A new structural topological optimization method based on design space adjustments

Although a discrete solid and void structural topology is typicallydesired, a continuous material density design field is usually assignedto the material points within the design domain to spatially indicateregions of solid and void material. The solid isotropic microstructurewith penalization material (SIMP) formulation is easy to implement in afinite element (FEM) framework. However, the material in those regions,where the values of density variables are between 0 and 1,is artificial. It is necessary to deal with those regions after theoptimum topological configuration is obtained. Then a new constraint,labeled the sum of the reciprocal variables (SRV), for 0/1topological design was introduced to obtain 0/1 topology solutions.The structuraldesign domain need be divided into some finite element mesh when structuraltopology optimization is made. Some optimization problems may need a largefinite element mesh, the authors propose a new structural topologicaloptimization method based on design space adjustments in order to solvingthis problem and obtaining 0/1 topology solutions. In topology optimization,a design space is specified by the number of design variables, and theirlayout or configuration. The proposed procedure has one efficient algorithmfor adjusting design space. First, the rational approximation for materialproperties (RAMP) is adopted to design the topology structural stiffnessmatrix filter function, and the design space can be adjusted in terms ofdesign space expansion and reduction. This capability is automatic when thedesign domain needs expansion or reduction, and it will not affect theproperty of mathematical programming method convergences. Second, to get aclearer topological configuration at each iteration step, by introducing thediscrete condition of topological variables, integrating with the originalobjective and introducing varying displacement constraint limitmeasurements, optimal series models with multi-constraints is formulated tomake the topological variables approach 0 or 1 as near as possible. Third, aheuristic algorithm is given to make the topology of the design structure beof solid/empty property and get the optimum topology during the secondoptimization adjustment phase. Finally, incorporating an incompletesecond-order series expansion for structural displacements, a new continuumstructural topological optimization method is proposed. The computationalefficiency is enhanced through the size reduction of optimization structuralfinite model and the adoption of the displacement iterative solving methodduring two optimization adjustment phases. The three simulation examplesshow that the proposed method is robust and practicable.