• Title, Summary, Keyword: Shape design sensitivity

### Optimal Shape Design of Container in HIPing Process by the Finite Element Method (유한요소법을 이용한 HIPing 공정에서의 컨테이너 형상 최적설계)

• 전경달
• Proceedings of the Korean Society for Technology of Plasticity Conference
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• pp.257-260
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• 1999
• It is very important to design the shape of container in HIPing process since the final shape and relative density distribution of the product are decisively dependent on the shape of container. A derivative based approach to determine the shape of container in HIPing process is presented. In this approach the optimal design problem is formulated on the basis of the finite element process. The process model the formulation for process optimal design and the schemes for the evaluation of the design sensitivity and an iterative procedure for optimization are described. In comparison with finite difference scheme the validity of the schemes for the evaluation of the design sensitivity is examined.

### A Boundary Method for Shape Design Sensitivity Analysis for Shape Optimization Problems and its Application (경계법을 이용한 형상최적화 문제의 설계민감도 해석 및 응용)

• 최주호;곽현구
• Proceedings of the Computational Structural Engineering Institute Conference
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• pp.355-362
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• 2004
• An efficient boundary-based technique is developed for addressing shape design sensitivity analysis in various problems. An analytical sensitivity formula in the form of a boundary integral is derived based on the continuum formulation for a general functional defined in problems. The formula, which is expressed in terms of the boundary solutions and shape variation vectors, can be conveniently used for gradient computation in a variety of shape design problems. While the sensitivity can be calculated independent of the analysis means, such as the finite element method (FEM) or the boundary element method (BEM), the FEM is used for the analysis in this study because of its popularity and easy-to-use features. The advantage of using a boundary-based method is that the shape variation vectors are needed only on the boundary, not over the whole domain. The boundary shape variation vectors are conveniently computed by using finite perturbations of the shape geometry instead of complex analytical differentiation of the geometry functions. The supercavitating flow problem and fillet problem are chosen to illustrate the efficiency of the proposed methodology. Implementation issues for the sensitivity analysis and optimization procedure are also addressed in these problems.

### A Boundary Method for Shape Design Sensitivity Analysis in Shape Optimization Problems and its Application (경계법을 이용한 형상최적화 문제의 설계민감도 해석 및 응용)

• Kwak Hyun-Gu;Choi Joo-Ho
• Journal of the Computational Structural Engineering Institute of Korea
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• v.18 no.3
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• pp.255-263
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• 2005
• This paper proposes an efficient boundary-based technique for the shape design sensitivity analysis in various disciplines. An analytical sensitivity formula in the form of a boundary integral is derived based on the continuum formulation for a general functional defined in the problems. The formula can be conveniently used for gradient computation in a variety of shape design problems. The advantage of using a boundary-based method is that the shape variation vectors are needed only on the boundary, not over the whole domain. The boundary shape variation vectors are conveniently computed by using finite. Perturbations of the shape geometry instead of complex analytical differentiation of the geometry functions. The potential flow problems and fillet problem are chosen to illustrate the efficiency of the proposed methodology.

### Shape Design Sensitivity Analysis for Stability of Elastic Structure (탄성 구조물의 안정성을 고려한 형상설계 민감도해석)

• Choi Joo-Ho;Yang Wook-Jin
• Proceedings of the Computational Structural Engineering Institute Conference
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• pp.841-846
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• 2006
• This paper addresses the method for the shape design sensitivity analysis of the buckling load in the continuous elastic body. The sensitivity formula for critical load is analytically derived and expressed in terms of shape variation, based on the continuum formulation of the stability problem. Though the buckling problem is more efficiently solved by the structural elements such as beam and shell, the elastic solids are considered in this paper because the solid elements can be used in general for any kind of structures whether they are thick or thin. The initial stress and buckling analysis is carried out by the commercial analysis code ANSYS. The sensitivity is computed by using the mathematical package MATLAB using the results of ANSYS. Several problems including straight and curved beams under compressive load, ring under pressure load, thin-walled section are chosen to illustrate the efficiency of the presented method.

### Shape Design Sensitivity Analysis for Stability of Elastic Structures (탄성 구조물의 안정성을 고려한 형상설계민감도해석)

• Choi, Joo-Ho
• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.1
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• pp.76-83
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• 2006
• This paper addresses the method for the shape design sensitivity analysis of the buckling load in the continuous elastic body. The sensitivity formula for critical load is analytically derived and expressed in terms of shape variation, based on the continuum formulation of the stability problem. Though the buckling problem is more efficiently solved by the structural elements such as beam and shell, the elastic solids are considered in this paper because the solid elements can be used in general for any kind of structures whether they are thick or thin. The initial stress and buckling analysis is carried out by the commercial analysis code ANSYS. The sensitivity is computed by using the mathematical package MATLAB using the results of ANSYS. Several problems including straight and curved beams under compressive load, ring under pressure load, thin-walled section and bottle shaped column are chosen to illustrate the efficiency of the presented method.

### Sensitivity Analysis of Linear Elastic Problem due to Variations of the Traction Boundary Conditions (하중경계조건의 변화에 대한 선형탄성문제의 민감도 해석)

• 이태원
• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.6
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• pp.1852-1860
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• 1991
• A shape design sensitivity of the elastic deformation due to a change of traction boundary condition is presented. The solution of governing equations for a linear elasticity problem is obtained by finite element method and the traction boundary is defined by design variables. The performance functional to be considered involves both the domain and boundary integral. Variations of geometry can be defined as design velocity. Using material derivative concept and adjoint equations, the design sensitivity is derived by Lagrange multiplier method. For a given geometry of a structure, the change of traction boundary is described by the tangential component of the design velocity only. The final result for the shape design sensitivity is formulated as the boundary integral form, the integrand is defined by tangential component of design velocity and first order derivatives of parameters. Numerical implementation of design sensitivity is discussed and is compared with the difference of the actual values.

### Shape Design Sensitivity Analysis for Interface Problem in Axisymmetric Elasticity

• Choi, Joo-Ho;Lee, Boo-Youn;Han, Jung-Suk
• Journal of Mechanical Science and Technology
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• v.14 no.2
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• pp.197-206
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• 2000
• A boundary integral equation method in the shape design sensitivity analysis is developed for the elasticity problems with axisymmetric non-homogeneous bodies. Functionals involving displacements and tractions at the zonal interface are considered. Sensitivity formula in terms of the interface shape variation is then derived by taking derivative of the boundary integral identity. Adjoint problem is defined such that displacement and traction discontinuity is imposed at the interface. Analytic example for a compound cylinder is taken to show the validity of the derived sensitivity formula. In the numerical implementation, solutions at the interface for the primal and adjoint system are used for the sensitivity. While the BEM is a natural tool for the solution, more generalization should be made since it should handle the jump conditions at the interface. Accuracy of the sensitivity is evaluated numerically by the same compound cylinder problem. The endosseous implant-bone interface problem is considered next as a practical application, in which the stress value is of great importance for successful osseointegration at the interface. As a preliminary step, a simple model with tapered cylinder is considered in this paper. Numerical accuracy is shown to be excellent which promises that the method can be used as an efficient and reliable tool in the optimization procedure for the implant design. Though only the axisymmetric problem is considered here, the method can be applied to general elasticity problems having interface.

### Design Sensitivity Analysis for Shape Optimization of Electromagnetic Device with Finite Element Method (설계민감도해석과 FEM에 의한 전자소자의 형상최적화)

• Ryu, Jae-Seop;Koh, Chang-Seop
• Proceedings of the KIEE Conference
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• pp.835-837
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• 2002
• This paper presents a shape optimization algorithm of electromagnetic devices using the design sensitivity analysis with FEM. The design sensitivity and adjoint variable formulas are derived for the 3D FEM with edge element. This algorithm is applied to 3D electro-magnet pole shape optimization problem to make a uniform flux density at the target region.

### 민감도법을 이용한 단조 공정에서의 예비성형체 설계

• 심현보;노현철
• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• pp.291-296
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• 2000
• The sensitivity method has been applied to find perform shape that results in the desired shape after forging. As a basic example, initial shape of specimen for the cylinder shape without barrelling after forging has been found. The method is then applied to various shapes of 3D free forging and initial shapes of the corresponding specimens after forging have been found successfully. The sensitivity method is proven to be an effective and accurate tool for the preform design.

### Design Sensitivity Analysis and Topology Optimization of Geometrically Nonlinear Structures (기하학적 비선헝 구조물의 설계 민감도해석 및 위상최적설계)

• Cho, Seonho;Jung, Hyunseung;Yang, Youngsoon
• Proceedings of the Computational Structural Engineering Institute Conference
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• pp.335-342
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• 2002
• A continuum-based design sensitivity analysis (DSA) method fur non-shape problems is developed for geometrically nonlinear elastic structures. The non-shape problem is characterized by the design variables that are not associated with the domain of system like sizing, material property, loading, and so on. Total Lagrangian formulation with the Green-Lagrange strain and the second Piola-Kirchhoff stress is employed to describe the geometrically nonlinear structures. The spatial domain is discretized using the 4-node isoparametric plane stress/strain elements. The resulting nonlinear system is solved using the Newton-Raphson iterative method. To take advantage of the derived analytical sensitivity In topology optimization, a fast and efficient design sensitivity analysis method, adjoint variable method, is employed and the material property of each element is selected as non-shape design variable. Combining the design sensitivity analysis method and a gradient-based design optimization algorithm, an automated design optimization method is developed. The comparison of the analytical sensitivity with the finite difference results shows excellent agreement. Also application to the topology design optimization problem suggests a very good insight for the layout design.