This paper presents a method for topology optimization that incorporates thermal radiation boundary conditions dependent on design variables. The design of mechanical structures involving thermal radiation is briefly described, along with the associated problems. We consider thermal radiation boundary conditions on partial boundaries of material domains that vary with design variables. During the optimization process, Partial Differential Equations (PDEs) expressing geometric features with high thermal radiation is introduced, and solutions are employed to numerically extract the boundaries. Therefore, a mathematical model is formulated to approximate the view factor, which relates the contribution of macro geometry to thermal radiation. Furthermore, a method for solving the governing equations is developed, leveraging the proposed method. Although we deal with nonlinear problems due to thermal radiation boundary conditions, the design sensitivity concerning the direction of descent of the objective functional can be determined by identifying the adjoint equations as in linear problems. In this study, the Finite Element Method (FEM) is used to solve PDEs of the heat transfer problem, and the level set functions are updated. Numerical examples in two and three dimensions are presented to verify the effectiveness and practicality of the proposed method.

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For the calculation of elastic structure frequency response, a commonly used method is the full mode method (FM). However, for a frequency range, this approach tends to be computationally expensive, especially in the process of topology optimization. Therefore, this study proposes to use the mode displacement method (MDM), which is one of the mode reduction methods. Similarly, for topology optimization in the frequency range, using this method to calculate the adjoint operator can greatly reduce the calculation cost of topological derivatives. The results show that in frequency range, using MDM can significantly improve the efficiency of calculating frequency response and topological derivatives while ensuring a certain accuracy.

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Is this study, we evaluate a shape derivative and Hilbertian-regularized gradient of cost functionals associated with solutions of boundary integral equations. We focus on two-dimensional problems with smooth bounded domains and parameterize them using periodic functions. The parameterization allows us to apply the Fréchet-differential calculus in a straightforward manner. We apply the Hilbertian regularization technique to obtain a gradient (descent direction) of the cost functionals. Some numerical examples are presented to verify the obtained sensitivity.

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This paper focuses on manufacturing the optimal structure obtained by topology optimization using molding techniques, e.g., casting and injection molding. In molding processes, products cannot geometrically be demolded if undercuts and interior voids exist in the structure. Thus, topology optimization that leads to a structure satisfying the geometric constraint for molding is required. In this study, we detect regions that violate the constraint using a fictitious anisotropic diffusion equation. Additionally, based on the concept of a coupled fictitious physical model, which overcomes the convergence problem in the previous formulation method, we formulate the optimization problem. After deriving design sensitivity and an optimization algorithm, we verify the validity of the proposed method through a numerical example.

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The slider-crank mechanism plays a crucial role in various mechanical systems, converting rotational motion into linear motion and vice versa. This mechanism, comprising multiple links, offers versatility in applications such as creating intricate strokes and incorporating adjustment mechanisms. However, manually designing the part layout and dimensions for desired functionality can be challenging. This study introduces a comprehensive optimization approach to determine the number, dimensions, and link structure within a slider-crank mechanism using topology optimization techniques. The linkage mechanism is represented as a topology-optimizable continuum, utilizing micropolar elasticity with independently definable bending and tensile deformation properties. The topology optimization problem is then formulated to enable the slider to produce the desired stroke curve using the proposed model. The proposed multi-material model is defined by the design variables of the Solid Isotropic Material with Penalization (SIMP) method, and the optimization problem is solved by a gradient-based optimization algorithm. Finally, we validate the effectiveness of this method through numerical examples.

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Buckling of an infinite Bernoulli-Euler beam resting on an elastic Winkler foundation characterized by a cubic nonlinearity is studied. Especially, theoretical formulae of the buckling load are derived based on the perturbation method for a beam with initial deflection and variable axial load. First, the snap-through buckling load is obtained for space-harmonic imperfections in both the initial deflection and the axial load. Next, the initial deflection and axial load fluctuation given by stationary random functions are considered. Expectation of the buckling load is described as a function of variance and power spectrum density of these uncertainties. Through buckling analyses, the theoretical buckling load is compared with numerical results. It is shown that the derived solutions can be a good approximation to the present problem.

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Material interpolation scheme and sensitivity analysis are studied in this research, with the aim to achieve topology optimization of rarefied gas flow structures. Choosing the discrete velocity method as the numerical approach for the Boltzmann equation, material interpolation scheme is developed by correcting the convection flux of the discretized convection equations and re-scaling the relaxation term of the Shakhov gas kinetic model. With the proposed interpolation scheme, material distribution can be effectively modelled using a pseudo design density. A discrete adjoint system is proposed for sensitivity analysis. The governing equation, the Boltzmann equation, in the optimization problem is replaced by the steady state condition of the numerical scheme. The discretized version of the governing equation results in a simple and straightforward way to formulate an adjoint system using the Lagrangian multiplier method. The numerical solution of the adjoint system can be obtained by a similar numerical approach, if the flux Jacobian of the original system is transposed. Numerical examples confirm the validity of the proposed methods, which can serve as the basis for structural optimization algorithms in rarefied flow systems.

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We focused on the transmission problems of the 2D Helmholtz equations and investigated the applicability of the fast direct solver of boundary element method when there is a high contrast material parameter ratio between the interior and exterior domains. For this study, we have proposed a modified version of the Burton-Miller integral equation, which is expected to compute proxy-based interpolation with high accuracy since it has wellsuited arrangement of integral operators. A proposed fast direct solver outperforms the conventional method in computational speed. However its numerical accuracy is inferior, and the reasons behind it could not be provided in this study. Additionally, through our numerical experiments, we have highlighted that there might not be any advantages in utilizing the PMCWHT integral equation within the framework of fast direct solvers.

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From a intuitive perspective, exact boundary representation emerges as the most favorable approach for topology optimization of structural systems based on the finite element method (FEM). Under exact boundary representation, the material domain can be precisely defined, granting the flexibility to impose arbitrary boundary conditions on newly generated boundaries throughout the optimization process. This newfound capability is achieved through the recently introduced exact volume constraint method, which effectively addresses the convergence challenges associated with exact boundary representation. However, one key consideration that has not yet been explored is the potential nonlinearity of the reaction-diffusion equation governing the evolution of the level set function. Consequently, the primary objective of this study is to expand upon the proposed topology optimization methodology, which incorporates exact boundary representation, to account for nonlinear aspects of the reaction-diffusion equation. Subsequently, we will conduct a comparative analysis of the results obtained using various proportional constants denoted as K in relation to the level set function ϕ.

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This paper presents a perturbation analysis of the excitation problem for an open domain. As a fundamental study, it addresses wave scattering by a crack in a two-dimensional unbounded domain to avoid fictitious eigenfrequency issues, which are encountered in a boundary integral equation. The modal amplitude is approximated using the perturbation method, employing a Taylor expansion around the complex-valued eigenfrequency for the open domain. The eigenfrequency problem for an open domain is solved using boundary element and Sakurai-Sugiura methods. Several numerical results demonstrate that the perturbation solutions evaluate the modal amplitude with real-valued frequency excitation.

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This paper presents an OMP-based meshfree method for anti-plane wave analysis. The developed meshfree method, OMP-Mf(s), uses not only fundamental solutions but also plane waves as basis functions and can select adequate basis functions using OMP. We applied this developed method to study plane wave scattering caused by interface debonding at the interface of two elastic solids. Several numerical results show that OMP-Mf(s) provides a good approximation of displacement wavefield for s = 2.

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Vehicle Platoon is the method of platooning the vehicles with a short vehicle-to-vehicle distance. It is effective to increase the traffic amount safely without constructing new roads. In the previous study, the mathematical model for controlling the vehicle velocity was defined by the car-following model. A theoretical study revealed that each vehicle in a platoon could control its velocity from the information of only the nearest frontal vehicle and the lead vehicle of the platoon. When a platoon turns left at a corner, the lead vehicle in the platoon changes in order, so the following vehicles must change the lead vehicle they should refer to. In this study, model parameters are determined by numerical simulation and then, their validity is discussed through experiments.

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This paper proposes a fast numerical method to calculate the so-called topological skeleton of two-dimensional objects. The proposed method is based on a generalised double-layer potential that provides a smoothed singed distance field for an object given in a surface format and is thus considered CAD-friendly. To efficiently evaluate the skeleton, we here incorporate the H-matrix method to calculate the potential. Numerical experiments show that, although sometimes the H-matrix method might become unstable, the skeleton can be calculated with sufficient accuracy within acceptable computational time in many practical cases.

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In this study, we investigate the large deformation analysis of a nonreciprocal gel under cylindrical indentation. The nonreciprocity of the gel is modeled by extending the framework of anisotropic linear elasticity [Wang et al., 2023. Mechanical nonreciprocity in a uniform composite material. Science 380, 192–198]. Plane-strain finite-element analysis is performed by assuming the frictionless between the gel and the rigid indenter, leading to reproducing the asymmetric response of the nonreciprocal gel. It is found that severe large deformations cause non-convergence of incremental calculations, which is resolved by introducing artificial viscosity and hourglass control. The combination prevents the occurrence of hourglass deformation modes around the area directly below the indenter as well as obtains converged solutions in efficient incremental calculations. The use of larger values of the two parameters causes the increase of computational efficiency and the decrease of computational accuracy. Parametric studies elucidate the existence of the proper region of the two parameters. Nonreciprocal gel, Tension compression asymmetry, Large deformations, FEA

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A determination of cracks using topology optimization In 3-D scalar wave scattering field is considered. We introduce the cost function which is the misfit function between the observed data and the numerical data on the boundary of the domain having the cracks. We determine the cracks as the minimizer of the cost function using the topological derivative. The determination of two cracks having the less forecast information are shown in this paper.

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A nonreciprocal gel consisting of hydrogel and nanosheet exhibits mechanical nonreciprocity, which has potential applications in mechanical engineering. An earlier study has revealed that this mechanical nonreciprocity is triggered by the tension-compression asymmetry resulting from the microscopic buckling behavior of nanosheets during compressive deformation, but the relevant influencing factors remain unknown. In this study, we investigate the microscopic buckling behavior and the resultant tension-compression asymmetry in a nonreciprocal gel subjected to uniaxial conditions. Eigenvalue buckling and post-buckling analyses equipped with computational homogenization are performed on a unit cell modeled as an elastic bilayer for which ratios of Young’s modulus and thickness are parameterized. The results confirm that selecting a dilute microscopic buckling with the characteristic wavelength or a non-dilute microscopic buckling with the infinite wavelength hinges on the ratios of Young’s modulus and thickness, which is consistent with the theoretical solution for the buckling behavior of a layered composite. We also elucidate that the tension-compression asymmetry is more pronounced as the Young’s modulus ratio increases or the thickness ratio decreases.

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We study the evolution of crease in an elastomer under three different loading conditions. Two- dimensional finite element analysis is performed by combining a non-linear perturbation approach to find a bifurcation solution for the flat surface in a metastable state. A generalized plane strain element is used to impose plane strain, uniaxial, and equibiaxial conditions on the elastomer. The solution is the deformation path for crease evolution, and the path ends at the critical strain for creasing 𝜀!.Thedepthandself-contactlengthofthecreases,whichareindicatorsofcreaseevolution, are described as functions of powers with constants and scaling exponents, which are expressed as linear functions of the crease interval.

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This paper proposes a stabilisation method for a finite element method using the Hilberttype operator for the heat equation. We show that the operator is identical to the original Hilbert-type operator HT up to a compact perturbation. Through a numerical example, it is also verified that the poposed method can control the computational cost and accuracy in a trade-off manner by changing parameters contained in the definition of the proposed operator.

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