Notice of RetractionOn solving the min-max problem of the stress of the structural elements in the structural topology optimization
In this paper, we deal with the min-max problem of the stress of the structural elements in the structural topology optimization. A generalized KS function is presented which transforms the local stress to global strain energy of structure through Von Mises Criterion. The ICM method is employed for solving the topology optimization problem. Some classic numerical examples are presented which provide quality solutions and the minimum stress design to obtain the final design.
Topology Optimization Using Parabolic Aggregation Function with Independent-Continuous-Mapping Method
This paper concentrates on finding the optimal distribution for continuum structure such that the structural weight with stress constraints is minimized where the physical design domain is discretized by finite elements. A novel Independent-Continuous-Mapping (ICM) method is proposed to convert equivalently the binary design variables which is used to indicate material or void in the various elements to independent continuous design variables. Moreover, three smooth mappings about weight, stiffness, and stress of the structural elements are introduced to formulate the objective function based on the so-called concepts of polish function and weighting filter function. A new general continuous approach for topology optimization is given which can eliminate the stress singularity phenomena more efficiently than the traditional -relaxation method, and an alternative strain energy method for the stress constraints is proposed to overcome the difficulty in stress sensitivity analyses. Mathematically, by means of a generalized aggregation KS-like function defined as the parabolic aggregation function, a topology optimization model is formulated with the weight objective and single parabolic global strain energy constraints. The numerical examples demonstrate that the proposed methods effectively remove the stress concentrations and generate black-and-white designs for practically sized problems.
Truss Topology Optimization with Stress and Displacement Constraints
Compliance minimization has been popular for obtaining optimum truss topologies because it is less computationally demanding than optimization for more general constraints. This advantage of compliance minimization led to the approach of optimizing the topology of the truss for minimum compliance, and then sizing the cross-sectional areas of that truss for the actual constraints. The present paper shows that the compliance minimization can occasionally lead to the wrong topology, and that the penalty associated with using the minimum-compliance topology can be substantial. To demonstrate this problem truss topology optimization subject to displacement and stress constraints is performed with a simultaneous analysis and design (SAND) procedure.