• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.3
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• pp.639-646
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• 1995

The objective of this study is to minimize the weight of a damped anisotropic roto-bearing system considering whirl natural frequency and stability. The system is modeled as an assemblage of rigid disks, flexible shafts and discrete bearings. The system design variables are the crosssectional areas of shaft elements and the properties of bearings. To analyze the system, the polynomial method which is derived by rearranging the calculations performed by a transfer matrix method is adopted. For the optimization, the optimization software IDOL (Integrated Design Optimization Library) which is based on the Augmented Lagrange Multiplier (ALM) method is employed. Also, an analytical design sensitivity analysis of the system is used for high accuracy and efficiency. To demonstrate the usefulness of the proposed optimal design program incorporating analysis, design sensitivity analysis, and optimization modules, a damped anisotropic rotor-bearing system is optimized to obtain 34$ weight reduction.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.3
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• pp.594-602
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• 1990

A computer-aided design system of involute cylindrical gears(spur and helical gears) for power transmission is developed, in which the volume of a gear unit is minimized with satisfying various design constraints. As the design constraints, bending strength and pitting resistance of AGMA 218.01, scoring of Dudley's flash temperature, contact ratio, and involute interference of pinion are considered and effective factors for strength calculation(life, reliability, hardness ratio, load distribution, velocity, etc.) are also included. This complicated nonlinear optimization problem is solved by using ALM(Augmented-Lagrange-Multiplier) method with self scaling BFGS(Broydon-Fletcher-Goldfarb-Shanno) method employed for unconstrained optimization programming. This design method can be easily applied to designing power transmission gear unit in the machines of various kinds. It is expected for the proposed method to be a contribution for an automated design of gear unit towards weight minimization, miniaturization and high strength of gear unit.

• Transactions of the Korean Society of Automotive Engineers
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• v.1 no.3
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• pp.74-82
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• 1993

Optimal designs of a 3-point and a 4-point engine mount system are presented for reducing the idle shake of a Front Wheel Drive(FWD) vehicle. Design variables used in this study are the locations, the angles and the stiffness of an engine mount system. The goal of the optimization is minimizing the transmitted force without violating the constraints such as static weight sag, resonant frequency and side limits of design variables. The Augmented Lagrange Multiplier(ALM) Method is used for solving the nonlinear constrained optimization. The generalized Jacobi and the impedence method are employed for a free vibration analysis and a forced response analysis. The trend of analysis results well meet that of the experimental results. The optimization results reveal that the 4-point system transmits less torque than the 3-point system. It is also found from the design sensitivity analysis that the vibration characteristics of the 4-point system is less sensitive than those of the 3-point system.

• Smart Structures and Systems
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• v.30 no.3
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• pp.221-237
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• 2022

This paper is concerned with nonlinear modeling and efficient numerical simulation of electrostrictive materials and structures. Two types of such materials are considered: relaxor ferroelectric ceramics and electrostrictive polymers. For ceramics, a geometrically linear formulation is developed, whereas polymers are studied in a geometrically nonlinear regime. In the paper, we focus on constitutive modeling first. For the reversible constitutive response under consideration, we introduce the augmented Helmholtz free energy, which is composed of a purely elastic part, a dielectric part and an augmentation term. For the elastic part, we involve an additive decomposition of the strain tensor into an elastic strain and an electrostrictive eigenstrain, which depends on the polarization of the material. In the geometrically nonlinear case, a corresponding multiplicative decomposition of the deformation gradient tensor replaces the additive strain decomposition used in the geometrically linear formulation. For the dielectric part, we first introduce the internal energy, to which a Legendre transformation is applied to compute the free energy. The augmentation term accounts for the contribution from vacuum to the energy. In our formulation, the augmented free energy depends not only on the strain and the electric field, but also on the polarization and an internal polarization; the latter two are internal variables. With the constitutive framework established, a Finite Element implementation is briefly discussed. We use high-order elements for the discretization of the independent variables, which include also the internal variables and, in case the material is assumed incompressible, the hydrostatic pressure, which is introduced as a Lagrange multiplier. The elements are implemented in the open source code Netgen/NGSolve. Finally, example problems are solved for both, relaxor ferroelectric ceramics and electrostrictive polymers. We focus on thin plate-type structures to show the efficiency of the numerical scheme and its applicability to thin electrostrictive structures.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.3
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• pp.591-599
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• 1994

A design system for power transmission bevel gears(straight, zerol, and spiral) is developed, in which the strength and durability of bevel gears can be estimated and the size of bevel gears can be minimized by introducing optimal techniques. The size of bevel gear pair as the object function to be minimized is the volume of equivalent spur gear pair at mean normal section, and the design variables to be determined are considered as the number of teeth, face width, diametral pitch, and spiral angle in spiral bevel gear. The strength(bending strength, pitting resistance) according to the AGMA standards, geometrical quantities, and operating characteristics(interference of pinion, contact ratio, etc.) are considered as the constraints in design optimization. The optimization with these constraints becomes nonlinear problem and that is solved with ALM(Augmented Lagrange Multiplier) method. The developed design method is applied to the example designs of straight, zerol, and spiral bevel gears. The design results are acceptable from the viewpoint of strength and durability within the design ranges of all other constraint, and the bevel gears are designed toward minimizing the size of gear pair. This design method is easily applicable to the design of bevel gears used as power transmitting devices in machineries, and is expected to be used for weight minimization of bevel gear unit.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.32 no.4
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• pp.249-256
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• 2019

This paper presents an optimization framework of electrical impedance tomography for characterizing electrical conductivity profiles of concrete structures in two dimensions. The framework utilizes a partial-differential-equation(PDE)-constrained optimization approach that can obtain the spatial distribution of electrical conductivity using measured electrical potentials from several electrodes located on the boundary of the concrete domain. The forward problem is formulated based on a complete electrode model(CEM) for the electrical potential of a medium due to current input. The CEM consists of a Laplace equation for electrical potential and boundary conditions to represent the current inputs to the electrodes on the surface. To validate the forward solution, electrical potential calculated by the finite element method is compared with that obtained using TCAD software. The PDE-constrained optimization approach seeks the optimal values of electrical conductivity on the domain of investigation while minimizing the Lagrangian function. The Lagrangian consists of least-squares objective functional and regularization terms augmented by the weak imposition of the governing equation and boundary conditions via Lagrange multipliers. Enforcing the stationarity of the Lagrangian leads to the Karush-Kuhn-Tucker condition to obtain an optimal solution for electrical conductivity within the target medium. Numerical inversion results are reported showing the reconstruction of the electrical conductivity profile of a concrete specimen in two dimensions.