• Journal of Power System Engineering
• /
• v.19 no.3
• /
• pp.55-62
• /
• 2015

This paper discusses a new model for investigating the micro-mechanical behavior of beam-like structures composed of various elastic moduli and complex geometries varying through the cross-sectional directions and also periodically-repeated along the axial directions. The original three-dimensional problem is first formulated in an unified and compact intrinsic form using the concept of decomposition of the rotation tensor. Taking advantage of two smallness of the cross-sectional dimension-to-length parameter and the micro-to-macro heterogeneity and performing homogenization along dimensional reduction simultaneously, the variational asymptotic method is used to rigorously construct an effective zeroth-order beam model, which is similar a generalized Timoshenko one (the first-order shear deformation model) capable of capturing the transverse shear deformations, but still carries out the zeroth-order approximation which can maximize simplicity and promote efficiency. Two examples available in literature are used to demonstrate the consistence and efficiency of this new model, especially for the structures, in which the effects of transverse shear deformations are significant.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2003.04a
• /
• pp.261-268
• /
• 2003

A first order shear deformable Loop-subdivision triangular element which can handle transverse shear deformation of moderately thick shell is developed. The developed element is general since it includes the effect of transverse shear deformation and has standard six degrees of freedom per node.(three translations and three rotations) The quartic box-spline function is employed as interpolation basis function. Numerical examples for the benchmark problems are analyzed in order to assess the performance of the newly developed subdivision shell element. Both in the uniform and in the distorted mesh configurations.

• Journal of Korean Association for Spatial Structures
• /
• v.1 no.2 s.2
• /
• pp.85-92
• /
• 2001

The structural behaviors of anisotropic laminated shells are quite different from that of isotropic shells, Also, the classical theory of shells based on neglecting transverse shear deformation is invalid for laminated shells. Thus, to obtain the more exact behavior of laminated shells, effects of shear deformation should be considered in the analysis. As the length of x-axis or y-axis is increase, the effects of transverse shear deformation are decrease because the stiffness for the axis according to the increasing of length is large gradually. In this paper, the governing equations for anisotropic laminated shallow shell including the effects of shear deformation are derived. And then, by using Navier's solutions for shallow shells having simple supported boundary, extensive numerical studies for anisotropic laminated shallow shells were made to investigate the effects of shear deformation for 3 typical shells. Also, static analysis is carried out for cross-ply laminated shells considering the effects of various geometrical parameters, e,g., the shallowness ratio, the thickness ratio and the ratio of a(length of x-axis)-to-b(length of y-axis). The results are compared with existed one and show good agreement.

• Structural Engineering and Mechanics
• /
• v.63 no.5
• /
• pp.683-689
• /
• 2017

In this paper, a hyperbolic shear deformation theory is presented for bending analysis of functionally graded beams. This theory used in displacement field in terms of thickness co-ordinate to represent the shear deformation effects and does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The governing equations are derived by employing the virtual work principle and the physical neutral surface concept. A simply supported functionally graded beam subjected to uniformly distributed loads and sinusoidal loads are consider for detail numerical study. The accuracy of the present solutions is verified by comparing the obtained results with available published ones.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.24 no.3
• /
• pp.249-257
• /
• 2011

In this paper, an systematic approach is presented, in which the mixed variational theorem is employed to incorporate independent transverse shear stresses into a classical higher-order shear deformation theory(HSDT). The HSDT displacement field is taken to amplify the benefits of using a classical shear deformation theory such as simple and straightforward calculation and numerical efficiency. Those independent transverse shear stresses are taken from the fifth-order polynomial-based zig-zag theory where the fourth-order transverse shear strains can be obtained. The classical displacement field and independent transverse shear stresses are systematically blended via the mixed variational theorem. Resulting strain energy expressions are named as an enhanced higher-order shear deformation theory via mixed variational theorem(EHSDTM). The EHSDTM possess the same computational advantage as the classical HSDT while allowing for improved through-the-thickness stress and displacement variations via the post-processing procedure. Displacement and stress distributions obtained herein are compared to those of the classical HSDT, three-dimensional elasticity, and available data in literature.

• Steel and Composite Structures
• /
• v.14 no.1
• /
• pp.85-104
• /
• 2013

The present work deals with the thermomechanical bending response of functionally graded plates resting on Winkler-Pasternak elastic foundations. Theoretical formulations are based on a recently developed refined trigonometric shear deformation theory (RTSDT). The theory accounts for trigonometric distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. Unlike the conventional trigonometric shear deformation theory, the present refined trigonometric shear deformation theory contains only four unknowns as against five in case of other shear deformation theories. The material properties of the functionally graded plates are assumed to vary continuously through the thickness, according to a simple power law distribution of the volume fraction of the constituents. The elastic foundation is modelled as two-parameter Pasternak foundation. The results of the shear deformation theories are compared together. Numerical examples cover the effects of the gradient index, plate aspect ratio, side-to-thickness ratio and elastic foundation parameters on the thermomechanical behavior of functionally graded plates. It can be concluded that the proposed theory is accurate and efficient in predicting the thermomechanical bending response of functionally graded plates.

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

• Computers and Concrete
• /
• v.18 no.6
• /
• pp.1213-1234
• /
• 2016

This paper describes a deformation-based strut-and-tie model for the flexural members at post-yield state. Boundary deformation conditions by flexural post-yield response are chosen in terms of the flexural bar strains as the main factor influenced on the shear strength. The main purpose of the proposed model is to predict the shear capacities of the flexural members associated with the given flexural deformation conditions. To verify the proposed strut-and-tie model, the estimated shear strengths depending on the flexural deformation are compared with the experimental results. The experimental data are in good agreement with the values obtained by the proposed model.

• Composites Research
• /
• v.19 no.5
• /
• pp.1-6
• /
• 2006

In this study, a closed-form analysis has been developed for the transverse shear behavior of thin-walled composite beams with closed cross-sections. The shear flow distributions and cross-section stiffness coefficients are derived analytically by using a mixed beam approach. The theory has been applied to single-celled composite box-beams with elastic couplings. The location of the shear center and the effect of transverse shear deformation on the static behavior of composite beams are investigated in the framework of the analysis. The present results are validated against those of a two-dimensional finite element analysis and a good correlation has been obtained for box-beam cases considered in this study.

• Proceedings of the KSR Conference
• /
• 2010.06a
• /
• pp.13-17
• /
• 2010

This presentation examines the characteristics of torsional vibration in axisymmetric out-of-plane vibrations of an annular Mindin plate. The out-of-plane vibration of circular or annular plates have been investigated since a long years ago by many researchers. When the classical Kirchhoff plate theory neglecting the effect of transverse shear deformation is applied to a thick plate, its out-of-plane natural frequencies are much different from reality. And so, since Minlin presented a plate theory considering the effect of rotary inertia and transverse shear deformation, many researches for the out-of-plane natural vibration of circular or annular Mindin plates have been performed. But almost all researchers missed the torsional vibration due to transverse shear deformation in axisymmetric out-of-plane vibrations of the circular or annular Mindin plate. Therefore, in this presentation, we verify the existence of torsional vibration of an annular plate and present the natural frequencies of an annular plate with free outer boundary surface.