• 한국해안·해양공학회논문집
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• 제22권1호
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• pp.47-57
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• 2010

Woo and Liu (2004)의 확장형 Boussinesq FEM 수치모형에서 한계점으로 지적되었던 수치진동현상과 계산 효율성이 크게 개선되었다. 수치진동을 해결하기 위해 subgrid scale stabilization method를 사용하였고, 계산효율성을 높이기 위해서 Hessian 연산자를 도입하였으며, 유속벡터에 대한 행렬 구성을 하나의 행렬로 구성하였다. 또한 추가변수에 대한 행렬은 mass lumping technique을 사용하여 대각행렬로 구성하였다. Vincent and Briggs(1989)의 파랑 굴절 및 회절에 대한 수치실험 결과 수치진동현상이 확연히 줄어 들은 것을 관찰할 수 있었으며, 수리실험 결과와도 상당히 일치하는 결과를 보였다. 이전 모형에 비해 약 10배의 계산소요시간이 줄어 향후 항만부진동이나 퇴적물 이동과 같은 현실적인 문제에 적용이 가능할 것으로 기대된다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제20권3호
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• pp.243-259
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• 2016

The Richards equation for water movement in unsaturated soil is highly nonlinear partial differential equations which are not solvable analytically unless unrealistic and oversimplifying assumptions are made regarding the attributes, dynamics, and properties of the physical systems. Therefore, conventionally, numerical solutions are the only feasible procedures to model flow in partially saturated porous media. The standard Finite element numerical technique is usually coupled with an Euler time discretizations scheme. Except for the fully explicit forward method, any other Euler time-marching algorithm generates nonlinear algebraic equations which should be solved using iterative procedures such as Newton and Picard iterations. In this study, lumped mass and distributed mass in the frame of Picard and Newton iterative techniques were evaluated to determine the most efficient method to solve the Richards equation with finite element model. The accuracy and computational efficiency of the scheme and of the Picard and Newton models are assessed for three test problems simulating one-dimensional flow processes in unsaturated porous media. Results demonstrated that, the conventional mass distributed finite element method suffers from numerical oscillations at the wetting front, especially for very dry initial conditions. Even though small mesh sizes are applied for all the test problems, it is shown that the traditional mass-distributed scheme can still generate an incorrect response due to the highly nonlinear properties of water flow in unsaturated soil and cause numerical oscillation. On the other hand, non oscillatory solutions are obtained and non-physics solutions for these problems are evaded by using the mass-lumped finite element method.

• Structural Engineering and Mechanics
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• 제14권3호
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• pp.245-262
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• 2002

The free vibration analysis of stiffened laminated composite plates has been performed using the layered (zigzag) finite element method based on the first order shear deformation theory. The layers of the laminated plate is modeled using nine-node isoparametric degenerated flat shell element. The stiffeners are modeled as three-node isoparametric beam elements based on Timoshenko beam theory. Bilinear in-plane displacement constraints are used to maintain the inter-layer continuity. A special lumping technique is used in deriving the lumped mass matrices. The natural frequencies are extracted using the subspace iteration method. Numerical results are presented for unstiffened laminated plates, stiffened isotropic plates, stiffened symmetric angle-ply laminates, stiffened skew-symmetric angle-ply laminates and stiffened skew-symmetric cross-ply laminates. The effects of fiber orientations (ply angles), number of layers, stiffener depths and degrees of orthotropy are examined.

• 한국자동차공학회논문집
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• 제4권5호
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• pp.16-25
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• 1996

In the present work a rigid-plastic finite element formulation using dynamic explicit time integration scheme is proposed for numerical analysis of auto-body panel stamping processes. 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. A damping scheme is proposed in order to achieve a stable solution procedure in dynamic sheet forming problems. In order to improve the drawbacks of the conventional membrane elements, BEAM(abbreviated from Bending Energy Augmented Membrane) elements are employed. Rotational damping and spring about the drilling direction are introduced to prevent a zero energy mode. The lumping scheme is employed for the diagonal mass matrix and linearizing dynamic formulation. A contact scheme is developed by combining the skew boundary condition and the direct trial-and-error method. Computations are carried out for analysis of complicated auto-body panel stamping processes such as forming of an oilpan, a fuel tank and a front fender. The numerical results of explicit analysis are compared with the implicit results with good agreements and it is shown that the explicit scheme requires much shorter computational time, especially when the problem becomes more complicated. It is thus shown that the proposed dynamic explicit rigid-plastic finite element method enables an effective computation for complicated autobody panel stamping processes.