• Steel and Composite Structures
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• v.28 no.6
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• pp.655-670
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• 2018

A coupled method, that combines the Ritz method and the finite element (FE) method, is proposed to solve the vibration problem of rectangular thin and thick plates with general boundary conditions. The eigenvalue partial differential equation(s) of the plate is (are) first reduced to a set of eigenvalue ordinary differential equations by the application of the Ritz method. The resulting eigenvalue differential equations are then reduced to an eigenvalue algebraic equation system using the finite element method. The natural boundary conditions of the plate problem including the free edge and free corner boundary conditions are also implemented in a simple and accurate manner. Various boundary conditions including simply supported, clamped and free boundary conditions are considered. Comparisons with existing numerical and analytical solutions show that the proposed mixed method can produce highly accurate results for the problems considered using a small number of Ritz terms and finite elements. The proposed mixed Ritz-FE formulation is also compared with the mixed FE-Ritz formulation which has been recently proposed by the present author and his co-author. It is found that the proposed mixed Ritz-FE formulation is more efficient than the mixed FE-Ritz formulation for free vibration analysis of rectangular plates with Levy-type boundary conditions.

• Structural Engineering and Mechanics
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• v.83 no.2
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• pp.273-282
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• 2022

In this paper, we propose a new concept for error estimation in finite element solutions, which we call mode-based error estimation. The proposed error estimation predicts a posteriori error calculated by the difference between the direct finite element (FE) approximation and the recovered FE approximation. The mode-based FE formulation for the recently developed self-updated finite element is employed to calculate the recovered solution. The formulation is constructed by searching for optimal bending directions for each element, and deep learning is adopted to help find the optimal bending directions. Through various numerical examples using four-node quadrilateral finite elements, we demonstrate the improved predictive capability of the proposed error estimator compared with other competitive methods.

• Interaction and multiscale mechanics
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• v.6 no.2
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• pp.173-195
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• 2013

Meshfree methods are known to have the capability to overcome the strict regularization requirements and numerical instabilities that encumber the finite element method (FEM) in large deformation problems. They are also more naturally suited for problems involving material perforation and fragmentation. To take advantage of the high efficiency of FEM and high accuracy of meshfree methods, a coupled finite element (FE) and reproducing kernel (RK, one of the meshfree approximations) formulation is described in this paper. The coupling of FE and RK approximation is implemented in an evolutionary fashion, where the extent and location of the evolution is dependent on a triggering criteria provided by the material constitutive laws. To enhance computational efficiency, Gauss quadrature is applied to integrate both FE and RK domains so that no state variable transfer is required when mesh conversion is performed. To control the hourglassing that might occur with 1-point integrated hexahedral grids, viscous type hourglass control is implemented. Meanwhile, the FEM version of the K&C concrete (KCC) model was modified to make it applicable in both FE and RK formulations. Results using this code and the KCC model are shown for the modeling of concrete responses under quasi-static, blast and impact loadings. These analyses demonstrate that fragmentation phenomena of the sort commonly observed under blast and impact loadings of concrete structures was able to be realistically captured by the coupled formulation.

• Tribology and Lubricants
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• v.19 no.6
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• pp.311-320
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• 2003

In this study a general Galerkin FE formulation of the incompressible Reynolds equation is derived for lubrication analyses of noncontacting mechanical face seals. Then, the formulation is applied to analyze the flexibly mounted stator­type reactor coolant pump seals of local nuclear power plants, which have deep straight grooves or plane coning on their primary seal ring faces. Their various lubrication performances have been predicted. Results show that the analyzed deep straight groove seal should have a net coning of less than 0.6 to satisfy the leakage limit. And for the same amount of equilibrium opening force the plane coning seal requires to have a 3 times higher dimensionless coning than the deep straight groove seal.

• Coupled systems mechanics
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• v.6 no.3
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• pp.351-367
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• 2017

In this article, the multiphysics response of magneto-electro-elastic (MEE) cantilever beam subjected to thermo-mechanical loading is analysed. The equilibrium equations of the system are obtained with the aid of the principle of total potential energy. The constitutive equations of a MEE material accounting the thermal fields are used for analysis. The corresponding finite element (FE) formulation is derived and model of the beam is generated using an eight noded 3D brick element. The 3D FE formulation developed enables the representation of governing equations in all three axes, achieving accurate results. Also, geometric, constitutive and loading assumptions required to dimensionality reduction can be avoided. Numerical evaluation is performed on the basis of the derived formulation and the influence of various mechanical loading profiles and volume fractions on the direct quantities and stresses is evaluated. In addition, an attempt has been made to compare the individual effect of thermal and mechanical loading with the combined effect. It is believed that the numerical results obtained helps in accurate design and development of sensors and actuators.

• Computers and Concrete
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• v.5 no.3
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• pp.243-260
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• 2008

The present article summarises the fundamental characteristics of concrete behaviour which underlie the formulation of an engineering finite element model capable of realistically predicting the behaviour of (plain or reinforced) concrete structural forms in a wide range of problems ranging from static to impact loading without the need of any kind of re-calibration. The already published evidence supporting the proposed formulation is complemented by four additional typical case studies presented herein; for each case, a comparative study is carried out between numerical predictions and the experimental data which reveals good agreement. Such evidence validates the material characteristics upon which the FE model's formulation is based and provides an alternative explanation regarding the behaviour of structural concrete and how it should be modelled which contradicts the presently (widely) accepted assumptions adopted in the majority of FE models used to predict the behaviour of concrete.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 2003.11a
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• pp.193-200
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• 2003

In this study a general Galerkin FE formulation of the incompressible Reynolds equation is derived for lubrication analyses of noncontacting mechanical face seals. Then, the formulation is applied to analyze the flexibly mounted stator-type reactor coolant pump seals of local nuclear power plants, which have deep straight grooves or plane coning on their primary seal ring faces. Their various lubrication performances have been predicted. Results show that the analyzed deep straight groove seal should have a net coning of less than $0.6\;{\mu}m$ to satisfy the leakage limit. And for the same amount of equilibrium opening force the plane coning seal requires to have a 3 times higher dimensionless coning than the deep straight groove seal.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1994.10a
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• pp.44-54
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• 1994

A variational formulation and the associated finite elemet equations have been derived for general three-dimensional deformation of a planar anisotropic rigid-plastic sheet metal which obeys the strain-rate potential proposed by BARLAT et al [13]. By using the natural convected coordinate system, the effect of geometric change and the rotation of planar anisotropic axes are considered efficiently. In order to check the validity of present formulation, a cylindrical cup and a square cup deep drawing test was modeled. good agreement was found between the FE simulation and the experiment. The results have shown that the present formulation for planar anisotropic deformation can be efficiently applied to the analysis of sheet metal working processes for planar anisotropic nonferrous metals.

• Computers and Concrete
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• v.1 no.3
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• pp.285-302
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• 2004

A FE-(FE-HE)-BE procedure is presented for dynamic analysis of concrete arch dams. In this technique, dam body is discretized by solid finite elements, while the reservoir domain is considered by a combination of fluid finite elements and a three-dimensional fluid hyper-element. Furthermore, foundation rock domain is handled by three-dimensional boundary element formulation. Based on this method, a previously developed program is modified, and the response of Morrow Point arch dam is studied for various conditions. Moreover, the effects of canyon shape on response of dam, is also discussed.

• Journal of Ship and Ocean Technology
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• v.12 no.4
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• pp.7-19
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• 2008

In preliminary ship design, a parametric study is a more realistic way to explore design space and analyze design problem than an optimization technique due to time-consuming computational work or a difficulty in incorporating all constraints into the optimization formulation. In the parametric study, feasible alternatives are examined in various aspects; the best one can be selected. Among the aspects, the strength assessment by FE analysis is an essential process in the ship design. This paper proposes a system to facilitate a parametric study for FE model based on design of experiment (DOE). It works on a FE pre-processor environment and assists a user to define a parametric study by interacting with FE model. It also provides an interface module with a FE solver in order to control the input file and extract predefined FE results from the output file. Based on the proposed system, a better understating and a better design are expected to be achieved.