| Topology optimization is a kind of structural optimization,which optimizes material distribution based on load conditions,constraints,and performance metrics within the design domain,seeking the best force path for the structure.It can effectively reduce the amount of materials under the premise of satisfying the structural performance,and its novel topological configuration can provide solutions for engineering innovation design.So,it has been favored by many scholars and engineering designers.In addition,with the continuous development of optimization theory in the actual structural engineering design,the traditional structure containing only a single material can no longer meet the higher requirements of the structural design field.Therefore,multi-material continuum structure topology optimization is not only considered to be one of the most complex and challenging topics in the field of structural optimization design,but also important for the development of structural design in practical engineering.Based on the Independent Continuous Mapping(ICM)method proposed by Prof.Sui Yun Kang in 1996,this paper establishes a continuum topology optimization model with the lightest weight as the objective function under the condition of structural displacement constraints.The effects of filtering functions and constraints on topology optimization results are discussed.The topology optimization of two materials and multi-material continuum structures under different displacement constraints and different elastic modulus ratios is studied.At the same time,using M language,the corresponding continuum structure topology optimization calculation program is developed in MATLAB software platform.Research has been carried out from the following main aspects:(1)Based on the ICM method,a new formulation of topology optimization is established to obtain the lightweight design of structure,which is seeking for minimization of weight with the prescribed constraint on nodal displacement.The influence of filtering functions and constraints on the optimal topology in the model is discussed.(2)The material interpolation function of the two-material continuum structure is proposed.And under the displacement constraints,a two-material continuum structure topology optimization model with the lowest structural weight as the objective function is established.For the displacement constraints condition,the first-order Taylor expansion is used to visualize it,and the second-order Taylor approximation is performed on the objective function.The quadratic programming in the mathematical programming theory is used to solve the topology optimization model.The typical planar continuum structure is compared and analyzed.The influence on the optimized structure of the two-material continuum is discussed from two aspects: the given constraints and the elastic modulus of the material.(3)The topology optimization research method of two-material continuum structure is extended,and the material interpolation function of multi-material continuum structure is proposed.Taking the three-material structure as an example,a multi-material continuum structure topology optimization model is established and optimized.The effects of different displacement constraint values and different material elastic moduli on the optimal topology of multi-material continuum are analyzed.And the feasibility of the topology optimization model is verified.(4)Based on the above theoretical research,using M language,a topology optimization calculation program for single material,two materials and multi-material continuum structure was developed.Numerical examples are used to verify the feasibility of the optimization method and the developed program.Based on the MATLAB software platform,a new multi-material continuum structure topology optimization design method is proposed to realize the initial concept design of the structure,which provides a new idea for topology optimization of multi-material continuum structure. |
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