• Proceedings of the Computational Structural Engineering Institute Conference
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• 1992.10a
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• pp.29-38
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• 1992

Approximate Constant Shear Angle Theory is usually used to take a transversal shear deformation of thick plate into consideration, which cannot be effectively considered the influence of transversal warping of cross-section with an increase of thickness. It right be the best way to represent the exact warping of cross-section. In this study, the derivation of warping function is attempted, and the effect of shear deformation and transversal warping is to be considered through the nolinear analysis of plate.

• Structural Engineering and Mechanics
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• v.59 no.3
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• pp.527-537
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• 2016

We describe a stress analysis of a single leaf flexure under torsion in which the warping effect is considered. The theoretical equations for the warping normal stress (${\sigma}_{xx}$) and shear stresses (${\tau}_{xz}$ and ${\tau}_{xy}$) are derived by applying the warping function of a rectangular cross-sectional beam and the twist angle equation that includes the warping torsion. The results are compared with those of the non-warping case and are verified using finite element analysis (FEA). A sensitivity analysis over the length, width, and thickness is performed and verified via FEA. The results show that the errors between the theory of warping stress results and the FEA results are lower than 4%. This indicates that the proposed theoretical stress analysis with warping is accurate in the torsion analysis of a single leaf flexure.

• International Journal of Aeronautical and Space Sciences
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• v.18 no.3
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• pp.467-473
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• 2017

This paper focuses on the investigation of three-dimensional (3D) warping effect on the stiffness constants of composite beams with closed section profiles. A finite element (FE) cross-sectional analysis is developed based on the Reissner's multifield variational principle. The 3D in-plane and out-of-plane warping displacements, and sectional stresses are approximated as linear functions of generalized sectional stress resultants at the global level and as FE shape functions at the local sectional level. The classical elastic couplings are taken into account which include transverse shear and Poisson deformation effects. A generalized Timoshenko level $6{\times}6$ stiffness matrix is computed for closed section composite beams with and without warping. The effect of neglecting the 3D warping on stiffness constants is shown to be significant indicating large errors as high as 93.3%.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.709-712
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• 2004

A study of the coupled flexural-torsional vibrations of thin-walled beams with monosymmetric cross-section is presented. The governing differential equations for free vibration of such beams are solved numerically to obtain natural frequencies and their corresponding mode shapes. The beam model is based on the Bernoulli-Euler beam theory and the effect of warping is taken into consideration. Numerical results are given for two specific examples of beams with free-free, clamped-free, hinged-hinged, clamped-hinged and clamped-clamped end constraints both including and excluding the effect of warping stiffness. The effect of warping stiffness on the natural frequencies and mode shapes is discussed and it is concluded that substantial error can be incurred if the effect is ignored.

• International Journal of Advanced Culture Technology
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• v.8 no.2
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• pp.159-164
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• 2020

The response analysis of frame structure with open section beams considering warping conditions and short duration load have been performed. When a beam of frame structure is subjected under torsional moment, the cross section will deform a warping as well as twist. For some thin-walled sections warping will be large, and accompanying warping restraint will induce axial and shear stresses and reduce the twist of beam which stiffens the beam in torsion. Because of impact or blast loads, the wave propagation effects become increasingly important as load duration decreases. This paper presents that a warping restraint in finite element model effects the behavior of beam deformation, dynamic mode shape and response analysis. The computer modelling of frame is discussed in linear beam element model and linear thin shell element model, also presents a correlation between computer predicted and actual experimental results for static deflection, natural frequencies and mode shapes of frame. A method to estimate the number of normal modes that are important is discussed.

• Journal of Aerospace System Engineering
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• v.12 no.4
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• pp.9-17
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• 2018

With an aim of considering the warping restraint effect, the results of the comparative study for several cases on the correction of the warping functions for the theoretical analysis of composite thin-walled beams with chord wise asymmetric closed cross-sections are presented in this study. To solve this problem, it is necessary to correct the warping function so as to satisfy the warping equilibrium condition like 1) without moving the position of the pole, 2) with only modifying the shape function using the existing pole, and 3) with moving the position of the pole. The cross-sectional characteristics of the cases were compared with each other. Finally, the cases were compared in order to correct the warping functions. The case 2) was observed to be more speedy and simple in computation compared to others.

• Journal of the Society of Naval Architects of Korea
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• v.33 no.1
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• pp.77-89
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• 1996

An enormous amount of efforts has been devoted to the development of finite elements for the bending problem of thick plates, especially based on Mindlin plate theory. Here, an approximate Constant Shear Angle Theory is usually used to take a transverse shear deformation of thick plate into consideration, which cannot be effectively considered the influence of transversal warping of cross-section with an increase of thickness. It might be the best way to represent the exact cross-sectional warping of the plate. The overall objective of this study is to develop a new formulation of plate including shear deformation and transversal warping, to perform extensive parametric studies comparing its results with those from Mindlin plate formulation, and to gain further insight into the influence of shear deformation and transversal warping of thick plate.

• Journal of Aerospace System Engineering
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• v.12 no.6
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• pp.41-49
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• 2018

In this study, the theoretical dynamic characteristics of a thin-walled composite beam with a single-cell of chordwise asymmetric cross-section was studied. Mathematical modeling was done by considering the transverse shear effects, the warping restraint effects, the constant taper ratio in the longitudinal direction of the beam, and the geometrical cross-section ratio. The mass coefficients, stiffness coefficients, and Eigen frequencies of the selected section were investigated. In particular, the effects of the taper ratio and cross-section ratio of the model on the Eigen frequencies were analyzed and compared when the asymmetry of the section was considered and the warping function was not corrected.

• Journal of the Korean Wood Science and Technology
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• v.28 no.1
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• pp.18-27
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• 2000

Even the same materials are assembled in flush door skin panel, warping is not simply prevented under the changes of environmental conditions since wood and wood-based material have large variations in their physical and mechanical properties. The parameters such as linear movement coefficient(LMC), modulus of elasticity (MOE), required to predict warping could be estimated by oven drying method and dynamic method instead of American Society for Testing Materials(ASTM) procedure. The relationship between warping and LMC was curvilinear, while it between warping and MOE was linear. LMC had a larger effect on warping than MOE. Material propensity of skin panel such as hardboard and plywood showed normal distributions. The variation of material properties, however, was much larger in plywood than in hardboard. Monte Carlo simulation also indicated that rejection ratio of flush door due to the occurrence of warping could be predicted with consideration of the relationship of warping and parameters of probability distribution of MOE, LMC, and moisture content.

• Journal of the Korean Wood Science and Technology
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• v.27 no.3
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• pp.99-116
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• 1999

Wooden hollow core flush door is one of the main products of furniture manufacturing and woodworking industries. Warping and buckling of the door is serious problems in service. It has been reported that warping is caused by differences of physical and mechanical properties of face and back of skin panel for the door. This study focused on the prediction of warping and buckling phenomena of the flush door using numerical models. Predictions from the models were also compared with the experimental results obtained from the doors with plywood and hardboard skin panels under various environmental conditions. Three elastic constitutive models, so called elastic beam model, plate model and plate-buckling model, were employed to predict warping and buckling of the doors. It was observed that warping was more pronounced in low humidity condition than in high humidity condition. The plate model considering Poisson's effect was reliable to predict warping more closely than elastic beam model in low humidity condition. The plate-buckling model, however, was the best in the fitting of predictions with the experimental results under high humidity condition because buckling was developed in face and back of skin panel at that condition.