| This thesis focuses on thermo-elastic topology optimization of structures subject to both mechanical and thermal loads. Such problems are of significant importance, for example, in aircraft industry where aerodynamic forces and thermal-gradients are common.;A popular topology optimization method for solving such problems is Solid Isotropic Material with Penalization (SIMP) where pseudo-densities are assigned to each finite element. With values varying between 0 and 1, the pseudo-densities serve as independent variables in the optimization process. Although popular and easy to implement, SIMP exhibits the deficiency of zero-slope at zero-density when solving thermo-elastic problems. This deficiency leads to convergence issues. To overcome such defects, another method, called Rational Approximation of Material Properties (RAMP), was proposed based on SIMP. However, since both methods fundamentally rely on parameterization of material properties as functions of pseudo-densities, they both suffer from ill-conditioned stiffness matrices, poorly defined boundary conditions and stress singularities.;A topological sensitivity based level-set method, called Pareto, is studied instead in this thesis. Pareto does not suffer from the above deficiencies, i.e., the stiffness matrices are well-conditioned, the boundary is well-defined and stress singularities do not arise. However, Pareto has only been demonstrated for pure elasticity, and constraints have not been addressed in a systematic way.;Therefore, the achievement of this research is extending Pareto from pure elasticity to thermo-elasticity, and addressing a variety of constraints that may arise in such problems..;Unlike in pure elasticity, for thermo-elastic problems, the displacements and stresses are computed after taking into account the additional thermal loads. The fundamental notion of topological sensitivity (exploited in Pareto) must therefore be extended to consider both elastic and thermal scenarios. The derivations of topological sensitivities with respect to a variety of mechanical properties, for example, compliance, stress, modal and buckling, are one of the key theoretical accomplishments in this thesis.;To address constraints, an augmented Lagrangian topological level-set method is proposed. By employing classic augmented Lagrangian algorithm, the proposed method is capable of solving topological optimization problems with multiple constraints. Specifically, the augmented Lagrangian algorithm and the concept of topological sensitivity are combined with level-set approach to absorb various constraints into a single objective. The augmented objective is then iteratively minimized by the classic Pareto method. In the process, questions of numerical efficiency and robustness are addressed.;Finally, the thermo-elastic topology optimization formulation is integrated with the proposed augmented Lagrangian level-set method to solve multi-constrained thermo-elastic design problems in an efficient and correct way. While most of topology optimization algorithms are tested on simple 2D benchmark examples, the developed method is tested and applied on a series of 3D large-scale industrial models, rendering the proposed algorithm efficient and robust for a variety of real world applications. |
