Topology optimization based on structural flexibility in the periodic loading

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76428/1/AIAA-2000-4737-762.pd

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

Topology optimization for flextensional actuators

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76744/1/AIAA-1998-4951-939.pd

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

Topology optimization of compliant mechanisms using the homogenization method

A procedure to obtain a topology of an optimal structure considering flexibility is presented. The methodology is based on a mutual energy concept for formulation of flexibility and the homogenization method. A multi-objective optimization problem is formulated as an application of compliant mechanism design. Some examples of the design of compliant mechanisms for plane structures are presented. © 1998 John Wiley & Sons, Ltd.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/34532/1/372_ftp.pd

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