• Steel and Composite Structures
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• v.19 no.2
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• pp.369-384
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• 2015

This work presents a free vibration analysis of functionally graded metal-ceramic (FG) beams with considering porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. For this purpose, a simple displacement field based on higher order shear deformation theory is implemented. The proposed 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, likewise, the shear components do not contribute toward bending moments. The most interesting feature of this theory is that it accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the beam without using shear correction factors. In addition, it has strong similarities with Euler-Bernoulli beam theory in some aspects such as equations of motion, boundary conditions, and stress resultant expressions. The rule of mixture is modified to describe and approximate material properties of the FG beams with porosity phases. By employing the Hamilton's principle, governing equations of motion for coupled axial-shear-flexural response are determined. The validity of the present theory is investigated by comparing some of the present results with those of the first-order and the other higher-order theories reported in the literature. Illustrative examples are given also to show the effects of varying gradients, porosity volume fraction, aspect ratios, and thickness to length ratios on the free vibration of the FG beams.

• Structural Engineering and Mechanics
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• v.90 no.3
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• pp.219-232
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• 2024

In current study, for the first time, Nonlinear Bending of a skew microplate made of a laminated composite strengthened with graphene nanosheets is investigated. A mixture of mechanical and thermal stresses is applied to the plate, and the reaction is analyzed using the First Shear Deformation Theory (FSDT). Since different percentages of graphene sheets are included in the multilayer structure of the composite, the characteristics of the composite are functionally graded throughout its thickness. Halpin-Tsai models are used to characterize mechanical qualities, whereas Schapery models are used to characterize thermal properties. The microplate's non-linear strain is first calculated by calculating the plate shear deformation and using the Green-Lagrange tensor and von Karman assumptions. Then the elements of the Couple and Cauchy stress tensors using the Modified Coupled Stress Theory (MCST) are derived. Next, using the Hamilton Principle, the microplate's governing equations and associated boundary conditions are calculated. The nonlinear differential equations are linearized by utilizing auxiliary variables in the nonlinear solution by applying the Frechet approach. The linearized equations are rectified via an iterative loop to precisely solve the problem. For this, the Differential Quadrature Method (DQM) is utilized, and the outcomes are shown for the basic support boundary condition. To ascertain the maximum values of microplate deflection for a range of circumstances-such as skew angles, volume fractions, configurations, temperatures, and length scales-a parametric analysis is carried out. To shed light on how the microplate behaves in these various circumstances, the resulting results are analyzed.

• Journal of the Korean Society of Safety
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• v.19 no.1
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• pp.117-123
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• 2004

The prediction to the hydroscopic moisture warping behaviors is analyzed for cellulose-based laminates using a numerical method base on a modified classical laminate(MCL) theory for hygroscopic moisture deformations with cycling testing data. The experimental measurement of the interferometric hygroscopic warping effects, moisture generator, and curvature of cellulose reinforced epoxy laminates is studied under cyclic environmental conditions using a Moire interferometer coupled. Accurate determination of curvatures provides a description of dimensional stability evolution; the tools for validation of computational internal stress and for the warpage prediction in model safety.

• Steel and Composite Structures
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• v.44 no.3
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• pp.371-388
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• 2022

The present study tackles the problem of forced vibration of imperfect axially functionally graded shell structure with truncated conical geometry. The linear and nonlinear large-deflection of the structure are considered in the mathematical formulation using von-Kármán models. Modified coupled stress method and principle of minimum virtual work are employed in the modeling to obtain the final governing equations. In addition, formulations of classical elasticity theory are also presented. Different functions, including the linear, convex, and exponential cross-section shapes, are considered in the grading material modeling along the thickness direction. The grading properties of the material are a direct result of the porosity change in the thickness direction. Vibration responses of the structure are calculated using the semi-analytical method of a couple of homotopy perturbation methods (HPM) and the generalized differential quadrature method (GDQM). Contradicting effects of small-scale, porosity, and volume fraction parameters on the nonlinear amplitude, frequency ratio, dynamic deflection, resonance frequency, and natural frequency are observed for shell structure under various boundary conditions.