Perpustakaan Digital ITB

In structural optimization studies, the goal is always to use materials efficiently while maintaining structural stiffness. Many methods exist to achieve this goal, including topology optimization. The application of topology in structural optimization not only helps achieve significant material savings while ensuring structural stiffness, but can also optimize highly complex structures or those compatible with advanced manufacturing technologies such as Additive Manufacturing (AM). One type of complex structure involves optimizing multiple materials within the design domain. Since materials have different stiffnesses and volume distributions within the computational domain, determining the optimal location of each material to meet the stiffness maximization constraints requires high precision and advanced computational capabilities. Optimization for multiple materials can be challenging for traditional optimization methods, but it represents a promising research direction for topology optimization. Topology optimization for multi-material is a powerful tool for lightweight or complex structures that require more than one material with different properties. To develop a new multimaterial optimization method, this study uses reaction-diffusion equation-based level set techniques as a foundation. Along with several other popular methods for single-material optimization such as Radial Basis Function (RBF) and Velocity Field Level Set (VFLS), the Reaction-Diffusion Equation (RDE) method has many advantages for multi-material optimization development, such as fast computation speed and high improvement potential. The RDE method is compared with RBF and VFLS to identify its advantages and disadvantages in terms of computational domain, convergence speed, compliance value, and the smoothness of the optimal shape. Next, the RDE method is improved by applying a new hyperbolic tangent function to control the appearance of intermediate density elements during optimization. This improvement not only reduces the number of convergence iterations but also significantly improves the method's convergence ability for complex problems such as non-regular domain problems. Methods for smoothing the optimal shape also are introduced in this study. From this adjusted and validated foundation, this research presents a new approach, called Logical Operation-based Multi-Material Level Set (LO-MMLS), that extends the multi-material level set method by using Boolean functions, specifically the AND operation, to control material generation at level set intersections with reaction-diffusion equation. Each material phase is a separate definition from the level set functions, derived by combining logic functions, which clearly and precisely define materials and avoid duplication during material regeneration in optimization. This research also incorporates a new hyperbolic tangent (tanh) function to control intermediate density values and improve design flexibility. Numerous computational examples demonstrate the new LO-MMLS method's ability to optimize multi-material structures with clearly distributed material regions, improving stiffness performance by up to 9.37% compared to previous methods. At the same time, the proposed method also demonstrates high computational efficiency, with fast computation time and low resource usage. This new method introduces a logical characteristic function rather than the one used in previous studies, optimizing up to 7 materials within the computational domain, with extremely low-volume constraints (4 materials with a volume ratio of 5% each and 3 with a volume ratio of 10% each).