• Computational Structural Engineering
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• v.7 no.4
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• pp.103-111
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• 1994

Based on a variational principle of the consistent shear deformable discrete laminate theory derived in the companion paper Part I, a finite element procedure for the vibration analysis of laminated composite plates is presented. The present formulation takes the in-plane displacements of an arbitrary layer, the rotations of the cross section of each layer and transverse displacement of the plate as the state variables at a nodal point of finite element, resulting in total nodal degree of freedom of 2(n+l) +1 for the n-layered laminate. Thus, it allows to specify displacement boundary conditions of layer stretching and/or rotation of layer cross sections around the plate edge and/or lateral displacement. The developed procedure is applied to the free vibration problem for sandwich-type hybrid laminates composed of layers with drastically different material properties whose elasticity solutions are known. Comparison of analysis results with other FEM solutions showed that the present formulation yields better accuracy.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.11
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• pp.1844-1851
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• 1997

Displacement fields and interface stresses are obtained by modifying the potential energy functional with a penalty function which enforces the continuity of stresses at the interface of two-materials. Based on the displacement field and the interface stresses, a new methodology to generate a continuous stress field over the entire domain including the interface of the dissimilar materials has been proposed by combining the L$^{2}$ projection method of stress-smoothing and the Loubignac's iterative method of improving the displacement field. Stress analysis was carried out on two examples which are made of highly dissimilar materials. As a result of the analysis, it is found that the proposed method provides improved continuity of the stress field over the entire domain as well as predicting accurate nodal stresses at the interface. In contrast, the conventional displacement-based finite element method provides significant stress discontinuties at the interfaces. In addition, it was found that the total strain energy evaluated from the improved continuous stress field converge to the exact value as increasing the number of iterations in the proposed method.

• Magazine of the Korean Society of Agricultural Engineers
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• v.36 no.1
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• pp.83-94
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• 1994

The first part of this study dealt with the determination of soil parameters for Lade's double work-hardening model using the raw data obtained from cubical and cylinderal triaxial tests At present, it should be investigated which test can simulated satisfactorily the behavior of soft clayey foundation. In this regard, plate bearing test on the 2-dimentional model foundation(218cm long, 40cm wide, 19&m high) was performed, and finite element analysis carried out to abtain the behavior of the foundation. Settlement, lateral displacement, displacement vector and mode of failure were measured and these values were compared with numerical values in order to validate the numerical program developed by authors. The FEM technique was based on Christain-Boehmer's method, in which the displacement is obtained at each nodal point while stress and pore water pressure at each element.In this research, Biot's equation, which explains was elahorately the phisical meaning of consolidation, was selected, as a governing equation, coupled with Lade's double surface work-hardening constitutive model.

• The korean journal of orthodontics
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• v.15 no.1
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• pp.7-22
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• 1985

The purpose of this study was to analyze the stress distribution and the displacement in the maxillary complex after the application of the reverse headgear. The direction of force was parallel to the occlusal plane. Orthopedic force,300gm, was applied to the maxilla of the dry human skull in a forward direction. The stress distribution and the displacement within the maxillary Complex was analyzed by a 3-dimensional finite element method. The results were as follows: 1. The stress distribution at the molar region was greater than that at the anterior. 2. The stress distribution at the lateral side of the premaxilla was greater than that at the middle aide, especially high stress was noted at the canine eminence. 9. Compressive stress was noted only at the frontozygomatic suture of the zygomatic arch. 4. A forward, upward, and sideward displacement was noted at the entire nodal points of the zygomaticomaxillary suture portion. A displacement with a slight rotation was observed on the transverse palatine suture. 5. The maximum stress was observed at the lateral side of the maxillary tuberosity area, and generally the forward and downward displacement was noted at all this area.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.5
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• pp.849-863
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• 1992

A very simple and computationally efficient numerical method is developed for the free vibration of isotropic and orthotropic composite triangular plates. A set of two-dimensional simple series functions is used as an admissible displacement functions in the Rayleigh-Ritz method to obtain the natural frequencies, nodal patterns and mode shapes for the plates. From the prescribed starting function satisfying only the geometric boundary conditions, the higher terms in the series functions are constructed with adding order of polynominal. Natural frequencies, nodal patterns and mode shapes are obtained for right triangular plates with three different support conditions. The obtained numerical results are presented, and the isotropic and some orthotropic cases are verified with other numerical methods in the liternature.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.23 no.6
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• pp.615-626
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• 2010

The discrete-layer model is proposed to analyze the edge-effect problem of laminates under extension and flexure. Based on three-dimensional elasticity theory, the displacement fields of each layer in a laminate have been treated discretely in terms of three displacement components across the thickness. The displacement fields at bottom and top surfaces within a layer are approximated by two-dimensional shape functions. Then two surfaces are connected by one-dimensional high order shape functions. Thus the p-convergent refinement on approximated one- and two-dimensional shape functions can be implemented independently of each other. The quality of present model is mostly determined by polynomial degrees of shape functions for given displacement fields. For nodal modes with physical meaning, the linear Lagrangian polynomials are considered. Additional modes without physical meaning, which are created by increasing nodeless degrees of shape functions, are derived from integrals of Legendre polynomials which have an orthogonality property. Also, it is assumed that mapping functions are linear in the light of shape of laminated plates. The results obtained by this proposed model are compared with those available in literatures. Especially, three-dimensional out-of-plane stresses in the interior and near the free edges are evaluated and convergence performance of the present model is established with the stress results.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.2
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• pp.338-347
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• 1995

Equations of motion and continuity equations of a hydraulic breaker are derived. Hydraulic pressures are defined with 6 state variables corresponding to 6 control volumes. Impact analysis procedure of the piston and chisel is developed based on the finite element nodal displacement description. Computer simulation is performed with given design parameters and the results are compared with experimental results.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.11
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• pp.1697-1704
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• 2001

A finite element model for polarization switching in electro-mechanically coupled materials is proposed and applied to predict the switching behavior of a two-dimensional ferroelectric ceramic. A complicated micro-structure existing in the material is modeled as il continuum body and a simple 3 node triangle finite element with nodal displacement and voltage degrees of freedom is used for a finite element analysis. The elements use nonlinear constitutive equations, switching criterion and kinetic relation, fur representation of material response at strong electric and stress fields. The polarization state of the material is represented by internal variables in each element, which are updated at each simulation step based on the proposed constitutive equations. The model reproduces strain and electric displacement hysteresis loops observed in the material.

• International Journal of Automotive Technology
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• v.7 no.1
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• pp.115-120
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• 2006

On a rotating contact surface of arbitrary shape, the relative velocity of the contact point sliding between the surfaces is computed with the basic geometries of the rotating surfaces, and the acceleration of the contact point between the contact surfaces is computed by using the relative velocity of the contact point. Thus the equation for the acceleration constraint between the contact surfaces in muitibody dynamics is not coupled with the parameters such as the relative velocity of the contact point. In case of the kinematic analysis, the acceleration of the contact point on any specific instant may also be efficiently computed by the present technique because the whole displacement of a full cycle need not be interpolated. Employing a cam-follower mechanism as a verification model, the acceleration of the contact point computed by the present technique is compared with that computed by differentiating the displacement interpolated with a large number of nodal points.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.12 no.4_1
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• pp.67-76
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• 1992

A hierarchical formulation based on p-version of the finite element method for linear elastic axisymmetric stress analysis is presented. This is accomplished by introducing additional nodal variables in the element displacement approximation on the basis of integrals of Legendre polynomials. Since the displacement approximation is hierarchical, the resulting element stiffness matrix and equivalent nodal load vectors are hierarchical also. The merits of the propoosed element are as follow: i) improved conditioning, ii) ease of joining finite elements of different polynomial order, and iii) utilizing previous solutions and computation when attempting a refinement. Numerical examples are presented to demonstrate the accuracy, efficiency, modeling convenience, robustness and overall superiority of the present formulation. The results obtained from the present formulation are also compared with those available in the literature as well as with the analytical solutions.