The objective of this paper is to introduce and demonstrate a robust method for multi-constrained topology optimization. The method is derived by combining the topological sensitivity with the classic augmented Lagrangian formulation.The primary advantages of the proposed method are: (1) it rests on well-established augmented Lagrangian formulation for constrained optimization, (2) the augmented topological levelset can be derived systematically for an arbitrary set of loads and constraints, and (3) the level-set can be updated efficiently. The method is illustrated through numerical experiments.

The focus of this paper is on topology optimization of continuum structures subject to thermally induced buckling. Popular strategies for solving such problems include Solid Isotropic Material with Penalization (SIMP) and Rational Approximation of Material Properties (RAMP). Both methods rely on material parameterization, and can sometimes exhibit pseudo buckling modes in regions with low pseudo-densities.Here we consider a level-set approach that relies on the concept of topological sensitivity. Topological sensitivity analysis for thermo-elastic buckling is carried out via direct and adjoint formulations. Then, an augmented Lagrangian formulation is presented that exploits these sensitivities to solve a buckling constrained problem. Numerical experiments in 3D illustrate the robustness and efficiency of the proposed method. D 10 20

Engineering structures must often be designed to resist thermally induced stresses. Significant progress has been made on the design of such structures through thermo-elastic topology optimization. However, a computationally efficient framework to handle stress-constrained large-scale problems is lacking. The main contribution of this paper is to address this limitation. In particular, a unified topological-sensitivity (TS) based level-set approach is presented in this paper for optimizing thermo-elastic structures subject to non-uniform temperatures. The TS fields for various thermo-elastic objectives are derived, and, to address multiple constraints, an augmented Lagrangian method is developed to explore Pareto topologies. Numerical examples demonstrate the capability of the proposed framework to solve large-scale design problems. Comparison is made between pure elastic problems, and its thermo-elastic counterpart, shedding light on the influence of thermo-elastic coupling on optimized topologies.

The objective of this paper is to introduce and demonstrate a 2 robust methodology for solving multi-constrained 3D topology 3 optimization problems. The proposed methodology is a 4 combination of the topological level-set formulation, 5 augmented Lagrangian algorithm, and assembly-free deflated 6 finite element analysis (FEA). 7 The salient features of the proposed method include: (1) it 8 exploits the topological sensitivity fields that can be derived for 9 a variety of constraints, (2) it rests on well-established 10 augmented Lagrangian formulation to solve constrained 11 problems, and (3) it overcomes the computational challenges 12 by employing assembly-free deflated FEA. The proposed 13 method is illustrated through several 3D numerical 14 experiments.

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