Concurrent Topology Optimization Of Structure And Material Of Coupled Thermoelastic Problem

There is currently widespread interest in porous materials, because of their specific properties, such as low bulk density, low thermal conductivity, active cooling, energy harvesting. These properties are expected of technological applications, which include thermal insulation, lightweight structural design, crash-worthiness, vibration control, acoustic damping and so on. Porous materials, including metal foams, lattice material, cellular material and porous ceramics, are often modeled approximately as homogeneous, with some fluctuations, porous material micro structure. Large pieces or blocks of these kinds of materials of almost homogeneous microstructure are available in today’s market. They are used to construct super-light structures.Concurrent topology optimization model provides the theoretical foundation to simultaneously design the topology of the structure and its material microstructure of the super-light structure. In the concurrent topology optimization model, macro and micro densities are introduced as the design variables for the macro structure and material microstructure independently. Penalization approaches are adopted at both scales to ensure clear topologies, i.e. SIMP in the micro scale and PAMP (Porous Anisotropic Material Penalization) in the macro scale. Optimizations at two scales are integrated into one system with homogenization theory. The design of material microstructure is concurrently optimized with the structural topology design in the macro scale, and the distribution of base material between two scales can be determined automatically by the optimization model. This thesis deals with the concurrent topology optimization of super-light structure under thermoelastic and coupled thermoelastic problems.Firstly, we concurrently optimize the structural topology and its material micro-structural topology with multi objectives in steady-state thermoelastic problems. In thermoelastic problems, the temperature of the structure is specified, and the topological changes of the structure has no effect on the temperature field. The multi-objective optimization formulation attempts to find minimum structural compliance under only mechanical loads and minimum thermal expansion of the surfaces we are interested in under only thermo loads. The proposed optimization model is applied to a sandwich elliptically curved shell structure, an axisymmetric structure and a3D structure. The advantage of the concurrent optimization model to single scale topology optimization model in improving the multi-objective performances of the thermoelastic structures is investigated. The influences of available material volume fraction and weighting coefficients are also discussed. Numerical examples demonstrate that the porous material is conducive to enhance the multi-objective performance of the thermoelastic structures in some cases, especially when lightweight structure is emphasized. An "optimal" material volume fraction is observed in some numerical examples.Secondly, this article deals with the concurrent topology optimization problem of coupled thermoelastic structures with steady-state heat conduction to achieve minimum structural compliance. In the coupled thermoelastic problem, change of the structural topology not only affects the displacement field. but also influences the temperature filed which again casts an influence on the displacement field. The. effective thermal conductivity tensor and elastic tensor of the porous anisotropic material are obtained through homogenization theory. The effects of mechanical load, thermal load and material volume are discussed through the examples. When we specify the material used on the micro scale, cellular material configurations are obtained in some examples. What’s more, in our numerical examples, the compliance of the coupled thermo elastic structure increases with the increase of the intensity of the heat flux. But, theoretically, the compliance could decrease with the intensity of the hear flux and we briefly illustrate the reasons.Lastly, concurrent topology optimization method is employed to improve thermal insulation and’stiffness performances of coupled thermoelastic structure. Prescribed temperature is imposed on the exterior surface of the structure and the interior surface of the structure is heat convection boundary. The thermal heat passes through the structure from the exterior to the interior. The thermal insulation objective is to minimize the temperature of the interior surface of the structure in order to minimize the thermal flux passes through the structure. And the stiffness objective is to minimize the displacement of the concerned area of the structure subjected to thermoelastic loads. We investigate and compare the two methods, one optimizes the topology of material microstructure, another optimizes concurrently structure/material topology. When only material microstructure is optimized, it is found that utilization of porous material is instructive when both thermal insulation and stiffness are considered as optimization objectives. And we illustrate this phenomenon with a one-dimension example. By comparing the above mentioned two design methods, it shows that concurrently topology optimization method is more advantageous in minimizing the objective and uses far less material with better structural performances achieved.All the optimization problems are realized through our extensions in OOFEM, which is open-source finite element code with object oriented architecture. On the basis of OOFEM, we add optimization classes containing the design variables, constraints, objective, and optimization solvers to solve concurrent topology optimization problem. The optimization classes possess functions to compute objective and constraint values and their sensitivities, to filter the design variables with volume preserving filter, to update design variables with optimization solvers, to set non-designable domains and so on. We also add classes representing homogeneous porous materials, whose effective thermal conductivity coefficient and elastic modulus are analyzed through the homogenization codes in the class. To improve the computational efficiency of3D homogenization problem, the preconditioned conjugate gradient iterative solver in OOFEM instead of the direct Skyline solver is employed. And, the incomplete LU decomposition with no fill up preconditioner is used to reduce the condition number of the global stiffness matrix in order to accelerate the convergence rate.