• Structural Engineering and Mechanics
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• v.61 no.1
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• pp.49-63
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• 2017

This paper presents an original hyperbolic (first present model) and parabolic (second present model) shear and normal deformation theory for the bending analysis to account for the effect of thickness stretching in functionally graded sandwich plates. Indeed, the number of unknown functions involved in these presents theories is only five, as opposed to six or even greater numbers in the case of other shear and normal deformation theories. The present theory accounts for both shear deformation and thickness stretching effects by a hyperbolic variation of ail displacements across the thickness and satisfies the stress-free boundary conditions on the upper and lower surfaces of the plate without requiring any shear correction factor. It is evident from the present analyses; the thickness stretching effect is more pronounced for thick plates and it needs to be taken into consideration in more physically realistic simulations. The numerical results are compared with 3D exact solution, quasi-3-dimensional solutions and with other higher-order shear deformation theories, and the superiority of the present theory can be noticed.

• Structural Engineering and Mechanics
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• v.15 no.2
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• pp.199-223
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• 2003

The formulation of a non-linear shear deformable shell element is presented for the solution of stability problems of stiffened plates and shells. The formulation of the geometrical stiffness presented here is exactly defined on the midsurface and is efficient for analyzing stability problems of thick plates and shells by incorporating bending moment and transverse shear resultant force. As a result of the explicit integration of the tangent stiffness matrix, this formulation is computationally very efficient in incremental nonlinear analysis. The element is free of both membrane and shear locking behaviour by using the assumed strain method such that the element performs very well in the thin shells. By using six degrees of freedom per node, the present element can model stiffened plate and shell structures. The formulation includes large displacement effects and elasto-plastic material behaviour. The material is assumed to be isotropic and elasto-plastic obeying Von Mises's yield condition and its associated flow rules. The results showed good agreement with references and computational efficiency.

• Steel and Composite Structures
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• v.26 no.2
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• pp.125-137
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• 2018

In this work, the bending and free vibration analysis of multilayered plates and shells is presented by utilizing a new higher order shear deformation theory (HSDT). The proposed involves only four unknowns, which is even less than the first shear deformation theory (FSDT) and without requiring the shear correction coefficient. Unlike the conventional HSDTs, the present one presents a novel displacement field which incorporates undetermined integral variables. The equations of motion are derived by using the Hamilton's principle. These equations are then solved via Navier-type, closed form solutions. Bending and vibration results are found for cylindrical and spherical shells and plates for simply supported boundary conditions. Bending and vibration problems are treated as individual cases. Panels are subjected to sinusoidal, distributed and point loads. Results are presented for thick to thin as well as shallow and deep shells. The computed results are compared with the exact 3D elasticity theory and with several other conventional HSDTs. The proposed HSDT is found to be precise compared to other several existing ones for investigating the static and dynamic response of isotropic and multilayered composite shell and plate structures.

• Coupled systems mechanics
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• v.8 no.5
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• pp.439-457
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• 2019

In this paper, a new application of a four variable refined plate theory to analyze the nonlinear bending of functionally graded plates exposed to thermo-mechanical loadings, is presented. This recent theory is based on the assumption that the transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces, and similarly, the shear components do not contribute toward bending moments. The derived transverse shear strains has a quadratic variation across the thickness that satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The material properties are assumed to vary continuously through the thickness of the plate according to a power-law distribution of the volume fraction of the constituents. The solutions are achieved by minimizing the total potential energy. The non-linear strain-displacement relations in the von Karman sense are used to derive the effect of geometric non-linearity. It is concluded that the proposed theory is accurate and simple in solving the nonlinear bending behavior of functionally graded plates.

• Journal of Korean Society of Steel Construction
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• v.10 no.1 s.34
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• pp.11-24
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• 1998

The composite sandwich plate is constructed by combining two laminated facings with high strength and a thick core of light weight material. The governing equations for the analysis of bending of simply supported sandwich plates with laminated facings are derived and analysed using the analytical method including the local shear deformations. The accuracy of the approach is ascertained by comparing solutions from the sandwich plate theory with composite facings to the laminate plate theory. Since the present analysis considers the bending stiffness of the core and also the transverse shear deformations of the laminated facings, it is expected that the analysis is capable to analyze the general anisotropic laminated plates with global shear deformations.

• Journal of KSNVE
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• v.2 no.4
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• pp.305-315
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• 1992

In order to investigate the effects of layer-wise in-plane displacements on vibration and damping characteristics of composite laminated plates, the finite element method based on the generalized laminated plate theory(GLPT) has been formulated. Specific damping capacity of each mode was obtained by modal strain energy method. To see the effect of transverse shear on deformation, the strain energy of stress components was computed. The accuracy of this study was examined for the cylindrical bending vibration of cross-ply plate strip. The results were very accurate compared with 3-D solutions. The numerical results show that through-thickness variation of in-plane displacements has not so much influence on the natural frequency, but has a great influence on the damping of composite plates, especially on the damping of thick composite plates since the damping is affected by local behavior while the natural frequency is affected by global behavior.

• Journal of the Korean Wood Science and Technology
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• v.48 no.5
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• pp.676-684
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• 2020

This study was carried out in order to evaluate the bending creep deflection of glulams and bolted glulams beam-to-beam connection with steel-gusset plates and bolts under changing relative humidity. The two types of glulam beams (130 mm in width, 175 mm in thickness, and 3000 mm in length) used in this study were made from domestic larch and composed of seven layers. The gussets were made of 8-mm-thick steel plates. Creep testing was conducted under constant loads in an uncontrolled environment. The test was carried out in a room that was well ventilated through a window. The creep test specimens were loaded for 33,000 hours. A bending creep test for the glulams was conducted through four-point loading. The applied stresses were 20% and 30% of the MOR in the static bending test for the glulam and bolted glulam, respectively. After 33,000 hours, the creep deflection of the glulam at a 20% stress level increased by 39% to 99%, while the creep deflection of the glulam at a 30% stress level increased by 27% to 67%, as compared with instantaneous elastic deflection. The relative creep increased during autumn and winter, and recovered during spring and summer. The relative creep of the bolted glulams was changed abruptly by loading up to 5,000 hours, but stabilized after 5,000 hours, and then gradually increased until 33,000 hours. The relative creep of the bolted glulam increased 2.11 times on average after 33,000 hours.

• Coupled systems mechanics
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• v.5 no.3
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• pp.269-283
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• 2016

A two new high-order shear deformation theory for bending analysis is presented for a simply supported, functionally graded plate with porosities resting on an elastic foundation. This porosities may possibly occur inside the functionally graded materials (FGMs) during their fabrication, while material properties varying to a simple power-law distribution along the thickness direction. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theories presented are variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. It is established that the volume fraction of porosity significantly affect the mechanical behavior of thick function ally graded plates. The validity of the two new theories is shown by comparing the present results with other higher-order theories. The influence of material parameter, the volume fraction of porosity and the thickness ratio on the behavior mechanical P-FGM plate are represented by numerical examples.

• Structural Engineering and Mechanics
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• v.55 no.2
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• pp.435-459
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• 2015

Parametric resonance of shear deformable composite skew plates subjected to non-uniform (parabolic) and linearly varying periodic edge loading is studied for different boundary conditions. The skew plate structural model is based on higher order shear deformation theory (HSDT), which accurately predicts the numerical results for thick skew plate. The total energy functional is derived for the skew plates from total potential energy and kinetic energy of the plate. The strain energy which is the part of total potential energy contains membrane energy, bending energy, additional bending energy due to additional change in curvature and shear energy due to shear deformation, respectively. The total energy functional is solved using Rayleigh-Ritz method in conjunction with boundary characteristics orthonormal polynomials (BCOPs) functions. The orthonormal polynomials are generated for unit square domain using Gram-Schmidt orthogonalization process. Bolotin method is followed to obtain the boundaries of parametric resonance region with higher order approximation. These boundaries are traced by the periodic solution of Mathieu-Hill equations with period T and 2T. Effect of various parameters like skew angle, span-to-thickness ratio, aspect ratio, boundary conditions, static load factor on parametric resonance of skew plate have been investigated. The investigation also includes influence of different types of linearly varying loading and parabolically varying bi-axial loading.

• Journal of Ocean Engineering and Technology
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• v.16 no.2
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• pp.38-43
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• 2002

Die-less forming is a cold forming process which is to bend thick flat plates into compound curved plates using two asymmetric rollers. This forming method has several advantages compared with line heating which is widely used to fabricate compound curved pieces in shipyards. The die-less forming, however, has scarcely been studied. Even the deformation mechanism in this forming process has not been understood clearly. So, in this paper, the deformation characteristics of die-less forming is investigated analytically and numerically. for the analytic investigation, slab method based on equilibrium equation is applied. And the mechanism of curvature generation is derived for the asymmetry in roller applied. And three dimensional numerical analyses are performed with realistic modeling of interactions between the rollers and work-piece using finite element program, ABAQUS. It is shown that curvature generation is mainly due to the difference of normal positive strain distribution between the top and bottom surface of the work-piece. And a convex-type curved plate is formed if the center region of the work-piece is rolled with asymmetric rollers of which the lower is larger than the upper in diameter.