any initial design structure, has been verified. In the Optimization problem with the stress constraint, in order to greatly reduce stress sensitivity analysis cost, all element stress constraints of the structure being optimized under a load case are replaced by several most potential active stress constraints and a generalized average stress constraint. The whole optimization process is divided into two phases and a phase transferring step operation. After incorporating smooth optimization algorithm,a procedure is proposed to solve the optimization problem of the first optimization adjustment phase. This design space adjustment capability is automatic when the design domain needs expansion or reduction, and it will not affect the property of mathematical programming method convergences. The topology obtained by the proposed method approaches to the vicinity of the optimum topology when the first optimization adjustment phase ends. Then, a heuristic algorithm is given to make the topology of the design structure be of solid/empty property and get the optimum topology during the second optimization adjustment phase. The computational efficiency is enhanced through the size reduction of optimization structural finite model and the adoption of the displacement iterative solving method during two optimization adjustment phases.For the methods, a lot of typical structural design simulation examples are given, and the examples show that the proposed method has strong ability to obtain the optimum topology. Results obtained show that the proposed methods in this thesis are correct and efficient, and are of good engineering application value.