Optimization of material distributions in mechanically loaded multi-material components using simulated annealing and evolutionary algorithms

Modern manufacturing processes, such as multi-material additive manufacturing or, to a lesser extent, compound casting, allow for an almost arbitrary distribution of different materials or, even more so, different local densities over the volume of a component. The difficulty lies in determining the optimum spatial distribution of the materials. Multi-Phase Topology Optimization (MPTO) is one approach to this end. This method is based on iterative, linear elastic Finite Element Method (FEM) simulations that provide elastic strain energy data at both the component and element level. Such information is used to redistribute several predefined material fractions, characterized by different values of elastic modulus, according to their relative properties, in order to minimize the total strain energy under a certain design load. The solution to such a minimization problem is the central part of this work. Achieving this aim means that a configuration has been identified which provides maximum stiffness under the conditions of the assumed load case. The present study compares different material redistribution and optimization techniques based on Genetic Algorithms and Simulated Annealing in combination with systematic constraints or approaches and compares them in terms of optimization results and performance. In general, such minimization problems offer multiple solutions. Therefore iterative minimization algorithms may settle into local, non-optimum minimum states. Genetic Algorithms and Simulated Annealing use partial randomization to generate new configurations, a key method for examining a much larger volume fraction of the entire search space than classical gradient-based algorithms allow. The main difference between these two methods is that, unlike Simulated Annealing, Genetic Algorithms build new material configurations from previous solutions through operations such as crossover and mutation. The cost functions used by both approaches depend on the FEM simulation, a computationally demanding task. As an example of a multi-material structure, a bending beam composed of three materials was used.