Development of Pareto topology optimization considering thermal loads

• Published in: Computer methods in applied mechanics and engineering Vol. 317; pp. 554 - 579
• Main Authors: Takalloozadeh, Meisam, Yoon, Gil Ho
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15.04.2017; Elsevier BV
• Subjects: Drucker–Prager criterion; Flux density; Hookes law; Mathematical analysis; Modulus of elasticity; Pareto method; Pareto optimization; Pareto optimum; Sensitivity; Sensitivity analysis; Strain; Stress-strain curves; Stresses; Studies; Temperature effects; Thermal analysis; Thermal load; Topology; Topology optimization; Topology optimization; Sensitivity analysis; Drucker–Prager criterion; Thermal load; Pareto method
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2016.12.030

In this research, we developed a level-set based topology optimization with a topological derivative formulation considering thermal load. Thermo-elasticity equations were utilized to obtain the sensitivity of the objective function after inserting a small hole in the domain. Total strain energy and the maximum stress in the design domain were taken as the objective functions. After taking the thermal loading effect into account, the total strain energy density function became a nonhomogeneous function of the strain. In addition, temperature variation changed Hooke’s law from a linear homogeneous to a linear nonhomogeneous expression including a zero order term. We derived the sensitivity value of the selected objective functions with respect to a perturbation in the structural domain under mechanical and thermal loads while considering these changes in the governing equations. We performed several numerical optimization problems to demonstrate the validity of the present level-set based Pareto topology optimization. Two types of examples (compliance and stress minimization) were solved based on the chosen objective functions. Furthermore, in the stress minimization examples, the derived formula was extended to consider thermal effects in the failure theories for pressure independent and dependent materials. •The sensitivity analysis under thermo-mechanical loading is performed.•The change in the maximum DP stress under topological perturbation is calculated.•PTO method is developed by using obtained topological derivative.•The structural compliance and stress minimization problems are solved.•The optimum topologies for the ductile and brittle structures are obtained.