Akihiro Takezawa

Shape and topology optimization based on the phase field method and sensitivity analysis

This paper discusses a structural optimization method that optimizes shape and topology based on the phase field method. The proposed method has the same functional capabilities as a structural optimization method based on the level set method incorporating perimeter control functions. The advantage of the method is the simplicity of computation, since extra operations such as re-initialization of functions are not required. Structural shapes are represented by the phase field function defined in the design domain, and optimization of this function is performed by solving a time-dependent reaction diffusion equation. The artificial double well potential function used in the equation is derived from sensitivity analysis. The proposed method is applied to two-dimensional linear elastic and vibration optimization problems such as the minimum compliance problem, a compliant mechanism design problem and the eigenfrequency maximization problem. The numerical examples provided illustrate the convergence of the various objective functions and the effect that perimeter control has on the optimal configurations.

Porous composite with negative thermal expansion obtained by photopolymer additive manufacturing

Additive manufacturing (AM) could be a novel method of fabricating composite and porous materials having various effective performances based on mechanisms of their internal geometries. Materials fabricated by AM could rapidly be used in industrial application since they could easily be embedded in the target part employing the same AM process used for the bulk material. Furthermore, multi-material AM has greater potential than usual single-material AM in producing materials with effective properties. Negative thermal expansion is a representative effective material property realized by designing a composite made of two materials with different coefficients of thermal expansion. In this study, we developed a porous composite having planar negative thermal expansion by employing multi-material photopolymer AM. After measurement of the physical properties of bulk photopolymers, the internal geometry was designed by topology optimization, which is the most effective structural optimization in terms of both minimizing thermal stress and maximizing stiffness. The designed structure was converted to a three-dimensional stereolithography (STL) model, which is a native digital format of AM, and assembled as a test piece. The thermal expansions of the specimens were measured using a laser scanning dilatometer. Negative thermal expansion corresponding to less than −1 × 10−4 K−1 was observed for each test piece of the N = 3 experiment.

Cross-Sectional Optimization of Whispering-Gallery Mode Sensor With High Electric Field Intensity in the Detection Domain

Optimal cross-sectional shapes for whispering-gallery mode sensors with prescribed emission wavelengths and resonance modes are generated through topology optimization based on the finite element method. The sensor is assumed to detect the state of the domain surrounded by the sensor. We identified the integral of the square of the electric field intensity over the detection domain and the quality factor (Q factor), which should be maximized, as key values for the sensor sensitivity, representing the detection limit for the relative permittivity change of the test object. Based on this, the integral of the square of the electric field intensity over the detection domain and the Q factor are studied as the optimization targets. In our numerical study, their optimal configuration characteristics are identified and analyzed. The resulting device has a small radius, a small detection domain and a concave shape with a center located next to the detection domain. We also succeeded in performing simultaneous optimization of the integral of the square of the electric field intensity over the detection domain and the Q factor.

Concurrent Design and Evaluation Based on Structural Optimization using Structural and Function-oriented Elements at the Conceptual Design Phase

Computer-aided engineering (CAE) has been successfully used in mechanical industries such as automotive industries. CAE enables us to quantitatively evaluate the mechanical performances of products and to propose an effective way to improve their performances using optimization techniques without building physical prototypes. However, CAE tools are usually utilized not at the conceptual design phase, but at the evaluation phase following the detailed design phase. This is because current CAE tools require detailed design data that does not yet exist at the conceptual design phase, and such tools also inhibit the provision of useful design suggestions that, ideally, match the way of thinking and insight of design engineers. Thus, at present, no CAE tools exist that can assist the conceptual design decision making process of design engineers. On the other hand, conceptual design processes are of great significance when seeking to create innovative and high-performance products and to shorten their development time. In order to fulfill the designer’s needs during the conceptual design phase, a new type of CAE method must be constructed, one that enables concurrent design support and evaluation, and fits the way design engineers think and explore design insights. This article presents a new structural optimization method that supports concurrent decision making so that design engineers can work to obtain innovative designs and evaluate the mechanical design details of mechanical structures at the conceptual design phase. This method is developed based on the concept of product-oriented analysis and discrete, function-oriented elements, such as beam and panel elements, since these can provide design suggestions concerning the structural evaluation of reasons as to why certain design ideas obtained are reasonable or optimal in the design sense. The basic ideas and specifications needed to construct the method are explained and the construction of the structural optimization design method is discussed. The optimization algorithm is developed using the ground structure approach and CONLIN sequential convex programming. The examples provided demonstrate the utility of the proposed methodology for supporting design engineers’ concurrent decision making, so that innovative mechanical designs can be evaluated at the conceptual design phase.

Phase field method to optimize dielectric devices for electromagnetic wave propagation

We discuss a phase field method for shape optimization in the context of electromagnetic wave propagation. The proposed method has the same functional capabilities as the level set method for shape optimization. The first advantage of the method is the simplicity of computation, since extra operations such as re-initialization of functions are not required. The second is compatibility with the topology optimization method due to the similar domain representation and the sensitivity analysis. Structural shapes are represented by the phase field function defined in the design domain, and this function is optimized by solving a time-dependent reaction diffusion equation. The artificial double-well potential function used in the equation is derived from sensitivity analysis. We study four types of 2D or 2.5D (axisymmetric) optimization problems. Two are the classical problems of photonic crystal design based on the Bloch theory and photonic crystal wave guide design, and two are the recent topics of designing dielectric left-handed metamaterials and dielectric ring resonators.

Structural Optimization Using Function-Oriented Elements to Support Conceptual Designs

This paper presents a new structural optimization method that supports decision-making processes to obtain innovative designs at the conceptual design phase. This method is developed based on structural and function-oriented elements, such as frame and panel elements that have specific functions. For each of the frame elements, the rotational angle denoting the principal direction of the second moment of inertia is included as a design variable, and a procedure to obtain the optimal angle is derived from Karush-Kuhn-Tucker conditions. For the panel elements, two types of panel elements are introduced based the assumed stress method. Several examples are provided to show the utility of the methodology presented here for mechanical design engineers.

Cross-Sectional Shape Optimization of Whispering-Gallery Ring Resonators

Optimal cross-sectional shapes of whispering-gallery ring resonators with prescribed emission wavelength and resonance mode are generated using topology optimization based on the finite element method. The two critical performance indices, the quality factor (Q factor) and mode volume of a resonator, are treated as the objective functions in the optimization. In our numerical study, characteristics of optimal configurations are identified and analyzed. Since the Q factor and mode volume have a tradeoff relationship, i.e., an increasing Q factor increases mode volume, a Pareto-optimal set of solutions can be identified under certain device specifications. These configurations achieve better performances than existing shapes in producing both a high Q factor and low mode volume.

Structural Topology Optimization Using Function-Oriented Elements Based on the Concept of First Order Analysis

Computer Aided Engineering (CAE) has been successfully utilized in mechanical industries, but few mechanical design engineers use CAE tools that include structural optimization, since the development of such tools has been based on continuum mechanics that limit the provision of useful design suggestions at the initial design phase. In order to mitigate this problem, a new type of CAE based on classical structural mechanics, First Order Analysis (FOA), has been proposed. This paper presents the outcome of research concerning the development of a structural topology optimization methodology within FOA. This optimization method is constructed based on discrete and function-oriented elements such as beam and panel elements, and sequential convex programming. In addition, examples are provided to show the utility of the methodology presented here for mechanical design engineers.Copyright

Design methodology using topology optimization for anti-vibration reinforcement of generators in a ship’s engine room:

Structural optimization for reinforcing the anti-vibration characteristics of the generators in the engine room of a ship is presented. To improve the vibration characteristics of the structures, topology optimization methods can be effective because they can optimize the fundamental characteristics of the structure with their ability to change the topology of the target structure. Topology optimization is used to improve the characteristics of the anti-vibration reinforcement of the generators in the engine room. First, an experimentally observed vibration phenomenon is simulated using the finite element method for frequency response problems. Next, the objective function used in topology optimization is set as the dynamic work done by the load based on the energy equilibrium of the structural vibration. The optimization problem is then constructed by adding the volume constraint. Finally, based on finite element analysis and the optimization problem, topology optimization is performed on several vibration cases to improve their performance and reduce weight.

Enhancement of non-resonant dielectric cloaks using anisotropic composites

Cloaking techniques conceal objects by controlling the flow of electromagnetic waves to minimize scattering. Herein, the effectiveness of homogenized anisotropic materials in non-resonant dielectric multilayer cloaking is studied. Because existing multilayer cloaking by isotropic materials can be regarded as homogenous anisotropic cloaking from a macroscopic view, anisotropic materials can be efficiently designed through optimization of their physical properties. Anisotropic properties can be realized in two-phase composites if the physical properties of the material are within appropriate bounds. The optimized anisotropic physical properties are identified by a numerical optimization technique based on a full-wave simulation using the finite element method. The cloaking performance measured by the total scattering width is improved by about 2.8% and 25% in eight- and three-layer cylindrical cloaking materials, respectively, compared with multilayer cloaking by isotropic materials. In all cloaking examples, the optimized microstructures of the two-phase composites are identified as the simple lamination of two materials, which maximizes the anisotropy. The same performance as published for eight-layer cloaking by isotropic materials is achieved by three-layer cloaking using the anisotropic material. Cloaking with an approximately 50% reduction of total scattering width is achieved even in an octagonal object. Since the cloaking effect can be realized using just a few layers of the laminated anisotropic dielectric composite, this may have an advantage in the mass production of cloaking devices.