• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 한국소음진동공학회 2009년도 춘계학술대회 논문집
• /
• pp.264-265
• /
• 2009

• Journal of the Computational Structural Engineering Institute of Korea
• /
• 제35권6호
• /
• pp.367-374
• /
• 2022

This papter presents the use of the automatic differential method based on the backpropagation method to obtain the design sensitivity and its application to topology optimization considering the stress constraints. Solving topology optimization problems with stress constraints is difficult owing to singularities, the local nature of stress constraints, and nonlinearity with respect to design variables. To solve the singularity problem, the stress relaxation technique is used, and p-norm for stress constraints is applied instead of local stresses for global stress measures. To overcome the nonlinearity of the design variables in stress constraint problems, it is important to analytically obtain the exact design sensitivity. In conventional topology optimization, design sensitivity is obtained efficiently and accurately using the adjoint variable method; however, obtaining the design sensitivity analytically and additionally solving the adjoint equation is difficult. To address this problem, the design sensitivity is obtained using a backpropagation technique that is used to determine optimal weights and biases in the artificial neural network, and it is applied to the topology optimization with the stress constraints. The backpropagation technique is used in automatic differentiation and can simplify the calculation of the design sensitivity for the objectives or constraint functions without complicated analytical derivations. In addition, the backpropagation process is more computationally efficient than solving adjoint equations in sensitivity calculations.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 한국전산구조공학회 2005년도 춘계 학술발표회 논문집
• /
• pp.309-316
• /
• 2005

In this paper, we develop continuum-based design sensitivity analysis (DSA) methods using both direct differential method (DDM) and adjoint variable method (AVM) for non-shape design problems. The developed DSA method is further utilized for the topology design optimization of 3-dimensional structures. In numerical examples, the analytical DSA results are verified using finite difference ones. The topology optimization method yields very reasonable results in physical point of view.

• Journal of the Optical Society of Korea
• /
• 제13권2호
• /
• pp.286-293
• /
• 2009

In this paper, we present an optimal shape design method for a dielectric microlens which is used to focus an incoming infrared plane wave in wideband, by exploiting the finite difference time domain (FDTD) technique and the topology optimization technique. Topology optimization is a scheme to search an optimal shape by adjusting the material properties, which are design variables, within the design space. And by introducing the adjoint variable method, we can effectively calculate a derivative of the objective function with respect to the design variable. To verify the proposed method, a shape design problem of a dielectric microlens is tested when illuminated by a transverse electric (TE)-polarized infrared plane wave. In this problem, the design variable is the dielectric constant within the design space of a dielectric microlens. The design objective is to maximally focus the incoming magnetic field at a specific point in wideband.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 한국소음진동공학회 2000년도 춘계학술대회논문집
• /
• pp.479-484
• /
• 2000

The topology optimization of electromagnetic systems is investigated and the TOPEM (Topology Optimization for Electromagnetic Systems) is developed using the finite element method (FEM). The design sensitivity equation for topology optimization is derived using the adjoint variable method. The proposed method is validated by applying it to the topology optimizations of a C-core actuator and an optical pickup actuator.

• Proceedings of the KIEE Conference
• /
• 대한전기학회 2003년도 하계학술대회 논문집 B
• /
• pp.705-707
• /
• 2003

The design of multi-domain that considers all components of the electromagnetic systems such as air, iron, magnet, and coil is investigated using the topology optimization, interpolation method, and FEM. The design sensitivity equation for the topology optimization is derived using the adjoint variable method and the continuum approach. The proposed method is applied to the topology optimization of C-core actuator.

• Proceedings of the KIEE Conference
• /
• 대한전기학회 2003년도 하계학술대회 논문집 B
• /
• pp.708-710
• /
• 2003

This paper presents design sensitivity analysis for the electromagnetic force and torque obtained from Coulomb's virtual work method using the adjoint variable method. And virtual displacement field is calculated from a static structural analysis. Derived equations are verified by comparison with finite different method. And topology optimization for a c-core is given as a verification example.

• Proceedings of the KIEE Conference
• /
• 대한전기학회 2005년도 제36회 하계학술대회 논문집 B
• /
• pp.939-941
• /
• 2005

This research presents a 3D multi-objective approach regarding both magnetic and thermal characteristics associated with design of C-core actuator. The adjoint variable topology sensitivity equations are derived using the continuum method for three dimension. The sensitivity is verified using the Finite Difference Method(FDM). Convection interpolation function is proposed for density method of topologies such that convection term can be taken into consideration for practical design in the process of the optimization.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• 제28권1호
• /
• pp.9-18
• /
• 2015

In this paper, we verify the optimal topology design for heat conduction problems in steady stated which is obtained numerically using the adjoint design sensitivity analysis(DSA) method. In adjoint variable method(AVM), the already factorized system matrix is utilized to obtain the adjoint solution so that its computation cost is trivial for the sensitivity. For the topology optimization, the design variables are parameterized into normalized bulk material densities. The objective function and constraint are the thermal compliance of the structure and the allowable volume, respectively. For the experimental validation of the optimal topology design, we compare the results with those that have identical volume but designed intuitively using a thermal imaging camera. To manufacture the optimal design, we apply a simple numerical method to convert it into point cloud data and perform CAD modeling using commercial reverse engineering software. Based on the CAD model, we manufacture the optimal topology design by CNC.

• Journal of Mechanical Science and Technology
• /
• 제16권8호
• /
• pp.1102-1108
• /
• 2002

In this study, a topological design sensitivity of the ai. bearing surface (ABS) is suggested by using an adjoint variable method. The discrete form of the generalized lubrication equation based on a control volume formulation is used as a compatible condition. A residual function of the slider is considered as an equality constraint function, which represents the slider in equilibrium. The slider thickness parameters at all grid cells are chosen as design variables since they are the topological parameters determining the ABS shape. Then, a complicated adjoint variable equation is formulated to directly handle the highly nonlinear and asymmetric coefficient matrix and vector in the discrete system equation of air-lubricated slider bearings. An alternating direction implicit (ADI) scheme is utilized for the numerical calculation. This is an efficient iterative solver to solve large-scale problem in special band storage. Then, a computer program is developed and applied to a slider model of a sophisticated shape. The simulation results of design sensitivity analysis (DSA) are directly compared with those of FDM at the randomly selected grid cells to show the effectiveness of the proposed approach. The overall distribution of DSA results are reported, clearly showing the region on the ABS where special attention should be given during the manufacturing process.