• Structural Engineering and Mechanics
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• v.36 no.6
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• pp.669-678
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• 2010

In general means, the stress concentration problem of elastic plate with a rectangular hole can be investigated by numerical methods, and only approximative results are derived. This paper deduces an analytical study of the stress concentration due to a rectangular hole in an elastic plate under bending loads. Base on classical elasticity theory and FEM applying the U-transformation technique, the uncoupled governing equations with 3-DOF are established, and the analytical displacement solutions of the finite element equations are derived in series form or double integral form. Therefore, the stress concentration factor can then be discussed easily and conveniently. For the plate subjected to unidirectional bending loads, the non-conforming plate bending element with four nodes and 12-DOF is taken as examples to demonstrate the application of the proposed method. The inner force distribution is obtained. The solutions are adequate for the condition when the hole is far away from the edges and the thin plate subjected to any transverse loadings.

• Transactions of the Korean Society of Automotive Engineers
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• v.6 no.4
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• pp.121-128
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• 1998

In this study, when tension and bending stress act on plate simultaneously, stress intensity factor is analyzed at crack tip with using BEM(Boundary Element Method). In this analysis, stress intensity factors(S.I.F) are defined for variable ligament, aspect and stress ratio($\sigma$T/$\sigma$B). Consequently, predicted that crack grow to depth direction at low aspect and ligament ratio in tension stress and to surface direction in bending stress. Tension and bending stress act on plate same time, effect of tension stress in the first stage and effect of bending stress in the after stage was to observed. The outbreak of secondary crack in backside is under the control of stress amplitude and predict that the point of outbreak is mear backside.

• Steel and Composite Structures
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• v.24 no.5
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• pp.523-536
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• 2017

A layerwise (LW) formulation based on the Galerkin method is presented to investigate the three-dimensional stress state in long sandwich plate which is subjected to tension force and pure bending moment. Based on the Galerkin method and the LW discretization approach, the equilibrium equations of elasticity for the long plate are written in the weak form and discretized through the thickness of the plate. The discretized equations are written in terms of displacement components of the numerical layers. The governing equations of the plate are solved analytically for the free edge boundary conditions. The distribution of stress state especially the 3D stress state in the vicinity of the edges of the sandwich plate which is subjected to tension and pure bending is studied. In order to increase the accuracy, the out of plane stresses are obtained by integrating the equilibrium equations of elasticity. The convergence and accuracy of the predictions are studied and various numerical results are presented for distribution of the in-plane and out of plane stresses in symmetric and un-symmetric sandwich plates.

• International Journal of Naval Architecture and Ocean Engineering
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• v.7 no.5
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• pp.805-816
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• 2015

In the present study, external restraints imposed normal to the plate during the cooling stage were determined to be effective for reduction of the angular distortion of butt-welded or fillet-welded plate. A welding analysis model under external force during the cooling stage was idealized as a prismatic member subjected to pure bending. The external restraint was represented by vertical force on both sides of the work piece and bending stress forms in the transverse direction. The additional bending stress distribution across the plate thickness was reflected in the improved inherent strain model, and a set of inherent strain charts with different levels of bending stress were newly calculated. From an elastic linear FE analysis using the inherent strain values taken from the chart and comparing them with those from a 3D thermal elasto-plastic FE analysis, welding deformation can be calculated.

• Structural Engineering and Mechanics
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• v.19 no.6
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• pp.707-720
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• 2005

The bending stress formula that taking into account the transverse deformation is developed for plane-curved, untwisted isotropic beams subjected to loadings that result in deformations in the plane of curvature. In order to account the transverse Poisson contraction effect, a new constitutive relation between force resultants, moment resultants, mid-plane strains and deformed curvatures for a curved plate is derived in a $6{\times}6$ matrix form. This constitutive relation will provide the fundamental basis to the analyses of curved structures composing of isotropic or anisotropic materials. Then, the bending stress formula of a curved isotropic beam can be deduced from this newly developed curved plate theory. The stress predictions by the present analysis are compared to those by the analysis that neglected the Poisson contraction effect. The results show that the Poisson effect becomes more significant as the Poisson ratio and the curvature are getting larger.

• Structural Engineering and Mechanics
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• v.33 no.4
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• pp.485-502
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• 2009

A new 8-node serendipity quadrilateral plate bending element (MQP8) based on the Mindlin-Reissner theory for the analysis of thin and moderately thick plate bending problems using Integrated Force Method is presented in this paper. The performance of this new element (MQP8) is studied for accuracy and convergence by analyzing many standard benchmark plate bending problems. This new element MQP8 performs excellent in both thin and moderately thick plate bending situations. And also this element is free from spurious/zero energy modes and free from shear locking problem.

• Structural Engineering and Mechanics
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• v.26 no.1
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• pp.43-68
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• 2007

Using the Mindlin-Reissner plate theory, many quadrilateral plate bending elements have been developed so far to analyze thin and moderately thick plate problems via displacement based finite element method. Here new formulation has been made to analyze thin and moderately thick plate problems using force based finite element method called Integrated Force Method (IFM). The IFM is a novel matrix formulation developed in recent years for analyzing civil, mechanical and aerospace engineering structures. In this method all independent/internal forces are treated as unknown variables which are calculated by simultaneously imposing equations of equilibrium and compatibility conditions. In this paper the force based new bilinear quadrilateral plate bending element (MQP4) is proposed to analyze the thin and moderately thick plate bending problems using Integrated Force Method. The Mindlin-Reissner plate theory has been used in the formulation of this element which accounts the effect of shear deformation. Standard plate bending benchmark problems are analyzed using the proposed element MQP4 via Integrated Force Method to study its performance with respect to accuracy and convergence, and results are compared with those of displacement based 4-node quadrilateral plate bending finite elements available in the literature. The results are also compared with the exact solutions. The proposed element MQP4 is free from shear locking and works satisfactorily in both thin and moderately thick plate bending situations.

• Journal of Mechanical Science and Technology
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• v.20 no.3
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• pp.335-344
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• 2006

A comprehensive review of through thickness transverse residual stress distributions in a range of as-welded and mechanically bent components made up of a range of steels has been carried out, and simplified generic transverse residual stress profiles for a plate and pipe components have been proposed. The geometries consisted of welded pipe butt joints, T-plate joints, tubular T-joints, tubular Y-joints and a pipe on plate joints as well as cold bent tubes and pipes. The collected data covered a range of engineering steels including ferritic, austenitic, C-Mn and Cr-Mo steels. Measured residual stress data, normalised with respect to the parent material yield stress, has shown a good linear correlation versus the normalised depth of the region containing the residual stress resulting from the welding or cold-bending process. The proposed simplified generic residual stress profiles based on the mean statistical linear fit of all the data provides a reasonably conservative prediction of the stress intensity factors. Whereas the profiles for the assessment procedures are fixed and case specific, the simple bilinear profiles for the residual stresses obtained by shifting the mean and bending stress from the mean regression line have been proposed and validated.

• Journal of Aerospace System Engineering
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• v.1 no.4
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• pp.28-36
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• 2007

This paper presents critical buckling loads of laminated composites under cylindrical bending. In-plane displacements are assumed to vary exponentially through plate thickness. The accuracy of this theory is examined for symmetric/antisymmetric cross-ply, angle-ply and unsymmetric laminates under cylindrical bending. Analytical solutions are provided to investigate the effect of transverse shear deformation on critical buckling loads of the laminated plates, and the results are compared with those obtained from the first-order shear deformation plate theory and the classical laminated plate theory.

• Journal of the Korea Convergence Society
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• v.8 no.3
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• pp.185-190
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• 2017

This study investigates the bending stress, shear stress and deformation energy happening at the inner fiber structure when the bending moment is applied to he specimen with flat shape composed of carbon fiber. As CFRP is composed of innumerable fibers with multi-axes, the stress under bending condition can be effectively distributed. Theses stresses is shown to increase again at the starting point as this angle of $60^{\circ}$. Therefore, the condition at the stacking angle of $60^{\circ}$ is seen to become most adequate under the state where the bending stress happens. On the basis of this study result, the damage property by the bending at the plate due to stacking angle was examined through the analytic approach. it is thought that this study can be devoted to the safe design for damage prevention and durabilty improvement. Also, the esthetic sense can be shown as the designed factor of shape with flat plate is grafted onto the convergence technique.