Numerical simulation of stress-based topological optimization of continuum structures under casting constraints

• Published in: Engineering with computers Vol. 38; no. 6; pp. 4919 - 4945
• Main Authors: Han, Yongsheng, Wang, Qian
• Format: Journal Article
• Language: English
• Published: London Springer London 01.12.2022; Springer Nature B.V
• Subjects: CAE) and Design; Calculus of Variations and Optimal Control; Optimization; Classical Mechanics; Computer Science; Computer-Aided Engineering (CAD; Control; Design optimization; Manufacturability; Math. Applications in Chemistry; Mathematical and Computational Engineering; Optimization; Original Article; Sensitivity; Structural strength; Systems Theory; Topology optimization; Topology optimization; Casting constraints; BESO method; Sensitivity analysis; Stress design
• ISSN: 0177-0667; 1435-5663
• DOI: 10.1007/s00366-021-01512-6

This paper, based on an extended bi-directional evolutionary structural optimization method, proposes a design approach to minimize the maximum von Mises stress of continuum structures subject to both material use and casting constraints. The stress singularity phenomenon is avoided naturally by the technique of discrete variable of the bi-directional evolutionary structural optimization method. The maximum von Mises stress is approximated by the global p -norm stress aggregation approach, and the adjoint method is adopted to derive the sensitivity numbers. Both sensitivity numbers and topological variables are filtered to overcome the highly nonlinear stress behavior and stabilize the optimization procedure. A series of comparison studies have been conducted to validate the effectiveness and practicability of the method on several benchmark design problems. Both two and four parting directions are investigated in this paper. The examples exhibit significant difference in the final topologies for designs with casting constraints. The casting constraints limit the range of solutions to topology optimization problems. Designs with casting constraints seek to satisfy manufacturability of the optimized structure at the expense of structural strength performance. The study demonstrates the importance of strength criteria for the design of continuum structures under casting constraints.