• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.34 no.3
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• pp.328-338
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• 1998

It is main objective of this approach to present a method to analyse stochastic design sensitivity for problems of structural dynamics with randomness in design parameters. A combination of the adjoint variable approach and the second oder perturbation method is used in the finite element approach. An alternative form of the constant functional that holds for all times is introduced to consider the time response of dynamic sensitivity. The terminal problem of the adjoint system is solved using equivalent homogeneous equations excited by initial velocities. The numerical procedures are shown to be much more efficient when based on the fold superposition method : the generalized co-ordinates are normalized and the correlated random variables are transformed to uncorrelated variables, where as the secularities are eliminated by the fast Fourier transform of complex valued sequences. Numerical algorithms have been worked out and proved to be accurate and efficient : they codes whose element derivative matrices can be explicitly generated. The numerical results of two cases - 2-dimensional portal frame and 3/4-cylindrical shell structure - for the deterministic and stochastic sensitivity analysis illustrates in this paper.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1992.10a
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• pp.19-24
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• 1992

Design sensitivity analysis method for the vibration of vehicle structure is developed using adjoint variable method. A variational approach with complex response method is used to derive sensitivity expression. To evaluate sensitivity, FEM analysis of ship deck and vehicle structure are performed using MSC/NASTRAN on the super computer CRAY2S, and sensitivity computation is carried on PC. The accuracy of sensitivity is verified by the results of finite difference method. When compared to structural analysis time on CRAY2S, sensitivity computation is remarkably economical. The sensitivity of vehicle frame can be used to reduce the vibration responses such as displacement and acceleration of vehicle.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.5
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• pp.1458-1467
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• 1996

A direct differentiationmethod is presented for the shape design sensitivity analysis of axisymmeetric elastic solids. Based on the exisymmetric boundary integralequaiton formulation, a new boundary ntegral equatio for sensitivity analysis is derived by taking meterial derivative to the same integral identity that was used in the adjoint variable melthod. Numerical implementation is performed to show the applicaiton of the theoretical formulation. For a simple example with analytic solution, the sensitivities by present method are compared with analytic sensitivities. As an application to the shape optimization, an optimal shape of a gas turbine disc toinimize the weight under stress constraints is found by incorporating the sensitivity analysis algorithm in an optimizatio program.

• Journal of the Society of Naval Architects of Korea
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• v.47 no.1
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• pp.58-66
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• 2010

Topology design optimization is a method to determine the optimal distribution of material that yields the minimal compliance of structures, satisfying the constraint of allowable material volume. The method is easy to implement and widely used so that it becomes a powerful design tool in various disciplines. In this paper, a large-scale topology design optimization method is developed using the efficient adjoint sensitivity and optimality criteria methods. Parallel computing technique is required for the efficient topology optimization as well as the precise analysis of large-scale problems. Parallelized finite element analysis consists of the domain decomposition and the boundary communication. The preconditioned conjugate gradient method is employed for the analysis of decomposed sub-domains. The developed parallel computing method in topology optimization is utilized to determine the optimal structural layout of human powered vessel.

• KIEE International Transaction on Electrical Machinery and Energy Conversion Systems
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• v.3B no.2
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• pp.79-83
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• 2003

The topology optimization for the magnet design is studied. The magnet design in the C-core actuator is investigated by using the derived topology optimization algorithm and finite element method. The design sensitivity equation for the topology optimization is derived using the adjoint variable method and the continuum approach.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.10a
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• pp.238-245
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• 2000

A general formulation for shape design sensitivity analysis over a plane arch structure is developed based on a variational formulation of curved beam in linear elasticity. Sensitivity formula is derived using the material derivative concept and adjoint variable method for the stress defined at a local segment. Obtained sensitivity expression, which can be computed by simple algebraic manipulation of the solution variables, is well suited for numerical implementation since it does not involve numerical differentiation. Due to the complete description for the shape and its variation of the arch, the formulation can manage more complex design problems with ease and gives better optimum design than before. Several examples are taken to show the advantage of the method, in which the accuracy of the sensitivity is evaluated. Shape optimization is also conducted with two design problems to illustrate the excellent applicability.

• Journal of Electrical Engineering and Technology
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• v.8 no.4
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• pp.780-786
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• 2013

In the reliability-based design optimization of electromagnetic devices, the accurate and efficient reliability assessment method is very essential. The first-order sensitivity-assisted Monte Carlo Simulation is proposed in the former research. In order to improve its accuracy for wide application, in this paper, the second-order sensitivity analysis is presented by using the hybrid direct differentiation-adjoint variable method incorporated with the finite element method. By combining the second-order sensitivity with the Monte Carlo Simulation method, the second-order sensitivity-assisted Monte Carlo Simulation algorithm is proposed to implement reliability calculation. Through application to one superconductor magnetic energy storage system, its accuracy is validated by comparing calculation results with other methods.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.3
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• pp.339-345
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• 2007

In this paper, a variational formulation for plane elasticity problems is derived based on an isogeometric approach. The isogeometric analysis is an emerging methodology such that the basis functions for response analysis are generated directly from NURBS (Non-Uniform Rational B-Splines) geometry. Furthermore, the solution space for the response analysis can be represented in terms of the same functions to represent the geometry, which enables to provide a precise construction method of finite element model to exactly represent geometry using B-spline base functions in CAD geometric modeling and analyze arbitrarily shaped structures without re-meshing. In this paper, a continuum-based adjoint sensitivity analysis method using the isogeometric approach is extensively derived for the plane elasticity problems. The conventional shape optimization using the finite element method has some difficulties in the parameterization of geometry In the isogeometric analysis, however, the geometric properties are already embedded in the B-spline basis functions and control points so that it has potential capability to overcome the aforementioned difficulties. Through some numerical examples, the developed isogeometric sensitivity analysis method is verified to show excellent agreement with finite difference sensitivity.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.53 no.8
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• pp.469-476
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• 2004

In this paper, a 3D shape optimization algorithm which guarantees a smooth optimal shape is presented using parameterized sensitivity analysis. The design surface is parameterized using Bezier spline and B-spline, and the control points of the spline are taken as the design variables. The parameterized sensitivity for the control points are found from that for nodal points. The design sensitivity and adjoint variable formulae are also derived for the 3D non-linear problems. Through an application to the shape optimization of 3D electromagnet to get a uniform magnetic field, the effectiveness of the proposed algorithm is shown.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.49 no.5
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• pp.327-337
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• 2000

In this paper, the design sensitivity formula for the control of the transient temperature distribution is developed using the direct differentiation method, and used for the optimal design of induction heating coil position. The temperature distribution is calculated using the heat source of the induced eddy current and heat diffusion equation. The physical property variations of the workpiece depending on the temperature are considered. The eddy current distribution and the temperature distribution are calculated with the 2D finite element procedure. The adjoint variable technique is employed in expressing the design sensitivity. The goal of the design is to have the desired distribution of the temperature on a specific region of the sensitivity. The goal of the design is to have the desired distribution of the temperature on a specific region sensitivity. The goal of the design is to have the desired distribution of the temperature on a specific region of the workpiece. The numerical example shows that the proposed design sensitivity analysis for the control of the transient temperature distribution is very useful and practical in the optimal design of induction heating coils.