Numerical simulation of RTM process using the extended finite element method combined with the level set method

Jung, Yeonhee,Kim, Seung Jo,Han, Woo-Suck SAGE Publications 2013 Journal of reinforced plastics and composites Vol.32 No.5

<P>Numerical simulation for resin transfer moulding manufacturing process is attempted using the extended finite element method combined with the level set method. The level set method is used to transport the resin flow front at each time step during the mould filling. Extended finite element method allows to obtaining a good numerical precision of the resin pressure near the resin flow front, where the gradient of the pressure could be discontinuous. The enriched shape functions of extended finite element method are derived using the level set values so as to correctly describe these shape functions with the resin flow front. In addition, the position of the resin flow front at each time step is calculated by an implicit characteristic Galerkin finite element method. Some examples are presented to validate our study in comparison with analytical or experimental results and to illustrate its industrial applications.</P>

Extended-FEM for the solid-fluid mixture two-scale problems with BCC and FCC microstructures

Sawada, Tomohiro,Nakasumi, Shogo,Tezuka, Akira,Fukushima, Manabu,Yoshizawa, Yu-Ichi Techno-Press 2009 Interaction and multiscale mechanics Vol.2 No.1

An aim of the study is to develop an efficient numerical simulation technique that can handle the two-scale analysis of fluid permeation filters fabricated by the partial sintering technique of small spherical ceramics. A solid-fluid mixture homogenization method is introduced to predict the mechanical characters such as rigidity and permeability of the porous ceramic filters from the micro-scale geometry and configuration of partially-sintered particles. An extended finite element (X-FE) discretization technique based on the enriched interpolations of respective characteristic functions at fluid-solid interfaces is proposed for the non-interface-fitted mesh solution of the micro-scale analysis that needs non-slip condition at the interface between solid and fluid phases of the unit cell. The homogenization and localization performances of the proposed method are shown in a typical two-dimensional benchmark problem whose model has a hole in center. Three-dimensional applications to the body-centered cubic (BCC) and face-centered cubic (FCC) unit cell models are also shown in the paper. The 3D application is prepared toward the computer-aided optimal design of ceramic filters. The accuracy and stability of the X-FEM based method are comparable to those of the standard interface-fitted FEM, and are superior to those of the voxel type FEM that is often used in such complex micro geometry cases.

Extended-finite element method as analysis model for Gauss point density topology optimization method

이동규,신수미 대한기계학회 2015 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.29 No.4

We investigated relaxations of stress concentrations near material boundaries between voids and solid areas, with respect to solutionsof FEM and extended (X)-FEM as analysis model of material topology optimization. The analysis models for FEM use SIMP materialdefined by an original constant element density, a constant element density determined by averaging nodal densities, and a Gauss pointdensity. For the X-FEM analysis model, 0-1 material properties at Gauss points bisected by a zero level set contour are used. Niche andridge enrichment functions and a Heaviside function were used to define continuous displacement fields with weak discontinuities in XFEM. Numerical examples of a deep beam under a lateral load and a given material density limitation provide the possibility of increasingthe merit of the present X-FEM for continuous material topology optimization design. It can be also extended to three-dimensional ornonlinear structural problems.

Extended framework of Hamilton's principle in heat diffusion

Kim, J.,Dargush, G.F.,Lee, H.S. Pergamon Press ; Elsevier Science Ltd 2016 International journal of mechanical sciences Vol.114 No.-

Based upon the extended framework of Hamilton's principle, a variational formulation in heat diffusion, as well as second sound phenomena is developed. This formulation is compatible with the initial and boundary conditions of a well-posed heat problem, and it correctly accounts for the governing partial differential equations, as its Euler-Lagrange equations. Thus, this new formulation provides a sound base to develop various unified space-time finite element methods. In order to validate the finite element representation over both space and time in the context of this formulation, two-dimensional lower-order space-time finite element methods are also developed with numerical investigations on representative examples.

Extended framework of Hamilton's principle for thermoelastic continua

Pergamon Press ; Elsevier Science Ltd 2017 COMPUTERS & MATHEMATICS WITH APPLICATIONS - Vol.73 No.7

<P>Based upon the extended framework of Hamilton's principle, a variational formulation for fully coupled thermoelasticity is presented. The resulting formulation can properly account for all the governing differential equations as well as initial boundary conditions. Thus, it provides the basis for a class of unified space time finite element methods. By employing bar elements in one-dimensional space along with linear shape functions temporally, the simplest space time finite element method is presented herein with representative examples for its validity. (C) 2017 Elsevier Ltd. All rights reserved.</P>

확장유한요소법을 이용한 아스팔트의 정적균열 성장 분석

지광습(Zi Goangseup),유성문(Yu Sungmun),챠우딘딴(Chau-Dinh Thanh),문성호(Mun Sungho) 대한토목학회 2010 대한토목학회논문집 D Vol.30 No.4D

본 논문에서는 아스팔트 포장의 균열 성장을 분석하기 위해서 확장유한요소법을 사용하였다. 또한 아스팔트의 점탄성 효과를 고려하기 위하여 맥스웰 체인을 이용한 점탄성 구성방정식을 사용하였으며, 균열 모델로는 선형점성균열 모델을 사용하였다. 특히 접탄성 구성방정식을 구성할 때 측정을 통해 얻어지는 온도별 변형계수와 지연시간을 Prony 급수를 이용해 재구성 한 크리프 곡선을 직접 사용하지 않고 연속적인 미분이 가능한 멱승 로그 식으로 대체하여 사용하였다. 역승 로그 식으로 완화시간 스펙트럼(relaxation spectrum)을 계산하여 맥스웰 체인의 부분탄성계수(partial moduli)를 도출하였다. 멱승 로그 적정 식을 통해 구한 맥스웰 체인의 부분 탄성계수는 크리프 곡선을 직접 이용하는 방법으로 구한 부분 탄성계수 보다 안정적인 형태의 곡선을 나타내어 해석을 용이하게 해준다. 개발된 정적균열 해석 모듈을 이용하여 아스팔트 시편의 온도별 정적균열 성장 실험 결과를 성공적으로 모사할 수 있었다. This paper studies static crack growth of asphalt pavement using the extended finite element method (XFEM). To consider nonlinear characteristics of asphalt concrete, a viscoelastic constitutive equation using the Maxwell chain is used. And a linear cohesive crack model is used to regularize the crack. Instead of constructing the viscoelastic constitutive law from the Prony approximation of compliance and retardation time measured experimentally, we use a smooth log-power function which optimally fits experimental data and is infinitely differentiable. The partial moduli of the Maxwell chain from the log-power function make analysis easy because they change more smoothly in a more stable way than the ordinary method such as the least square method. Using the developed method, we can simulates the static crack growth test results satisfactorily.

Level-Set-Based Topology Optimization Using Remeshing Techniques for Magnetic Actuator Design

Seungmin Jeong,Sunghoon Lim,Seungjae Min IEEE 2016 IEEE transactions on magnetics Vol.52 No.3

<P>This paper proposes a new level-set-based topology optimization method for magnetic actuator design using remeshing techniques that can generate meshes on the exact structural boundaries to improve the accuracy of finite-element analysis. Two remeshing techniques, such as the modified adaptive mesh method and the extended finite-element method (XFEM), are introduced for the optimization process. To control the computational time with meshing that is economical and analysis that is accurate, a new resolution parameter that can manage the level of mesh density around the level-set boundaries is employed in the modified adaptive mesh method. In the XFEM, the enrichment term in the element shape function is employed to track the exact outer boundary of the actuator. The optimization problem is formulated to maximize the magnetic force between the core and an armature under the volume constraint of the ferromagnetic material. To verify the effectiveness of the proposed method, it is applied to an electromagnetic problem for an optimal C-core actuator design that is very sensitive to structural boundaries.</P>

확장유한요소법을 이용한 이음새 간극 해석

김남호(Nam H. Kim),원준호(Junho Won),Matthew Pais,최주호(Jooho Choi) 대한기계학회 2010 대한기계학회 춘추학술대회 Vol.2010 No.11

Modeling a gap in mechanical joints is a challenging computational mechanics problem because (1) is shows a nonlinear behavior and (2) the dimension of the gap is much smaller than that of structures. The conventional finite element method requires modeling the detailed geometry of the gap embedded in large structures. In this paper, a new approach is proposed using the extended finite element method to model the gap in joints. The fundamental idea is to utilize the enrichment function to describe the behavior of gap within the element. The proposed method does not require modeling the detailed geometry of the gap, but allowing the enriched node can move freely within the gap. A simple Heaviside step function is used to enrichment. Numerical examples are shown using one-dimensional bar elements.

확장유한요소법을 이용한 타이어 비드부 균열 진전 가시화 기법 개발

박한석(Hanseok Park),김성래(Seongrae Kim),강민성(Mingsung Kang),성기득(Kideug Sung),석창성(Changsung Seok) 한국자동차공학회 2011 한국자동차공학회 학술대회 및 전시회 Vol.2011 No.11

The durability of the tire is a very important performance and a matter that should be considered a top priority during tire development in terms of passenger safety and vehicle protection. Also, social necessity for the eco-friendly cars are rapidly growing because of high oil prices and environmental regulations, so the early commercialization of electric vehicles is becoming possible. For this reason, the development of high durability tire was required in the tire industry that can endure the high weight of the electric car. To ensure tire durability, it is necessary to evaluate and analyze about bead crack propagation. Estimation of the cracking problem has been studied by various methods. Of them, using the FEM(Finite Element Method) requires re-mesh process and computing time. However XFEM (eXtended Finite Element Method) developed by Belytschko does not require re-mesh process according to the crack propagation, so it is easy to apply to the crack propagation method. Because of these advantages, XFEM has been used to deal with crack problems in many recent papers. Therefore, in this paper, we apply XFEM to tire fracture problem to visualize crack propagation in the bead area and aspects of fracture is compared with FMVSS 109 endurance test result.

초기 균열이 존재하는 터빈 블레이드의 동적 거동 및 균열진전 양상 예측

최동권(Dongkwon Choi),황선필(Seon-Pil Hwang),손동우(Dongwoo Sohn) 대한기계학회 2017 대한기계학회 춘추학술대회 Vol.2017 No.11

In order to increase power generation efficiency, turbines are operating with increasingly longer blades at higher pressure and temperature. Therefore, fault diagnosis and failure prediction of turbine blades are becoming more important. In this study, structural and damage analysis of rotating blades are conducted using the finite element method and extended finite element method. For healthy blades, we find stress concentration areas of the blades. Furthermore, considering initial cracks that exist in the weak areas of the blades, we investigate the effects of the cracks on the dynamic behaviors and discuss the tendency of crack propagation.