• Structural Engineering and Mechanics
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• v.90 no.3
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• pp.233-252
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• 2024

This research explores a new finite element model for the free vibration analysis of bi-directional functionally graded (BDFG) beams. The model is based on an efficient higher-order shear deformation beam theory that incorporates a trigonometric warping function for both transverse shear deformation and stress to guarantee traction-free boundary conditions without the necessity of shear correction factors. The proposed two-node beam element has three degrees of freedom per node, and the inter-element continuity is retained using both C1 and C0 continuities for kinematics variables. In addition, the mechanical properties of the (BDFG) beam vary gradually and smoothly in both the in-plane and out-of-plane beam's directions according to an exponential power-law distribution. The highly elevated performance of the developed model is shown by comparing it to conceptual frameworks and solution procedures. Detailed numerical investigations are also conducted to examine the impact of boundary conditions, the bi-directional gradient indices, and the slenderness ratio on the free vibration response of BDFG beams. The suggested finite element beam model is an excellent potential tool for the design and the mechanical behavior estimation of BDFG structures.

• Interaction and multiscale mechanics
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• v.2 no.3
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• pp.277-293
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• 2009

The Enriched Free Mesh Method (EFMM) is a patch-wise procedure in which both a displacement field on an element and a stress/strain field on a cluster of elements connected to a node can be defined. On the other hand, the Superconvergent Patch Recovery (SPR) is known to be an efficient post-processing procedure of the finite element method to estimate the error norm at a node. In this paper, we discuss the relationship between solutions of the EFMM and those of the SPR through several convergence studies. In addition, in order to solve the demerit of the smoothing effect on the fracture mechanics fields, we implement a singular stress field to a local patch in the EFMM, and its effectiveness is investigated.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1995.10a
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• pp.102-108
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• 1995

Internal contact scheme between two free surfaces on one deforming body has been proposed by using the penalty method. It has been imposed to be internal boundary condition on two-dimensional thermo-viscoplastic finite element method so as to analyze one deforming body, which has two free surfaces penetrating each others. Analysis of side pressing with a circular void and a inclined elliptic hole have been carried out in order to verity the proposed contact scheme. A finite element code imposed internal boundary condition has been applied to two-dimensional analysis of free forging of large ingot with a void. Through the analysis, effects of working parameters in order to consolidate voids have been investigated.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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• pp.465-472
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• 1998

In this study, analytic solution and finite element formulation for the free vibration analysis of thin-walled circular arch, based on linearized virtual work and Vlasov's assumption, including restrained warping effect and second order terms of finite semitangential rotations, is presented. The total potential energy is derived by applying the Hellinger-Reissner principle. In this formulation, all displacement parameters of deformation are defined at the centroid axis. For the finite element formulation, the two node cubic Hermitian polynomials are utilized as shape functions. In special case, potential energy functional of thin-walled curved beam with monosymmetric cross section is derived. From this methodology, analytic solution for the free vibration of monosymmetric circular arch with simply supported is derived. In order to illustrate the accuracy of this study, various parameter studies for free vibration of circular arches are presented and compared with numerical solution analyzed by the FEM using straight beam element.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.10a
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• pp.78-85
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• 2002

This paper deals with the finite element model of the monitor for the simulation of directional free drop tests such as backward, sideward, edge and vertex drop. The model was made for an unconditional stable solution for the explicit integration algorithm. The general behaviors at the time of impact were found to well correlate with the actual situation in terms of acceleration, displacement, contact force and stress of monitor components even though the experiment of the associated drop is performed for the validity of the model.

• Proceedings of the KSME Conference
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• 2008.11b
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• pp.2558-2561
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• 2008

In the present study, a parallel Taylor-Galerkin/level set based two-phase flow code was developed using finite element discretization and domain decomposition method based on MPI (Message Passing Interface). The proposed method can be utilized for the analysis of a large scale free surface problem in a complex geometry due to the feature of FEM and domain decomposition method. Four-step fractional step method was used for the solution of the incompressible Navier-Stokes equations and Taylor-Galerkin method was adopted for the discretization of hyperbolic type redistancing and advection equations. A Parallel ILU(0) type preconditioner was chosen to accelerate the convergence of a conjugate gradient type iterative solvers. From the present parallel numerical experiments, it has been shown that the proposed method is applicable to the simulation of large scale free surface flows.

• Structural Engineering and Mechanics
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• v.14 no.3
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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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1998.04a
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• pp.353-358
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• 1998

In general, we have used the finite element method(FEM) to find natural frequencies of plates. In this method, however, it is necessary to use a large amount of computer memory and computation time because the FEM requires many degrees of freedom for finding natural frequencies of plates correctly. Therefore it was very difficult to analyze the free vibration of plates correctly on personal computer. For overcoming this disadvantage of the FEM, the authors have developed the finite element-transfer stiffness coefficient method(FE-TSCM) which is based on the concept of modeling techniques in the FEM and the transfer of the stiffness coefficient in the transfer stiffness coefficient method. In this paper, we formulate free vibration analysis algorithm of rectangular plates using the FE-TSCM. Some numerical examples of rectangular plates are proposed, and their results and computation times obtained by the FE-TSCM are compared with those by the FEM and the finite element-transfer matrix method in order to demonstrate the accuracy and efficiency of the FE-TSCM.

• Architectural research
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• v.16 no.2
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• pp.67-74
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• 2014

Free vibration analysis of thin shells is carried out by using isogeometric approach. For this purpose, a thin shell element based on Kirchhoff-Love shell theory is developed. Non-uniform rational B-spline surface (NURBS) definition is introduced to represent the geometry of shell and also used to derive all terms required in the isogeometric element formulation. Gauss integration rule is used for stiffness and mass matrices. The present shell element is then applied to examine vibrational behaviours of thin plate and shell structures. From numerical results, it is found be that reliable natural frequencies and associated mode shapes of thin shell structures can be predicted by the present isogeometric shell element.

• Journal of Mechanical Science and Technology
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• v.17 no.1
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• pp.64-76
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• 2003

In this work, a new penalty formulation is proposed for the analysis of Mindlin-Reissner plates by using the element-free Galerkin method. A penalized weak form for the Mindlin-Reissner Plates is constructed through the exterior penalty method to enforce the essential boundary conditions of rotations as well as transverse displacements. In the numerical examples, some typical problems of Mindlin-Reissner plates are analyzed, and parametric studies on the order of integration and the size of influence domain are also carried out. The effect of the types of background cells on the accuracy of numerical solutions is observed and a proper type of background cell for obtaining optimal accuracy is suggested. Further, optimal order of integration and basis order of Moving Least Squares approximation are suggested to efficiently handle the irregularly distributed nodes through the triangular type of background cells. From the numerical tests, it is identified that unlike the finite element method, the proposed element-free Galerkin method with penalty technique gives highly accurate solution without shear locking in dealing with Mindlin-Reissner plates.