Abstract
Abstract The first-order shear deformation theory (FSDT) is a relatively simple tool that has been found to yield accurate results in the non-local problems of sandwich structures, such as buckling and free vibration. However, a key factor in practical application of the theory is determination of the transverse shear correction factor (K), which appears as a coefficient in the expression for the transverse shear stress resultant. The physical basis for this factor is that it is supposed to compensate for the FSDT assumption that the shear strain is uniform through the depth of the cross section. In the present paper, the philosophies and results of K determination for homogeneous rectangular cross sections are first reviewed, followed by a review and discussion for the case of sandwich structures.
Highlights
THE PURPOSE OF using sandwich construction in the first place is to provide a stronger and stiffer structure for the same weight, or a lighter structure to carry the same load, as a homogeneous or compact-laminate flexural member
The transverse shear strains resulting from the transverse shear stresses produce additional deflection and flexibility, which usually must be taken into account
Six methods for the evaluation of the shear correction factor have been discussed in the paper. Three of these methods yield the value of this factor equal to unity, irrespectively of geometry and stiffnesses of the sandwich components. In these examples, we compare the factors obtained by the other three methods: modeling the sandwich structure as a discrete mass system (Equation 7), method based on the comparison of the shear strain energies (Equations 10, 12), and the method based on the comparison of the average strains (Equation 14)
Summary
THE PURPOSE OF using sandwich construction in the first place is to provide a stronger and stiffer structure for the same weight, or a lighter structure to carry the same load, as a homogeneous or compact-laminate flexural member. One prediction utilized matching pure thickness-shear waves and gave K 1⁄4 2/12, or approximately 0.822 His other prediction was based on short-wavelength flexural waves and gave an implicit result that depended on Poisson’s ratio. In a very important analysis, Hutchinson and Zillmer [12] used an exact series solution of the dynamic elasticity equations and worked backward to obtain the value of K to match the frequencies with those of FSDT They showed that K depends upon , and on mode number, width/depth and depth/length ratios. Note that this value of K has been adopted in numerous studies utilizing FSDT Another method, originally proposed by Bert et al [14], results in the factor that depends only on geometry (thickness of the facings and the core) of a symmetrically laminated sandwich structure. As is shown in the examples, the value of this shear correction factor approaches zero, as the ratio of the shear stiffness of the facings to that of the core is increased
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