A new structural topological optimization method based on design space adjustments

Although a discrete solid and void structural topology is typically desired, a continuous material density design field is usually assigned to the material points within the design domain to spatially indicate regions of solid and void material. The solid isotropic microstructure with penalization material (SIMP) formulation is easy to implement in a finite 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 the optimum topological configuration is obtained. Then a new constraint, labeled the sum of the reciprocal variables (SRV), for 0/1 topological design was introduced to obtain 0/1 topology solutions. The structural design domain need be divided into some finite element mesh when structural topology optimization is made. Some optimization problems may need a large finite element mesh, the authors propose a new structural topological optimization method based on design space adjustments in order to solving this problem and obtaining 0/1 topology solutions. In topology optimization, a design space is specified by the number of design variables, and their layout or configuration. The proposed procedure has one efficient algorithm for adjusting design space. First, the rational approximation for material properties (RAMP) is adopted to design the topology structural stiffness matrix filter function, and the design space can be adjusted in terms of design space expansion and reduction. This capability is automatic when the design domain needs expansion or reduction, and it will not affect the property of mathematical programming method convergences. Second, to get a clearer topological configuration at each iteration step, by introducing the discrete condition of topological variables, integrating with the original objective and introducing varying displacement constraint limit measurements, optimal series models with multi-constraints is formulated to make the topological variables approach 0 or 1 as near as possible. Third, 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. Finally, incorporating an incomplete second-order series expansion for structural displacements, a new continuum structural topological optimization method is proposed. 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. The three simulation examples show that the proposed method is robust and practicable.