Shape Design Sensitivity Analysis for Interface Problem in Axisymmetric Elasticity

Choi, Joo-Ho,Lee, Boo-Youn,Han, Jung-Suk The Korean Society of Mechanical Engineers 2000 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.14 No.2

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.

입 벌림 인식과 팝업 메뉴를 이용한 시선추적 마우스 시스템 성능 개선

변주영,정기철,Byeon, Ju Yeong,Jung, Keechul 한국멀티미디어학회 2020 멀티미디어학회논문지 Vol.23 No.12

An important factor in eye-tracking PC interface for general paralyzed patients is the implementation of the mouse interface, for manipulating the GUI. With a successfully implemented mouse interface, users can generate mouse events exactly at the point of their choosing. However, it is difficult to define this interaction in the eye-tracking interface. This problem has been defined as the Midas touch problem and has been a major focus of eye-tracking research. There have been many attempts to solve this problem using blink, voice input, etc. However, it was not suitable for general paralyzed patients because some of them cannot wink or speak. In this paper, we propose a mouth-pop-up, eye-tracking mouse interface that solves the Midas touch problem as well as becoming a suitable interface for general paralyzed patients using a common RGB camera. The interface presented in this paper implements a mouse interface that detects the opening and closing of the mouth to activate a pop-up menu that the user can select the mouse event. After implementation, a performance experiment was conducted. As a result, we found that the number of malfunctions and the time to perform tasks were reduced compared to the existing method.

A discontinuous Galerkin method for elliptic interface problems with application to electroporation

Guyomarc'h, Gré,gory,Lee, Chang-Ock,Jeon, Kiwan John Wiley Sons, Ltd. 2009 Communications in numerical methods in engineering Vol.25 No.10

<P>We solve elliptic interface problems using a discontinuous Galerkin (DG) method, for which discontinuities in the solution and in its normal derivatives are prescribed on an interface inside the domain. Standard ways to solve interface problems with finite element methods consist in enforcing the prescribed discontinuity of the solution in the finite element space. Here, we show that the DG method provides a natural framework to enforce both discontinuities weakly in the DG formulation, provided the triangulation of the domain is fitted to the interface. The resulting discretization leads to a symmetric system that can be efficiently solved with standard algorithms. The method is shown to be optimally convergent in the L<SUP>2</SUP>-norm. We apply our method to the numerical study of electroporation, a widely used medical technique with applications to gene therapy and cancer treatment. Mathematical models of electroporation involve elliptic problems with dynamic interface conditions. We discretize such problems into a sequence of elliptic interface problems that can be solved by our method. We obtain numerical results that agree with known exact solutions. Copyright © 2008 John Wiley & Sons, Ltd.</P>

Free vibration analysis of beams with various interfaces by using a modified matched interface and boundary method

Zhiwei Song,Wei Li,Xiaoqiao He,De Xie 국제구조공학회 2019 Structural Engineering and Mechanics, An Int'l Jou Vol.72 No.1

This paper proposes a modified matched interface and boundary (MMIB) method to analyze the free vibration of beams with various interfaces caused by steps, intermediate rigid and elastic supports, intermediate concentrated masses and spring-mass systems, etc. A new strategy is developed to determine the parameters in the iterative computation of MMIB. The MMIB procedures are established to deal with boundary conditions and various interface conditions, which overcomes the shortcoming of the traditional MIB. A number of examples are utilized to illustrate the performance of MMIB method. Numerical results indicate that the MMIB method is a highly accurate and convergent approach for solving interface problems.

SPECTRAL LEGENDRE AND CHEBYSHEV APPROXIMATION FOR THE STOKES INTERFACE PROBLEMS

PEYMAN HESSARI,AND BYEONG-CHUN SHIN 한국산업응용수학회 2017 Journal of the Korean Society for Industrial and A Vol.21 No.3

The numerical solution of the Stokes equation with discontinuous viscosity and singular force term is challenging, due to the discontinuity of pressure, non-smoothness of velocity, and coupled discontinuities along interface.In this paper, we give an efficient algorithm to solve this problem by employing spectral Legendre and Chebyshev approximations.First, we present the algorithm for a problem defined in rectangular domain with straight line interface. Then it is generalized to a domain with smooth curve boundary and interface by employing spectral element method. Numerical experiments demonstrate the accuracy and efficiency of our algorithm and its spectral convergence.

Refocusing Product Interaction Design from the Perspective on Users' Problem-Solving Knowledge

Choi, Jung Min(최정민) 한국디자인지식학회 2014 디자인지식저널 Vol.29 No.-

Technological aids provided by products and systems have reduced people’s problem-solving efforts in everyday practices. It is crucial for users to learn how to operate a system, and yet their acquisition of problem-solving knowledge of a task domain is largely disregarded in the current design process. Without enough problem-solving knowledge, users may not be able to creatively adjust their product use to meet their variable needs. Also, users’ experiences with a product can be confined to step-by-step operational procedures. Therefore, a product/system should be designed to support users’ development of problem-solving abilities through interaction. This research proposes a methodological framework which emphasizes the incorporation of users’ problem-solving knowledge into the design processes. Example products are selected to more effectively explain the difference between the proposed approach and existing approaches. By supporting users’ acquisition of problem-solving knowledge, product UI designs will be able to help users produce higher-quality results and higher-level of satisfaction through interaction.

Analysis of multiscale mortar mixed approximation of nonlinear elliptic equations

Arshad, Muhammad,Park, Eun-Jae,Shin, Dong-wook Elsevier 2018 COMPUTERS & MATHEMATICS WITH APPLICATIONS - Vol.75 No.2

<P><B>Abstract</B></P> <P>A multiscale mortar mixed finite element method is established to approximate non-linear second order elliptic equations. The method is based on non-overlapping domain decomposition and mortar finite element methods. The existence and uniqueness of the approximation are demonstrated, and a priori <SUP> L 2 </SUP> -error estimates for the velocity and pressure are derived. An error bound for mortar pressure is proved. Convergence estimates of the mortar pressure are based on a linear interface formulation having the discrete-pressure dependent coefficient. Optimal order convergence is achieved on the fine scale by a proper choice of mortar space and polynomial degree of approximation. The quadratic convergence of the Newton–Raphson method is proved for the nonlinear algebraic system arising from the mortar mixed formulation of the problem. Numerical experiments are performed to support theoretic results.</P>

ROBUST A POSTERIORI ERROR ESTIMATOR FOR LOWEST-ORDER FINITE ELEMENT METHODS OF INTERFACE PROBLEMS

KWANG-YEON KIM 한국산업응용수학회 2016 Journal of the Korean Society for Industrial and A Vol.20 No.2

In this paper we analyze an a posteriori error estimator based on flux recovery for lowest-order finite element discretizations of elliptic interface problems. The flux recovery considered here is based on averaging the discrete normal fluxes and/or tangential derivatives at midpoints of edges with weight factors adapted to discontinuous coefficients. It is shown that the error estimator based on this flux recovery is equivalent to the error estimator of Bernardi and Verfürth based on the standard edge residuals uniformly with respect to jumps of the coefficient between subdomains. Moreover, as a byproduct, we obtain slightly modified weight factors in the edge residual estimator which are expected to produce more accurate results.

Crack propagation and deviation in bi-materials under thermo-mechanical loading

Mourad Chama,Benali Boutabout,Abdelkader Lousdad,Wafa Bensmain,Bel Abbes Bachir Bouiadjra 국제구조공학회 2014 Structural Engineering and Mechanics, An Int'l Jou Vol.50 No.4

This paper presents a finite element based numerical model to solve two dimensional bi-material problems. A bi-material beam consisting of two phase materials ceramic and metal is modelled by finite element method. The beam is subjected simultaneously to mechanical and thermal loadings. The mainobjective of this study is the analysis of crack deviation located in the brittle material near the interface. The effect of temperature gradient, the residual stresses and applied loads on crack initiation, propagation and deviation are examined and highlighted.

Crack propagation and deviation in bi-materials under thermo-mechanical loading

Chama, Mourad,Boutabout, Benali,Lousdad, Abdelkader,Bensmain, Wafa,Bouiadjra, Bel Abbes Bachir Techno-Press 2014 Structural Engineering and Mechanics, An Int'l Jou Vol.50 No.4

This paper presents a finite element based numerical model to solve two dimensional bi-material problems. A bi-material beam consisting of two phase materials ceramic and metal is modelled by finite element method. The beam is subjected simultaneously to mechanical and thermal loadings. The main objective of this study is the analysis of crack deviation located in the brittle material near the interface. The effect of temperature gradient, the residual stresses and applied loads on crack initiation, propagation and deviation are examined and highlighted.