A topology optimization method based on the level set method incorporating a fictitious interface energy

This paper proposes a new topology optimization method, which can adjust the geometrical complexity of optimal configurations, using the level set method and incorporating a fictitious interface energy derived from the phase field method. First, a topology optimization problem is formulated based on the level set method, and the method of regularizing the optimization problem by introducing fictitious interface energy is explained. Next, the reaction–diffusion equation that updates the level set function is derived and an optimization algorithm is then constructed, which uses the finite element method to solve the equilibrium equations and the reaction–diffusion equation when updating the level set function. Finally, several optimum design examples are shown to confirm the validity and utility of the proposed topology optimization method

Layout Optimization of the Beam Spot Locations Scanned by Electromagnets in Particle Beam Therapy

This paper presents a layout optimization method of the spot locations of pencil beam scanning for particle beam cancer therapy. With the pencil beam scanning technique, the particle beam is scanned from spot to spot in the tumor by using scanning magnets. To provide clinically ideal dose distributions and less-invasive treatment to the patients, both the spot locations and the number of particles given to each spot should be optimized. However, the spot layout is fixed with a lattice pattern in many prior studies. We propose the optimization method to derive the non-lattice spot layout to realize an acceptable dose distribution with a reduced number of spots. With the proposed method, a large enough number of spots were located densely at the initial state, and then the spots with the smallest contribution were removed one by one through iterations. The number of particles given to each spot was determined by solving a quadratic problem. Furthermore, we also propose the idea to accelerate the optimization process by simultaneously removing multiple spots. The algorithm was confirmed by numerical examples of both two-dimensional and three-dimensional cases. The dose quality with the optimized spot layout was better than that with the conventional lattice spot patterns, with all tested cases. In the optimized spot layout, the spots were located on the closed lines which were concentric to the target contour. We also confirmed the proposed method of multiple-remotion can accelerate the optimization process without violating the dose quality

Topology optimization for maximizing linear buckling load based on level set method

Stability and buckling have attracted extensive attention in the design of structural elements, especially in the design of thin-walled structures since they may naturally have poor stability and be prone to buckling failure. This paper proposes a level-set based topology optimization (TO) method that can maximize the lowest linear buckling load under a mean compliance constraint. First, we conduct the linearized buckling analysis and formulate the optimum design problem. Second, we derive the design sensitivity and revisit the reaction-diffusion equation-based level-set topology optimization. Finally, we solve several two-dimensional benchmark problems and the design results are presented to validate the proposed method

ROBUST PRODUCT DESIGN OPTIMIZATION METHOD USING HIERARCHICAL REPRESENTATIONS OF CHARACTERISTICS

ABSTRACT Product design optimizations usually require the optimization of not only all performance characteristics, but also the robustness of certain performance characteristics. Obtaining optimum design solutions is far from easy, since this requires evaluations of numerous related characteristics that usually have complicated and conflicting interrelationships. Some of these characteristics can include variations of one type or another, such as manufacturing process variations, variations pertaining to the environments where the product is used, variations in how long-term use affects certain product characteristics, and so on. The difficulty of obtaining optimum design solutions is thus compounded by the need to carry out specific optimizations that provide sufficient robustness to safely accommodate anticipated ranges of variations. This paper expands the hierarchical multiobjective optimization method based on simplification and decomposition of characteristics so that optimizations can be concurrently conducted for both performance characteristics and maximization of robustness against characteristic variances. A principal cause of variations in performance characteristics is variations in the contact conditions of joints, and the utility of the proposed robust product design optimization method is demonstrated by applying it to machine-tool models that include joints. INTRODUCTION In today's product manufacturing environment, a wide range of factors such as product performances (such as the speed, accuracy and efficiency in accomplishing certain tasks), product qualities (such as performance variance and robustness) and operational and manufacturing costs must be considered when designing and producing machine products. To create successful products, numerous product characteristics need to be concurrently evaluated so that the specific requirements need to satisfy the product performances and qualities can all be satisfied to the highest possible degree. To accomplish these tasks, appropriate system optimization methods must be constructed and then used effectively. There are two main obstacles to achieving sophisticated system optimization results for product designs. One pertains to the problem of obtaining suitable optimum design solutions, and the other to whether or not the obtained solutions have sufficient robustness and can successfully accommodate the variations in design variables and parameters that will occur during product manufacturing and later usage of the product. These two problems are of equal importance in product design optimizations, since insufficient robustness can ultimately spoil what might be considered a superior design in situations where the need for adequate robustness is not adequately recognized

Manufacturability evaluation for molded parts using fictitious physical models, and its application in topology optimization

Manufacturing methods using molds, such as casting and injection molding, are widely used in industries. A basic requirement when using such manufacturing methods is that design engineers must design products so that they incorporate certain geometrical features that allow the mold parts to be removed from the created solid object. In the present study, we propose a manufacturability evaluation method especially adapted for the use of molds. To evaluate the manufacturability, we introduce fictitious physical models that are described by steady-state anisotropic advection-diffusion equations. In these fictitious physical models, material domains have a virtual source term and the advection directions are aligned with the directions along which the mold parts are parted. Void regions, where the values of all fictitious physical fields are high, then represent either undercut geometries that would prevent the mold from being released, or interior voids that cannot be cast. Consequently, manufacturability can be evaluated using these fictitious physical fields. Furthermore, in the present study, we integrate this evaluation method with topology optimization and propose a scheme for imposing a molding constraint within the topology optimization procedure. This newly proposed topology optimization method can consider the position of mold parting lines prior to the detailed optimization procedure. Several numerical examples are provided to demonstrate the validity and effectiveness of the proposed method

DETC2005-85137 RELIABILITY-BASED TOPOLOGY OPTIMIZATION CONSIDERING MULTICRITERIA USING FRAME ELEMENTS

ABSTRACT Since decision-making at the conceptual design stage critically affects final design solutions at the detailed design stage, conceptual design support techniques are practically mandatory if the most efficient realization of optimal designs is desired. Topology optimization methods using discrete elements such as frame elements enable a useful understanding of the underlying mechanics principles of products, however the possibility of changing prior assumptions concerning utilization environments exists since the detailed design process starts after the completion of conceptual design decisionmaking. In order to avoid product performance reductions due to such later-stage environmental changes, this paper discusses a reliability-based topology optimization method that can secure specified design goals even in the face of environmental factor uncertainty. This method can optimize mechanical structures with respect to two principal characteristics, namely structural stiffness and eigen-frequency. Several examples are provided to illustrate the utility of the method presented here for mechanical design engineers

イデンテキ アルゴリズム オ モチイタ キカイ システム サイテキ セッケイホウ

京都大学0048新制・論文博士博士(工学)乙第11657号論工博第3849号新制||工||1351(附属図書館)23470UT51-2005-D575京都大学大学院工学研究科精密工学専攻(主査)教授 吉村 允孝, 教授 松久 寛, 教授 椹木 哲夫学位規則第4条第2項該当Doctor of EngineeringKyoto UniversityDA

Multilevel Redundancy Allocation Optimization Using Hierarchical Genetic Algorithm

This paper proposes a generalized formulation for multilevel redundancy allocation problems that can handle redundancies for each unit in a hierarchical reliability system, with structures containing multiple layers of subsystems and components. Multilevel redundancy allocation is an especially powerful approach for improving the system reliability of such hierarchical configurations, and system optimization problems that take advantage of this approach are termed multilevel redundancy allocation optimization problems (MRAOP). Despite the growing interest in MRAOP, a survey of the literature indicates that most redundancy allocation schemes are mainly confined to a single level, and few problem-specific MRAOP have been proposed or solved. The design variables in MRAOP are hierarchically structured. This paper proposes a new variable coding method in which these hierarchical design variables are represented by two types of hierarchical genotype, termed ordinal node, and terminal node. These genotypes preserve the logical linkage among the hierarchical variables, and allow every possible combination of redundancy during the optimization process. Furthermore, this paper developed a hierarchical genetic algorithm (HGA) that uses special genetic operators to handle the hierarchical genotype representation of hierarchical design variables. For comparison, the customized HGA, and a conventional genetic algorithm (GA) in which design variables are coded in vector forms, are applied to solve MRAOP for series systems having two different configurations. The solutions obtained when using HGA are shown to be superior to the conventional GA solutions, indicating that the HGA here is especially suitable for solving MRAOP for series systems

Matlab code for a level set-based topology optimization method using a reaction diffusion equation

This paper presents a simple Matlab implementation for a level set-based topology optimization method in which the level set function is updated using a reaction diffusion equation, which is different from conventional level set-based approaches (Allaire et al. 2002, 2004; Wang et al. 2003) that use the Hamilton-Jacobi equation to update the level set function. With this method, the geometrical complexity of optimized configurations can be easily controlled by appropriately setting a regularization parameter. We explain the code in detail, and also the derivation of the topological derivative that is used in the level set-based topology optimization. Numerical results for stiffness maximization problems are provided to facilitate the reader’s understanding. The presented code is intended for educational purposes only. This paper was inspired by previously published papers presenting Matlab code for a SIMP method (Sigmund 2001; Andreassen et al. 2011), a level set-based method (Challis 2010), and FreeFem ++ code for a structural optimization method (Allaire and Pantz 2006). Readers can investigate results provided by these different methods and discover the prominent aspects of each particular method. The code presented here can be downloaded from http://​www.​osdel.​me.​kyoto-u.​ac.​jp/​members/​yamada/​codes.​html

Toru Matsushima Conceptual Design Method for Reducing Brake Squeal in Disk Brake Systems Considering Unpredictable Usage Factors

Minimizing brake squeal is one of the most important issues in the development of high performance braking systems. Furthermore, brake squeal occurs due to the changes in unpredictable factors such as the friction coefficient, contact stiffness, and pressure distribution along the contact surfaces of the brake disk and brake pads. This paper proposes a conceptual design method for disk brake systems that specifically aims to reduce the occurrence of low frequency brake squeal at frequencies below 5 kHz by appropriately modifying the shapes of brake system components to obtain designs that are robust against changes in the above unpredictable factors. A design example is provided and the validity of the obtained optimal solutions is then verified through real-world experiments. The proposed optimization method can provide useful design information at the conceptual design stage during the development of robust disk brake systems that maximize the performance while minimizing the occurrence of brake squeal despite the presence of unpredictable usage factors