• Proceedings of the Korean Society For Composite Materials Conference
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• 2004.10a
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• pp.69-72
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• 2004

A new three-node triangular shell element based on higher order zig-zag theory is developed for laminated composite shells with multiple delaminations. The present higher order zig-zag shell theory is described in a general curvilinear coordinate system and in general tensor notation. All the complicated curvatures of surface including twisting curvatures can be described in an exact manner in the present shell element because this element is based on geometrically exact surface representation. The displacement field of the proposed finite element includes slope of deflection, which requires continuity between element interfaces. Thus the nonconforming shape function of Specht's three-node triangular plate bending element is employed to interpolate out-of-plane displacement. The present element passes the bending and twisting patch tests in flat surface configurations. The developed element is evaluated through the eigenvalue problems of composite cylindrical shells with multiple delaminations. Through the numerical examples it is demonstrated that the proposed shell element is efficient because it has minimal degrees of freedom per node. The present shell element should serve as a powerful tool in the prediction of natural frequency and modes of multi-layered thick laminated shell structures with arbitrary-shaped multiple delaminations.

• Proceeding of KASS Symposium
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• 2008.05a
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• pp.95-100
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• 2008

A 4-node assumed strain finite element based on higher order shear deformation theory is developed to investigate the behaviours of symmetric and unsymmetric laminated composite plates. The present element is based on Reddy's higher order shear deformation theory so that it can consider the parabolic distribution of shear deformation through plate thickness direction. In particular, assumed strain method is adopted to alleviate the shear locking phenomena inherited plate elements based on higher order shear deformation theory. The present finite element has seven degrees of freedom per node and denoted as HSA4. Numerical examples are carried out for symmetric and unsymmetric laminated composite plate with various thickness values. Numerical results are compared with reference solutions produced by other higher order shear deformation theories.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1409-1419
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• 2017

We introduce an extrapolated Crank-Nicolson characteristic finite element method to approximate solutions of a convection dominated Sobolev equation. We obtain the higher order of convergence in both the spatial direction and the temporal direction in $L^2$ normed space for the extrapolated Crank-Nicolson characteristic finite element method.

• East Asian mathematical journal
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• v.33 no.3
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• pp.295-308
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• 2017

We introduce a Crank-Nicolson characteristic finite element method to construct approximate solutions of a nonlinear Sobolev equation with a convection term. And for the Crank-Nicolson characteristic finite element method, we obtain the higher order of convergence in the temporal direction and in the spatial direction in $L^2$ normed space.

• East Asian mathematical journal
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• v.32 no.5
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• pp.729-744
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• 2016

A Crank-Nicolson characteristic finite element method is introduced to construct approximate solutions of a Sobolev equation with a convection term. The higher order of convergences in the temporal direction and in the spatial direction in $L^2$ normed space are verified for the Crank-Nicolson characteristic finite element method.

• Structural Engineering and Mechanics
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• v.53 no.4
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• pp.625-644
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• 2015

In this paper, a two-layer partial interaction composite beams model considering the higher order shear deformation of sub-elements is built. Then, the governing differential equations and boundary conditions for static analysis of linear elastic higher order composite beams are formulated by means of principle of minimum potential energy. Subsequently, analytical solutions for cantilever composite beams subjected to uniform load are presented by Laplace transform technique. As a comparison, FEM for this problem is also developed, and the results of the proposed FE program are in good agreement with the analytical ones which demonstrates the reliability of the presented exact and finite element methods. Finally, parametric studies are performed to investigate the influences of parameters including rigidity of shear connectors, ratio of shear modulus and slenderness ratio, on deflections of cantilever composite beams, internal forces and stresses. It is revealed that the interfacial slip has a major effect on the deflection, the distribution of internal forces and the stresses.

• East Asian mathematical journal
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• v.38 no.3
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• pp.293-319
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• 2022

In this paper, we introduce a higher order split least-squares characteristic mixed element scheme for Sobolev equations. First, we use a characteristic mixed element method to manipulate both convection term and time derivative term efficiently and obtain the system of equations in the primal unknown and the flux unknown. Second, we define a least-squares minimization problem and a least-squares characteristic mixed element scheme. Finally, we obtain a split least-squares characteristic mixed element scheme for the given problem whose system is uncoupled in the unknowns. We establish the convergence results for the primal unknown and the flux unknown with the second order in a time increment.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.6
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• pp.1365-1381
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• 1990

A $C^{0}$ continuous displacement finite element method based on a higher-order shear deformation theory is employed in the prediction of the transient response of laminated composite plates subjected to low-velocity impact. A modified contact law was applied to calculate the contact force during impact. The discrete element chosen is a nine-noded quadrilateral with 5 degree-of-freedom per node. The Wilson-.theta. time integration algorithm is used for solving the time dependent equations of the impactor and the central difference method was adopted to perform time integration of the plate. Numerical results, including the contact force history, deflection, and velocity history, are presented. Comparisons of numerical results using a higher order theory and a first-order theory show that using a higher order theory provides more accurate results. Effects of boundary condition, impact velocity, and mass of the impactors are also discussed.d.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.7 no.1
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• pp.65-73
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• 1987

An efficient plate bending finite element has been developed using higher-order inplane displacement profiles of the plate. The 6-noded, 21-d.o.f. triangular element including shear deformation effect has been derived from the plate-like continuum by the Galerkin's weighted residual method. Square plate examples were tested with selected element meshes and several aspect ratios for their static behavior under uniformly distributed load. The result of the example tests indicated consistently good performance of the present higher-order plate bending element in comparison with the thin and thick plate solution and other existing finite element solutions.

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.257-270
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• 2018

An extrapolated Crank-Nicolson characteristic finite element method is introduced for approximate solutions of nonlinear Sobolev equations with a convection term. And we obtain the higher order of convergence for approximate solutions in the temporal and the spatial directions with respect to $L^2$ norm.