• Title/Summary/Keyword: Implicit Formulation

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Springback Analyses in Sheet Metal Stamping Processes (박판 성형에서의 스프링백 해석과 산업적 응용)

  • 양동열;이상욱;윤정환;유동진
    • Proceedings of the Korean Society for Technology of Plasticity Conference
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    • 1998.06a
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    • pp.1-8
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    • 1998
  • The explicit and implicit time integration methods are applied effectively to analyze sheet metal stamping processes, which include the forming stage and the springback stage consecutively. The explicit time integration method has better merits in the forming stage including highly complicated three-dimensional contact conditions. By contrary, the implicit time integration method is better for analyzing springback since the complicated contact conditions are removd and the computing time to get the final static state is short. In this work, brief descriptions of the formulation and the factor study for springback simulations are presented. Further, the simulated results for the S-rail and the roof pannel stamping processes are shown and discussed.

DISCONTINUOUS GALERKIN SPECTRAL ELEMENT METHOD FOR ELLIPTIC PROBLEMS BASED ON FIRST-ORDER HYPERBOLIC SYSTEM

  • KIM, DEOKHUN;AHN, HYUNG TAEK
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.25 no.4
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    • pp.173-195
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    • 2021
  • A new implicit discontinuous Galerkin spectral element method (DGSEM) based on the first order hyperbolic system(FOHS) is presented for solving elliptic type partial different equations, such as the Poisson problems. By utilizing the idea of hyperbolic formulation of Nishikawa[1], the original Poisson equation was reformulated in the first-order hyperbolic system. Such hyperbolic system is solved implicitly by the collocation type DGSEM. The steady state solution in pseudo-time, which is the solution of the original Poisson problem, was obtained by the implicit solution of the global linear system. The optimal polynomial orders of 𝒪(𝒽𝑝+1)) are obtained for both the solution and gradient variables from the test cases in 1D and 2D regular grids. Spectral accuracy of the solution and gradient variables are confirmed from all test cases of using the uniform grids in 2D.

Stress Integration Algorithm for an Anisotropic Hardening Constitutive Model of Geomaterials (지반재료의 비등방경화 구성모델에 대한 응력적분 알고리즘)

  • Oh Se-Boong;Lee Jin-Gu;Kim Tae-Gyeong
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2005.04a
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    • pp.343-350
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    • 2005
  • A constitutive model was implemented in ABAQUS code. The constitutive equation can model the behavior for overall range of strain level from small to large deformation, which is based on anisotropic hardening rule and total stress concept. The formulation includes (1) finite strain formulation on the basis of Jaumann rate, (2) implicit stress integration and (3) consistent tangent moduli. Therefore the mathematical background was established in order that large deformation analysis can be performed accurately and efficiently with the anisotropic constitutive model. In the large deformation analyses, geometric nonlinearity was considered and the result of analyses with the proposed model was compared with that of Mises model for the overall strain range behavior.

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Finite Element Simulation of Axisymmetric Tube Hydroforming Processes (축대칭 튜브 하이드로포밍 공정의 유한요소 시뮬레이션)

  • Kim Y. S.;Keum Y. T.
    • Proceedings of the Korean Society for Technology of Plasticity Conference
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    • 2001.10a
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    • pp.58-61
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    • 2001
  • An implicit finite element formulation for axisymmetric tube hydroforming is investigated. In order to describe normal anisotropy of the tube, Hill's non-quadratic yield function is employed. The frictional contact between die and tube and frictionless contact between tube and fluid are considered using the mesh-normal vector computed from finite element mesh of the tube. In order to verify the validity of the developed finite element formulation, the axisymmetric tube bulge test is simulated and simulation results are compared with experimental measurements. In the axisymmetric tube hydroforming process, an optimal hydraulic curve is pursued by performing the simulation with various internal pressures and axial forces.

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Finite Element Simulation of Axisymmeric Tube Hydroforming Processes (축대칭 튜브 하이드로포밍 공정의 유한요소 시뮬레이션)

  • 김용석;금영탁
    • Transactions of Materials Processing
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    • v.11 no.1
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    • pp.75-83
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    • 2002
  • Recently, the hydroforming process is widely applied to the automotive industry and rapidly spreaded to other industries. In this paper, An implicit finite element formulation for simulating axisymmetric tube hydroforming processes is performed. In order to describe normal anisotropy of the tube, Hill's non-quadratic yield function is employed. The frictional contact between die and tube and the frictionless contact between tube and fluid are considered using the mesh-normal vectors computed from the finite element mesh of the tube. The complete set of the governing relations comprising equilibrium and interfacial equations is linearized for Newton-Raphson procedure. In order to verify the validity of the developed finite element formulation, the axisymmetric tube bulge test is simulated and the simulation results are compared with experimental measurements. In a simulation of stepped circular tube hydroforming processes, an optimal hydraulic pressure curve is pursued by considering simultaneously internal pressures and axial forces.

Nonlinear Dynamic Analysis using Petrov-Galerkin Natural Element Method (페트로프-갤러킨 자연요소법을 이용한 비선형 동해석)

  • Lee, Hong-Woo;Cho, Jin-Rae
    • Proceedings of the KSME Conference
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    • 2004.11a
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    • pp.474-479
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    • 2004
  • According to our previous study, it is confirmed that the Petrov-Galerkin natural element method (PGNEM) completely resolves the numerical integration inaccuracy in the conventional Bubnov-Galerkin natural element method (BG-NEM). This paper is an extension of PG-NEM to two-dimensional nonlinear dynamic problem. For the analysis, a constant average acceleration method and a linearized total Lagrangian formulation is introduced with the PG-NEM. At every time step, the grid points are updated and the shape functions are reproduced from the relocated nodal distribution. This process enables the PG-NEM to provide more accurate and robust approximations. The representative numerical experiments performed by the test Fortran program, and the numerical results confirmed that the PG-NEM effectively and accurately approximates the nonlinear dynamic problem.

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Rigid-Plastic Explicit Finite Element Formulation for Two-Dimensional Analysis of Sheet Metal Processes (2차원 박판성형공정해석을 위한 강소성 외연적 유한 요소수식화)

  • 안동규;정동원;양동열
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 1993.10a
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    • pp.206-211
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    • 1993
  • The explicit scheme for finite element analysis of sheet metal forming problems has been widely used for providing practical solution since it improves the convergency problem,memory size and computational time especially for the case of complicated geometry and large element number. In the present work, a basic formulation for rigid-plastic explicit finite element analysis of plain strain sheet metal forming problems has been proposed. The effect of some basic parameters involved in the dynamic analysis has been studied in detail. A direct trial-and-error method is introduced to treat contact and friction. In order to show the validity and effectiveness of the proposed explicit scheme, computation are carried out for cylindrical punch stretching and the computational results are compared with those by the implicit scheme as well as with a commercial code. The proposed rigid-plastic explicit element method can be used as a robust and efficient computational method for analysis of sheet method forming.

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Improved formulation for a structure-dependent integration method

  • Chang, Shuenn-Yih;Wu, Tsui-Huang;Tran, Ngoc-Cuong
    • Structural Engineering and Mechanics
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    • v.60 no.1
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    • pp.149-162
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    • 2016
  • Structure-dependent integration methods seem promising for structural dynamics applications since they can integrate unconditional stability and explicit formulation together, which can enable the integration methods to save many computational efforts when compared to an implicit method. A newly developed structure-dependent integration method can inherit such numerical properties. However, an unusual overshooting behavior might be experienced as it is used to compute a forced vibration response. The root cause of this inaccuracy is thoroughly explored herein. In addition, a scheme is proposed to modify this family method to overcome this unusual overshooting behavior. In fact, two improved formulations are proposed by adjusting the difference equations. As a result, it is verified that the two improved formulations of the integration methods can effectively overcome the difficulty arising from the inaccurate integration of the steady-state response of a high frequency mode.

Numerical analysis of propagation of macrocracks in 3D concrete structures affected by ASR

  • Moallemi, S.;Pietruszczak, S.
    • Computers and Concrete
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    • v.22 no.1
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    • pp.1-10
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    • 2018
  • In this study an implicit algorithm for modeling of propagation of macrocracks in 3D concrete structures suffering from alkali-silica reaction has been developed and implemented. The formulation of the problem prior to the onset of localized deformation is based on a chemo-elasticity approach. The localized deformation mode, involving the formation of macrocracks, is described using a simplified form of the strong discontinuity approach (SDA) that employs a volume averaging technique enhanced by a numerical procedure for tracing the propagation path in 3D space. The latter incorporates a non-local smoothening algorithm. The formulation is illustrated by a number of numerical examples that examine the crack propagation pattern in both plain and reinforced concrete under different loading scenarios.

A Study on Optimal Traffic Signal Controls in Urban Street Networks (도시 가로망에서의 최적교통신호등 결정모형의 실용화에 관한 연구)

  • 이승환
    • Journal of Korean Society of Transportation
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    • v.5 no.1
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    • pp.3-23
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    • 1987
  • Traffic signal control problems in urban street networks are formulated in two ways. In the formulations network flows are assumed to satisfy the user route choice criterion. the first formulation which is called implicit substiuation incorporates user route behavior implicitly in the objective function by recognizing the dependence of the link flows on the signal variables. On the other hands, the second one which is called 'penalty formulation' consists in expressing the route choice conditions in the form of a single nonlinear constraint. Approximate solution algorithm for each of the formulations was investigated in detail and computer codes were written to examine key aspects of each algorithm. A test was done on a network which is small in size but sufficiently complex in representing real-world traffic conditions and the test result shows that both algorithms produce converged solutions. It is recommended, however, that further studies should be done in order to compare the performance of each algorithm more in depth.

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