• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2004.10a
• /
• pp.355-362
• /
• 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.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.30 no.1 s.244
• /
• pp.76-83
• /
• 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.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2006.04a
• /
• pp.841-846
• /
• 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.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.18 no.3
• /
• pp.255-263
• /
• 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.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.15 no.6
• /
• pp.1852-1860
• /
• 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.

• Proceedings of the KIEE Conference
• /
• 2002.07b
• /
• pp.835-837
• /
• 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.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
• /
• 2000.10a
• /
• pp.291-296
• /
• 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.

• Journal of Mechanical Science and Technology
• /
• v.14 no.2
• /
• pp.197-206
• /
• 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.

• The Transactions of the Korean Institute of Electrical Engineers
• /
• v.40 no.9
• /
• pp.859-865
• /
• 1991

This paper presents a new shaoe optimal design method using Desing Sensitivity Analysis. Design Sensitivity, defined as the variation of the object function with respect to the design variables, is based on the total differentiation of the matrix equation obtained from discretization of governing equations with respect to design variables. Analysis of the various characteristics adn calculation of Design Sensitivity of optimization model are achieved by using finite or boundary element methods. The proposee algorithm is applied to the optimal shape design of high voltage electrode under specified conditions. It is shown, from the numerical results, that the algorithm is very useful for the optimal shape design of electric apparatus.

• Proceedings of the KIEE Conference
• /
• 1991.07a
• /
• pp.93-96
• /
• 1991

This paper describes a new algorithm based on design sensitivity analysis for optimal shape design of electrostatic devices. The design sensitivity, the variation of the object function with respect to the design variables, is derived by using implicit differentiation and direct boundary element methods. The proposed algorithm is applied to the optimal shape design of a concentric cable and the rod electrode enclosed by earthed case, It is shown, from the numerical results, that the algorithm is very usefull for the optimal shape design of the electrostatic devices.