• Journal of Mechanical Science and Technology
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• 제15권4호
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• pp.413-421
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• 2001

A simple procedure to add and remove material simultaneously along the boundary is developed to optimize the shape of a two dimensional elastic problems and to minimize the maximum von Mises stress. The results for the two dimensional infinite plate with a hole, are close to the theoretical results of an elliptical boundary and the stress concentration is reduced by half for the fillet problem. The proposed shape optimization method, when compared with existing derivative based shape optimization methods has many features such as simplicity, applicability, flexibility, computational efficiency and a much better control on stresses on the design boundary.

• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 2003년도 춘계학술대회논문집
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• pp.443-447
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• 2003

The BEM (Boundary Element Method) is a computational technique for the approximate solution of problems in continuum mechanics. In the BEM both volume and surface integrals transformed into boundary integral equations. So, we applied the ECM (Electrochemical Machining) process to boundary problem, because our focus is only deformed shape. The ECM process is modeled as a two-dimensional problem assuming constant properties of electrolyte, and an incremental formulation is used with automatic mesh regeneration. As a result the final shape is roughly agreed with experimental shape. But, it has an error of exact shape, because a chemically factor is not considered

• Korean Journal of Mathematics
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• 제16권1호
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• pp.25-40
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• 2008

We are concerned with a free boundary problem for the 2D Stokes channel flows, which determines the profile of the wing for the channel, so that the given traction force is to be distributed along the wing of the channel. Using the domain embedding technique, the free boundary problem is transferred into the shape optimization problem through the compliant formulation by releasing the traction condition along the variable boundary. The justification of the formulation will be discussed.

• Structural Engineering and Mechanics
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• 제8권1호
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• pp.73-84
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• 1999

This paper is concerned with shape optimization problems by the boundary element method (BEM) emphasizing the use of a reduced basis reanalysis technique proposed recently by the author. Problems of this class are conventionally carried out iteratively through an optimizer; a sequential quadratic programming-based optimizer is used in this study. The iterative process produces a succession of intermediate designs. Repeated analyses for the systems associated with these intermediate designs using an exact approach such as the LU decomposition method are time consuming if the order of the systems is large. The newly developed reanalysis technique devised for boundary element systems is utilized to enhance the computational efficiency in the repeated system solvings. Presented numerical examples on optimal shape design problems in electric potential distribution and elasticity show that the new reanalysis technique is capable of speeding up the design process without sacrificing the accuracy of the optimal solutions.

• Structural Engineering and Mechanics
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• 제15권5호
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• pp.535-550
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• 2003

In this paper, a boundary-type meshfree method, the boundary radial point interpolation method (BRPIM), is presented for solving boundary value problems of two-dimensional solid mechanics. In the BRPIM, the boundary of a problem domain is represented by a set of properly scattered nodes. A technique is proposed to construct shape functions using radial functions as basis functions. The shape functions so formulated are proven to possess both delta function property and partitions of unity property. Boundary conditions can be easily implemented as in the conventional Boundary Element Method (BEM). The Boundary Integral Equation (BIE) for 2-D elastostatics is discretized using the radial basis point interpolation. Some important parameters on the performance of the BRPIM are investigated thoroughly. Validity and efficiency of the present BRPIM are demonstrated through a number of numerical examples.

• 대한수학회지
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• 제37권1호
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• pp.31-44
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• 2000

We study a free boundary problem satisfying Bernoulli type boundary condition along which the gradient of a piecewise harmonic solution jumps zero to a given constant value. In such problem, the free boundary splits the domain into two regions, the zero set and the harmonic region. Our main interest is to identify the global shape and the location of the zero set. In this paper, we find the lower and the upper bound of the zero set. In a convex domain, easier estimation of the upper bound and faster disk test technique are given to find a rough shape of the zero set. Also a simple proof on the convexity of zero set is given for a connected zero set in a convex domain.

• Structural Engineering and Mechanics
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• 제51권5호
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• pp.773-792
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• 2014

In this paper, we study the inverse mode shape problem for an Euler-Bernoulli beam, using an analytical approach. The mass and stiffness variations are determined for a beam, having various boundary conditions, which has a prescribed polynomial second mode shape with an internal node. It is found that physically feasible rectangular cross-section beams which satisfy the inverse problem exist for a variety of boundary conditions. The effect of the location of the internal node on the mass and stiffness variations and on the deflection of the beam is studied. The derived functions are used to verify the p-version finite element code, for the cantilever boundary condition. The paper also presents the bounds on the location of the internal node, for a valid mass and stiffness variation, for any given boundary condition. The derived property variations, corresponding to a given mode shape and boundary condition, also provides a simple closed-form solution for a class of non-uniform Euler-Bernoulli beams. These closed-form solutions can also be used to check optimization algorithms proposed for modal tailoring.

• 로봇학회논문지
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• 제12권3호
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• pp.322-331
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• 2017

In this paper we present a novel robotic palpation method for the lump shape estimation using contact pressure distribution. Many previous researches about the robotic palpation have used a stiffness map, which is not suitable to obtain geometrical information of a lump. As a result, they require a large data set and long palpation time to estimate the lump shape. Instead of using the stiffness map, the proposed palpation method uses the difference between the normal force direction and the surface normal to detect the lump boundary and estimate its normal. The palpation trajectory is generated by the normal of the lump boundary to track the lump boundary in real-time. The proposed approach requires small data set and short palpation time for the lump shape estimation since the shape can be directly estimated from the optimally generated palpation trajectory. An experiment result shows that our method can find the lump shape accurately in real-time with small data and short time.

• 대한기계학회논문집A
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• 제24권11호
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• pp.2705-2712
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• 2000

In meshless methods some techniques to impose essential boundary conditions have been developed since the approximations do not satisfy Kronecker delta properties at nodal points. In this study, new scheme for imposing essential boundary conditions is developed. Weight functions are modified by multiplying with auxiliary weight functions and the resulting shape functions satisfy Kronecker delta property on the bound ary nodes. In addition, the resulting shape functions possess and interpolation features on the boundary segments where essential boundary conditions are prescribed. Therefore the essential boundary conditions can be exactly satisfied with the new method. More importantly, the impositions of essential boundary conditions using the present method is relatively easy as in finite element method. Numerical examples show that the method also retains high convergence rate comparable to Lagrange multiplier method.

• 대한기계학회논문집A
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• 제24권3호
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• pp.803-809
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• 2000

For the effective analysis of an engineering problem, meshless methods which require only positioning finite points without the element meshing recently have been proposed and being studied extensively. Meshless methods have difficulty in imposing essential boundary conditions directly, because non-interpolate shape functions originated from an approximation process are used. So some techniques, which are Lagrange multiplier method, modified variational principles and coupling with finite elements and so on, were introduced in order to impose essential boundary conditions. In spite of these methods, imposition of essential boundary conditions have still many problems like as non-positive definiteness, inaccuracy and negation of meshless characteristics. In this paper, we propose a new method which modifies shape function. Through numerical tests, convergence, accuracy and validity of this method are compared with the standard EFGM which uses Lagrange multiplier method or modified variational principles. According to this study, the proposed method shows the comparable accuracy and efficiency.