arXiv subjects

Takayuki Yamada

Publications and source records attributed to Takayuki Yamada.

31 records · Page 2Linked to original sources

arXiv2023

Topology optimization method with nonlinear diffusion

This paper is concerned with topology optimization based on a level set method using (doubly) nonlinear diffusion equations. Topology optimization using the level set method is called level set-based topology optimization, which is possible to determine optimal configurations that minimize objective functionals by updating level set functions. In this paper, as an update equation for level set functions, (doubly) nonlinear diffusion equations with reaction terms are derived, and then the singularity and degeneracy of the diffusion coefficient are applied to obtain fast convergence of configurations and damping oscillation on boundary structures. In particular, the reaction terms in the proposed method do not depend on the topological derivatives, and therefore, sensitivity analysis to determine a descent direction for objective functionals is relaxed. Furthermore, a numerical algorithm for the proposed method is constructed and applied to typical minimization problems to show numerical validity. This paper is a justification and generalization of the method using reaction-diffusion equations developed by one of the authors in Yamada et al. (2010).

math.OC↗

arXiv2023

Two-Phase Topology Optimization for Metamaterials with Negative Poisson's Ratio

Although recent developments in 3D printing technology have made it possible to fabricate metamaterials with characteristic mechanical properties, it is not easy to fabricate complex shapes containing cavities. In this study, a composite structure comprising two types of materials without a cavity was optimized. Moreover, a mechanical metamaterial with a negative Poisson's ratio that can be fabricated using an additive manufacturing method was developed. First, a homogenization method that characterizes the properties of composite structures was briefly described. Then, an optimization problem to realize a negative Poisson's ratio was formulated, and a level set-based topology optimization method was proposed to solve the abovementioned problem. Next, three-dimensional numerical examples are presented to confirm the effectiveness of the proposed method, and the deformation behaviors of the optimized designs are numerically examined. Furthermore, a sample containing the optimized design with negative Poisson's ratio for the tensile test was fabricated using a 3D printer. We conducted some experiments to evaluate its mechanical performance.

physics.app-ph↗

arXiv2023

Level set-based multiscale topology optimization for a thermal cloak design problem using the homogenization method

Artificially designed composite materials consist of microstructures, that exhibit various thermal properties depending on their shapes, such as anisotropic thermal conductivity. One of the representative applications of such composite materials for thermal control is the thermal cloak. This study proposed a topology optimization method based on a level set method for a heat conduction problem to optimally design composite materials that achieve a thermal cloak. The homogenization method was introduced to evaluate its effective thermal conductivity coefficient. Then, we formulated a multiscale topology optimization method for the composite materials in the framework of the homogenization method, where the microstructures were optimized to minimize objective functions defined using the macroscopic temperature field. We presented examples of optimal structures in a two-dimensional problem and discussed the validity of the obtained structures.

cs.CE↗

arXiv2023

Exceptional points in cylindrical elastic media with radiation loss

Exceptional points (EPs) are singular points on a parameter space at which some eigenvalues (scattering poles) and their corresponding eigenmodes coalesce. This study shows the existence of second- and third-order EPs in cylindrical elastic systems with radiation loss. We consider multilayered cylindrical solids under the plane-strain condition placed in a background elastic or acoustic medium. Elastic and acoustic waves propagating in the background media are subject to the radiation loss. We optimize the radii and the material constants of the multilayered solids, such that some scattering poles coalesce on the complex frequency plane. Some numerical experiments are performed to confirm that the coalescence originates from EPs. We expect that this study provides a new approach for enhancing mechanical sensors.

physics.class-ph↗

arXiv2023

Optimal design of compliant displacement magnification mechanisms using stress-constrained topology optimization based on effective energy

In this paper, stress-constrained topology optimization is applied to the design of compliant displacement magnification mechanisms. By formulating the objective function based on the concept of effective energy, it is not necessary to place artificial spring components at the boundaries of the output and input ports as in previous methods. This makes it possible to design mechanisms that do not receive a reaction force at the output port, such as sensors. Furthermore, by imposing a constraint on the maximum stress evaluated in terms of the p-norm of the von Mises equivalent stress, problems such as stress concentration can be avoided. Several numerical examples of displacement magnification mechanisms are provided to demonstrate the effectiveness of the proposed method.

cs.CE↗

arXiv2022

Topology optimization for acoustic structures considering viscous and thermal boundary layers using a sequential linearized Navier-Stokes model

This study proposes a level set-based topology optimization method for designing acoustic structures with viscous and thermal boundary layers in perspective. Acoustic waves propagating in a narrow channel are damped by viscous and thermal boundary layers. To estimate these viscothermal effects, we first introduce a sequential linearized Navier-Stokes model based on three weakly coupled Helmholtz equations for viscous, thermal, and acoustic pressure fields. Then, the optimization problem is formulated, where a sound-absorbing structure comprising air and an isothermal rigid medium is targeted, and its sound absorption coefficient is set as an objective function. The adjoint variable method and the concept of the topological derivative are used to approximately obtain design sensitivity. A level set-based topology optimization method is used to solve the optimization problem. Two-dimensional numerical examples are provided to support the validity of the proposed method. Moreover, the mechanisms that lead to the high absorption coefficient of the optimized design are discussed.

cs.CE↗

arXiv2022

Topology optimization with a closed cavity exclusion constraint for additive manufacturing based on the fictitious physical model approach

This paper proposes a topology optimization method that considers the geometric constraint of no closed cavities to improve the effectiveness of additive manufacturing based on the fictitious physical model approach. First, the basic topology optimization concept and level set-based method are introduced. Next, the fictitious physical model for a geometric constraint in the topology optimization framework is discussed. Then, a model for the geometric constraint of no closed cavities for additive manufacturing is proposed. Numerical examples are provided to validate the proposed model. In addition, topology optimization considering the geometric constraint is formulated, and topology optimization algorithms are constructed using the finite element method. Finally, optimization examples are provided to validate the proposed topology optimization method.

cs.SE↗

arXiv2022

A coupled-mode theory for two-dimensional exterior Helmholtz problems based on the Neumann and Dirichlet normal mode expansion

This study proposes a novel coupled-mode theory for two-dimensional exterior Helmholtz problems. The proposed approach is based on the separation of the entire space R2 into a fictitious disk and its exterior. The disk is allocated in such a way that it comprises all the inhomogeneity; therefore, the exterior supports cylindrical waves with a continuous spectrum. For the interior, we expand an unknown wave field using normal modes that satisfy some auxiliary boundary conditions on the surface of the disk. For the interior expansion, we propose combining the Neumann and Dirichlet normal modes. We show that the proposed expansion sacrifices L2 orthogonality but significantly improve the convergence. Finally, we present some numerical verifications of the proposed coupled-mode theory.

math.NA↗

arXiv2021

Extended level set method: a multiphase representation with perfect symmetric property, and its application to multi material topology optimization

This paper provides an extended level set (X-LS) based topology optimiza- tion method for multi material design. In the proposed method, each zero level set of a level set function ϕij represents the boundary between materials i and j. Each increase or decrease of ϕij corresponds to a material change between the two materials. This approach reduces the dependence of the initial configuration in the optimization calculation and simplifies the sensitivity analysis. First, the topology optimization problem is formulated in the X-LS representation. Next, the reaction-diffusion equation that updates the level set function is introduced, and an optimization algorithm that solves the equilibrium equations and the reaction-diffusion equation using the fi- nite element method is constructed. Finally, the validity and utility of the proposed topology optimization method are confirmed using two- and three- dimensional numerical examples.

cs.CE↗

arXiv2021

Topology optimization of acoustic metasurfaces by using a two-scale homogenization method

In this paper, we propose a level set-based topology optimization method for the unit-cell design of acoustic metasurfaces by using a two-scale homogenization method. Based on previous works, we first propose a homogenization method for acoustic metasurfaces that can be combined with topology optimization. In this method, a nonlocal transmission condition depending on the unit cell of the metasurface appears in a macroscale problem. Next, we formulate an optimization problem within the framework of a level set-based topology optimization method, wherein an objective functional is expressed as the macroscopic responses obtained through the homogenization, and material distributions in the unit cell are set as design variables. A sensitivity analysis is conducted based on the concept of the topological derivative. To confirm the validity of the proposed method, two-dimensional numerical examples are provided. First, we provide a numerical example that supports the validity of the homogenization method, and we then perform optimization calculations based on the waveguide settings of the acoustic metasurfaces. In addition, we discuss the mechanism of the obtained optimized structures.

cs.CE↗

arXiv2021

Topology optimization considering the distortion in additive manufacturing

Additive manufacturing is a free-form manufacturing technique in which parts are built in a layer-by-layer manner. Laser powder bed fusion is one of the popular techniques used to fabricate metal parts. However, it induces residual stress and distortion during fabrication that adversely affects the mechanical properties and dimensional accuracy of the manufactured parts. Therefore, predicting and avoiding the residual stress and distortion are critical issues. In this study, we propose a topology optimization method that accounts for the distortion. First, we propose a computationally inexpensive analytical model for additive manufacturing that uses laser powder bed fusion and formulated an optimization problem. Next, we approximate the topological derivative of the objective function using an adjoint variable method that is then utilized to update the level set function via a time evolutionary reaction-diffusion equation. Finally, the validity and effectiveness of the proposed optimization method was established using two-dimensional design examples.

cs.CE↗

arXiv2020

Test for mean matrix in GMANOVA model under heteroscedasticity and non-normality for high-dimensional data

This paper is concerned with the testing bilateral linear hypothesis on the mean matrix in the context of the generalized multivariate analysis of variance (GMANOVA) model when the dimensions of the observed vector may exceed the sample size, the design may become unbalanced, the population may not be normal, or the true covariance matrices may be unequal. The suggested testing methodology can treat many problems such as the one- and two-way MANOVA tests, the test for parallelism in profile analysis, etc., as specific ones. We propose a bias-corrected estimator of the Frobenius norm for the mean matrix, which is a key component of the test statistic. The null and non-null distributions are derived under a general high-dimensional asymptotic framework that allows the dimensionality to arbitrarily exceed the sample size of a group, thereby establishing consistency for the testing criterion. The accuracy of the proposed test in a finite sample is investigated through simulations conducted for several high-dimensional scenarios and various underlying population distributions in combination with different within-group covariance structures. Finally, the proposed test is applied to a high-dimensional two-way MANOVA problem for DNA microarray data.

stat.ME↗

arXiv2019

Geometric Shape Features Extraction Using a Steady State Partial Differential Equation System

A unified method for extracting geometric shape features from binary image data using a steady state partial differential equation (PDE) system as a boundary value problem is presented in this paper. The PDE and functions are formulated to extract the thickness, orientation, and skeleton simultaneously. The main advantages of the proposed method is that the orientation is defined without derivatives and thickness computation is not imposed a topological constraint on the target shape. A one-dimensional analytical solution is provided to validate the proposed method. In addition, two-dimensional numerical examples are presented to confirm the usefulness of the proposed method.

cs.CV↗