• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.11
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• pp.2245-2252
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• 2002

Design sensitivity analysis scheme is proposed in an elasto -plastic finite element method with explicit time integration using a direct differentiation method. The direct differentiation is concerned with large deformation, the elasto-plastic constitutive relation, shell elements with reduced integration and the contact scheme. The design sensitivities with respect to the process parameter are calculated with the direct analytical differentiation of the governing equation. The sensitivity results obtained from the present theory are compared with that obtained by the finite difference method in a class of sheet metal forming problems such as hemi-spherical stretching and cylindrical cup deep-drawing. The result shows good agreement with the finite difference method and demonstrates that the preposed sensitivity calculation scheme is a pplicable in the complicated sheet metal forming analysis and design.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1996.06a
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• pp.97-109
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• 1996

In the present work computations are carried out for analysis of complicated sheet metal forming process such as forming of a rear hinge. Finite element formulation using dynamic explicit time integration scheme and step-wise combined Implicit/Explicit scheme are introduced for numerical analysis of sheet metal forming process. The rigid-plastic finite element method based on membrane elements has long been employed as a useful numerical technique for the analysis of sheet metal forming because of its time effectiveness. The explicit scheme in general use is based on the elastic-plastic modelling of material requiring large computation time. In finite element simulation of sheet metal forming processes, the robustness and stability of computation are important requirements since the computation time and convergency become major points of consideration besides the solution accuracy due to the complexity of geometry and boundary conditions. The implicit scheme employs a more reliable and rigorous scheme in considering the equilibrium at each step of deformation, while in the explicit scheme the problem of convergency is eliminated at the cost of solution accuracy. The explicit approach and the implicit approach have merits and demerits, respectively. In order to combine the merits of these two methods a step-wise combined implicit/explicit scheme has been developed.

• Journal of Mechanical Science and Technology
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• v.17 no.4
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• pp.538-544
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• 2003

Although many methodologies exist for determining the constrained equations of motion, most of these methods depend on numerical approaches such as the Lagrange multiplier's method expressed in differential/algebraic systems. In 1992, Udwadia and Kalaba proposed explicit equations of motion for constrained systems based on Gauss's principle and elementary linear algebra without any multipliers or complicated intermediate processes. The generalized inverse method was the first work to present explicit equations of motion for constrained systems. However, numerical integration results of the equation of motion gradually veer away from the constraint equations with time. Thus, an objective of this study is to provide a numerical integration scheme, which modifies the generalized inverse method to reduce the errors. The modified equations of motion for constrained systems include the position constraints of index 3 systems and their first derivatives with respect to time in addition to their second derivatives with respect to time. The effectiveness of the proposed method is illustrated by numerical examples.

• Earthquakes and Structures
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• v.8 no.6
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• pp.1325-1348
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• 2015

Real-time hybrid testing (RTHT) involves virtual splitting of the structure into two parts: physical substructure that contains the key region of interest which is tested in a laboratory and numerical substructure that contains the remaining part of the structure in the form of a numerical model. This paper numerically assesses four step-by-step integration methods (Central difference method (CDM), Operator splitting method (OSM), Rosenbrock based method (RBM) and CR-integration method (CR)) which are widely used in RTHT. The methods have been assessed in terms of stability and accuracy for various realistic damping ratios of the physical substructure. The stability is assessed in terms of the spectral radii of the amplification matrix while the accuracy in terms of numerical damping and period distortion. In order to evaluate the performance of the methods, five carefully chosen examples have been studied - undamped SDOF, damped SDOF, instantaneous softening, instantaneous hardening and hysteretic system. The performance of the methods is measured in terms of a non-dimensional error index for displacement and velocity. Based on the error indices, it is observed that OSM and RBM are robust and performs fairly well in all the cases. CDM performed well for undamped SDOF system. CR method can be used for the system showing softening behaviour. The error indices indicate that accuracy of OSM is more than other method in case of hysteretic system. The accuracy of the results obtained through time integration methods for different damping ratios of the physical substructure is addressed in the present study. In the presence of a number of integration methods, it is preferable to have criteria for the selection of the time integration scheme. As such criteria are not available presently, this paper attempts to fill this gap by numerically assessing the four commonly used step-by-step methods.

• Journal of Korean Society of Transportation
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• v.14 no.2
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• pp.89-118
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• 1996

The development and implementation of a real-time, traffic adaptive control scheme based on fuzzy logic through Video Image Detector systems (VIDs) is presented. Through VIDs based image processing, fuzzy logic can be used for a real-time traffic adaptive signal control scheme. Fuzzy control logic allows linguistic and inexact traffic data to be manipulated as a useful tool in designing signal timing plans. The fuzzy logic has the ability to comprehend linguistic instructions and to generate control strategy based on a priori verbal communication. The implementation of fuzzy logic controller for a traffic network is introduced. Comparisons are made between implementations of the fuzzy logic controller and the actuated controller in an isolated intersection. The results obtained from the application of the fuzzy logic controller are also compared with those corresponding to a pretimed controller for the coordinated intersections. Simulation results from the comparisons indicate the performance of the system is between under the fuzzy logic controller. Integration of the aforementioned schemes into and ATMS framework will lead to real-time adjustment of the traffic control signals, resulting in significant reduction in traffic congestion.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.9
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• pp.1562-1570
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• 2003

The prediction of the inelastic behavior of the structure is an essential part of reliability assessment procedure, because most of the failures are induced by the inelastic deformation, such as creep and plastic deformation. During decades, there has been much progress in understanding of the inelastic behavior of the materials and a lot of inelastic constitutive equations have been developed. The complexity of these constitutive equations generally requires a stable and accurate numerical method. The radial return mapping is one of the most robust integration scheme currently used. Nonlinear kinematic hardening model of Armstrong-Fredrick type has recovery term and the direction of kinematic hardening increment is not parallel to that of plastic strain increment. In this case, The conventional radial return mapping method cannot be applied directly. In this investigation, we expanded the radial return mapping method to consider the nonlinear kinematic hardening model and implemented this integration scheme into ABAQUS by means of UMAT subroutine. The solution of the non-linear system of algebraic equations arising from time discretization with the generalized midpoint rule is determined using Newton method and bisection method. Using dynamic yield condition derived from linearization of flow rule, the integration scheme for elastoplastic and viscoplastic constitutive model was unified. Several numerical examples are considered to demonstrate the efficiency and applicability of the present method.

• 한국전산유체공학회:학술대회논문집
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• 2001.05a
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• pp.38-44
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• 2001

An efficient Gauss-Seidel time integration scheme is developed for solving the Euler and Navier-Stokes equations on unstructured meshes. Roe's FDS is used for the explicit residual computations and van Leer's FVS for evaluating implicit flux Jacobian. To reduce the memory requirement to a minimum level, off-diagonal flux Jacobian contributions are repeatedly calculated during the Gauss-Seidel sub-iteration process. Computational results based on the present scheme show that approximately $15\%$ of CPU time reduction is achieved while maintaining the memory requirement level to $50-60\%$ of the original Gauss-Seidel scheme.

• Wind and Structures
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• v.34 no.1
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• pp.59-72
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• 2022

In this work the numerical results of the flow around a 5:1 rectangular cylinder at Reynolds numbers 3 000 and 40 000, zero angle of attack and smooth incoming flow condition are presented. Implicit Large Eddy Simulations (ILES) have been performed with a high-order accurate spatial scheme and an implicit high-order accurate time integration method. The spatial approximation is based on a discontinuous Galerkin (dG) method, while the time integration exploits a linearly-implicit Rosenbrock-type Runge-Kutta scheme. The aim of this work is to show the feasibility of high-fidelity flow simulations with a moderate number of DOFs and large time step sizes. Moreover, the effect of different parameters, i.e., dimension of the computational domain, mesh type, grid resolution, boundary conditions, time step size and polynomial approximation, on the results accuracy is investigated. Our best dG result at Re=3 000 perfectly agrees with a reference DNS obtained using Nek5000 and about 40 times more degrees of freedom. The Re=40 000 computations, which are strongly under-resolved, show a reasonable correspondence with the experimental data of Mannini et al. (2017) and the LES of Zhang and Xu (2020).

• Journal of Korea Game Society
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• v.17 no.1
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• pp.89-98
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• 2017

This paper presents a novel ARAP (as-rigid-as-possible) approach to real-time simulation of physics-based deformation. To cope with one, two and three dimensional deformable bodies in an efficient, robust and uniform manner, we introduce a deformation graph of oriented particles and formulate the corresponding ARAP deformation energy. For stable time integration of the oriented particles, we develop an implicit integration scheme formulated in a variational form. Our method seeks the optimal positions and rotations of the oriented particles by iteratively applying an alternating local/global optimization scheme. The proposed method is easy to implement and computationally efficient to simulate complex deformable models in real time.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.3
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• pp.32-41
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• 1995

In the analysis of metal forming processes by the finite element method, there are many numerical instabilities such as element locking, hourglass mode and shear locking. These instabilities may have a bad effect upon accuracy and convergence. The present work is concerned with improvement of stability and efficiency in two-dimensional rigid-plastic finite element method using various type of elemenmts and numerical intergration schemes. As metal forming examples, upsetting and backward extrusion are taken for comparison among the methods: various element types and numerical integration schemes. Comparison is made in terms of stability and efficiency in element behavior and computational efficiency and a new scheme of adaptive directional reduced integration is introduced. As a result, the finite element computation has been stabilized from the viewpoint of computational time, convergency, and numerical instability.