Research On Topology Optimization Methods Of Continuum Structure Based On Variable Density Method

The purposes of structure optimization are economical materials usage and reasonable stress distribution , whereas topology optimization is a important part of structure optimization,and is a most challenging topic in the field of structural optimization. Topology optimization aims at finding the optimal distribution of materials in a prescribed design domain and the optimal way of component connection in a discrete structure. A improved structure topology could enhance the structure performance or decrease weight of it, and this lead to more benefit, so topology optimization have been the hot research work in the world in last years. Topology optimization is a valuable tool for designers since it can provide novel conceptual designs. Although a lot of achievements have been made in topology optimization, there are still some problems need further explorations. This whole paper is focused on topology optimization of continuum structure. The following three aspects are deeply investigated in this paper: The basic theory of topology optimization, the methods to overcome numerical instabilities in calculation, the topology optimization algorithms based on variable density method. The main research work in this paper is as follows:1. The two material interpolation schemes usually applied in engineering design are introduced: solid isotropic microstructures with penalization (SIMP) and rational approximation of material properties (RAMP). Based on the theories of density interpolation schemes and topology Optimality Criteria method, with the objective of minimizing compliance of the structure, and the constraint condition of the material volume, the corresponding optimality criteria is derived by using RAMP interpolation model.2. Considering the numerical instabilities, such as checkerboards and mesh dependencies, a new hybrid filtering method is presented, which can eliminate numerical problems effectively. The methodologies for new hybrid filtering method presented in this paper are programmed using MATLAB. The validity of the methodologies in this paper is proved by several illustrated examples.3. Aimed at the disadvantage of SIMP (Solid Isotropic Material with Penalization) and RAMP (Rational Approximation of Material properties) on penalty function, a new penalty function is proposed. Based on the new penalty function, OC (Optimization Criteria) algorithm are used for the topology optimization problem of continuum structure by practical numerical examples(MBB and short cantilever beams), the more satisfactory results were obtained compare to using normal variable density method, the feasibility and effectiveness of the optimal model is verified.