This paper describes a level set-based topology optimization method for unsteady state Navier-Stokes flow. Many methods for topology optimization applying to fluid mechanics have focused on steady state while most of all fluid phenomena should be considered as unsteady state problem. Therefore, fluid flow problem for topology optimization method should also be solved as unsteady state problem. In addition, wall treatment of fluid field such as velocity has to be considered as another theory such as boundary layer problem. In order to consider wall treatment, applying an immersed boundary method to boundary condition on wall is an effective method so that we apply the immersed boundary method on wall of optimized structure in our method. As a result, we can obtain the optimized structure by applying our method. Some examples are provided and the effectiveness of the method is discussed.
While topology optimization is promising for additive manufacturing structures, challenges arise in designing multi-material assemblies. The size often surpasses additive manufacturing build volumes, hindering successful manufacturing. Additionally, intricate topology-optimized structures complicate the assembly and decomposition of multiple material components. Addressing the aforementioned issues can be achieved by incorporating dimensional and assembly constraints into the optimization process. So far, these constraints have only been studied and implemented separately, leading to suboptimal solutions. Simply applying these two constraints together can also lead to excessive computational complexity. This paper introduces a multi-material topology optimization framework that considers both dimensional and assembly constraints. We propose an assembly direction-aligned method for dimensional constraints to reduce computational costs and an adaptive weighting factor for assembly constraints to enhance numerical stability. Validation through numerical examples and successful fabrication and assembly of a 3D-printed prototype underscore the framework's efficacy in ensuring the manufacturability and assemblability of structures designed via topology optimization.
In this study, we propose a topology optimization method for dynamic problems to control the deformation of the structure. To derive a structure that minimizes the deformation due to transient loads for an isotropic linear elastic model, the strain energy and the squared norm of dynamic compliance are set as objective functions. The topology optimization method applies a density method based on the RAMP method. In the case of the density method, since a optimal structure is obtained by an optimization algorithm based on the gradient method, it is necessary to formulate design sensitivity equations that can appropriately take into account the target optimization problem. A generalized sensitivity analysis method is proposed by introducing the adjoint method and applying Newmark’s β method, which considers the displacement as an unknown quantity , and considering the equations of motion. Furthermore, the accuracy of the sensitivity is verified by using the finite difference method as a benchmark, and it is shown that the proposed design sensitivity has high accuracy. Finally, as a numerical example, we derive optimal structures for several optimization problems and discuss the optimization problem settings to obtain a structure that can control vibrations. The validity of the proposed method is demonstrated by deriving the optimal structure to control the vibration.
This paper presents a new structural optimization method for the design of compliant electro thermal micro actuators based on the level set method and the Finite Element Method (FEM). Compliant electro thermal actuator designed to be flexible to achieve a specified motion as a actuator by intentionally designing configurations that exploit thermal expansion effects in elastic material when appropriate portions of the actuator structure are imposed electric voltage. First, an optimization problem is formulated that addresses the design of compliant electro thermal micro actuators considering the magnitude of the displacement at the output location. Based on the optimization formulation and the level set method, a new structural optimization algorithm is constructed that employs the FEM when solving the equilibrium equations and updating the level set function. Finally, a design example is provided to confirm the usefulness of the proposed structural optimization method.
This paper proposes a design method for disc brake systems that aims to reduce brake squeal and improve cooling performance. The minimization of brake squeal, one of the most important issues that must be addressed when developing high-performance braking systems, can be achieved by maximizing the natural frequencies of the brake system structure. Maximizing the cooling performance of the brake system is an equally important design issue that affects braking forces and the performance of the braking system. In this paper, a topology optimization method is employed to maximize not only the natural frequencies but also the cooling performance in a simplified model of a brake disc. The optimization problem is formulated as a multi-objective problem, using a level set method in order to achieve clear structural boundaries in the obtained optimal configurations. Several numerical examples are provided to confirm the validity and utility of the presented design method.
Design of mechanical structures to maximise acoustic performance is one of important factors in mechanical engineering. The design based on the trial and error approach has, however, some difficulties to obtain appropriate acoustic performance. To resolve this issue, this paper presents a level set-based topology optimisation method for three-dimensional exterior acoustic problems using the Boundary Element Method (BEM) and Fast Multiple Method (FMM). It is shown that the obtained optimal configuration by the proposed method is clear and smooth. Through a numerical example, we have confirmed the efficiency of the proposed method.
