• Journal of the Computational Structural Engineering Institute of Korea
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• v.27 no.5
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• pp.337-343
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• 2014

This paper presents a continuum-based shape design sensitivity analysis(DSA) method for crack propagation problems using a reproducing kernel method(RKM), which facilitates the remeshing problem required for finite element analysis(FEA) and provides the higher order shape functions by increasing the continuity of the kernel functions. A linear elasticity is considered to obtain the required stress field around the crack tip for the evaluation of J-integral. The sensitivity of displacement field and stress intensity factor(SIF) with respect to shape design variables are derived using a material derivative approach. For efficient computation of design sensitivity, an adjoint variable method is employed tather than the direct differentiation method. Through numerical examples, The mesh-free and the DSA methods show excellent agreement with finite difference results. The DSA results are further extended to a shape optimization of crack propagation problems to control the propagation path.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.1
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• pp.141-152
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• 1993

A generalized method is presented for shape design sensitivity analysis of axisymmetric thermal conducting solids. The shape sensitivity formula of a general performance functional arising in shape optimal design problem is derived using the material derivative concept and the adjoint variable method. The method for deriving the formula is based on standard axisymmetric boundary integral equation formulation. It is then applied to obtain the sensitivity formulas for temperature and heat flux constraints imposed over a small segment of the boundary. To show the accuracy of the sensitivity analysis, numerical implementations are done for three examples. Sensitivities calculated by the presented method are compared with analytic sensitivities for two examples with analytic solutions, and compared with sensitivies by finite difference for a cooling fin example.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.6
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• pp.549-558
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• 2012

A topology optimization method for phononic crystals is developed for the design of sound barriers, using the level set approach. Given a frequency and an incident wave to the phononic crystals, an optimal shape of periodic inclusions is found by minimizing the norm of transmittance. In a sound field including scattering bodies, an acoustic wave can be refracted on the obstacle boundaries, which enables to control acoustic performance by taking the shape of inclusions as the design variables. In this research, we consider a layered structure which is composed of inclusions arranged periodically in horizontal direction while finite inclusions are distributed in vertical direction. Due to the periodicity of inclusions, a unit cell can be considered to analyze the wave propagation together with proper boundary conditions which are imposed on the left and right edges of the unit cell using the Bloch theorem. The boundary conditions for the lower and the upper boundaries of unit cell are described by impedance matrices, which represent the transmission of waves between the layered structure and the semi-infinite external media. A level set method is employed to describe the topology and the shape of inclusions. In the level set method, the initial domain is kept fixed and its boundary is represented by an implicit moving boundary embedded in the level set function, which facilitates to handle complicated topological shape changes. Through several numerical examples, the applicability of the proposed method is demonstrated.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.6
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• pp.559-567
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• 2012

A level set based topological shape optimization method for nonlinear structure considering hyper-elastic problems is developed. To relieve significant convergence difficulty in topology optimization of nonlinear structure due to inaccurate tangent stiffness which comes from material penalization of whole domain, explicit boundary for exact tangent stiffness is used by taking advantage of level set function for arbitrary boundary shape. For given arbitrary boundary which is represented by level set function, a Delaunay triangulation scheme is used for current structure discretization instead of using implicit fixed grid. The required velocity field in the actual domain to update the level set equation is determined from the descent direction of Lagrangian derived from optimality conditions. The velocity field outside the actual domain is determined through a velocity extension scheme based on the method suggested by Adalsteinsson and Sethian(1999). The topological derivatives are incorporated into the level set based framework to enable to create holes whenever and wherever necessary during the optimization.

• Composites Research
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• v.27 no.6
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• pp.248-253
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• 2014

In this study, tapered double cantilever beam specimens are designed with the variable of angle to investigate the fracture property at the bonded surface of adjoint structure. These specimens are made with four kinds of models as the length of 200 mm and the slanted angles of bonded surfaces on specimens of $6^{\circ}$, $8^{\circ}$, $10^{\circ}$ and $12^{\circ}$. By investigating experiment and analysis result of these specimens, the maximum loads are happened at 120 N, 137 N, 154 N and 171 N respectively in cases of the specimens with slanted angles of $6^{\circ}$, $8^{\circ}$, $10^{\circ}$ and $12^{\circ}$. As the analysis result approach the experimental value, it is confirmed to have no much difference with the values of experiment and analysis. It is thought that the material property can be investigated effectively on shear behavior of the material composed of aluminum foam bonded with adhesive through simulation instead of experiment by applying this study method.