• Computers and Concrete
• /
• v.25 no.3
• /
• pp.225-244
• /
• 2020

The influence of boundary conditions on the bending and free vibration behavior of functionally graded sandwich plates resting on a two-parameter elastic foundation is examined using an original novel high order shear theory. The Hamilton's principle is used herein to derive the equations of motion. The number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. This theory includes indeterminate integral variables and contains only four unknowns in which any shear correction factor not used, with even less than the conventional theory of first shear strain (FSDT). Unlike any other theory, the number of unknown functions involved in displacement field is only four, as against five, six or more in the case of other shear deformation theories. Galerkin's approach is utilized for FGM sandwich plates with six different boundary conditions. The accuracy of the proposed solution is checked by comparing it with other closed form solutions available in the literature.

• Steel and Composite Structures
• /
• v.27 no.1
• /
• pp.109-122
• /
• 2018

In This work an analysis of the propagation of waves of functionally graduated plates is presented by using a high order hyperbolic (HSDT) shear deformation theory. This theory has only four variables, which is less than the theory of first order shear deformation (FSDT). Therefore, a shear correction coefficient is not required. Unlike other conventional shear deformation theories, the present work includes a new field of displacement which introduces indeterminate integral variables. The properties of materials are supposed classified in the direction of the thickness according to two simple distributions of a power law in terms of volume fractions of constituents. The governing equations of the wave propagation in the functionally graded plate are derived by employing the Hamilton's principle. The analytical dispersion relation of the functionally graded plate is obtained by solving an eigenvalue problem. The convergence and the validation of the proposed theoretical numerical model are performed to demonstrate the efficacy of the model.

• Structural Engineering and Mechanics
• /
• v.75 no.2
• /
• pp.157-174
• /
• 2020

In the present paper, a simple analytical model is developed based on a new refined parabolic shear deformation theory (RPSDT) for free vibration and buckling analysis of orthotropic rectangular plates with simply supported boundary conditions. The displacement field is simpler than those of other higher-order theories since it is modeled with only two unknowns and accounts for a parabolic distribution of the transverse shear stress through the plate thickness. The governing differential equations related to the present theory are obtained from the principle of virtual work, while the solution of the eigenvalue problem is achieved by assuming a Navier technique in the form of a double trigonometric series that satisfy the edge boundary conditions of the plate. Numerical results are presented and compared with previously published results for orthotropic rectangular plates in order to verify the precision of the proposed analytical model and to assess the impacts of several parameters such as the modulus ratio, the side-to-thickness ratio and the geometric ratio on natural frequencies and critical buckling loads. From these results, it can be concluded that the present computations are in excellent agreement with the other higher-order theories.

• International Journal of Aeronautical and Space Sciences
• /
• v.14 no.4
• /
• pp.310-323
• /
• 2013

In this paper, the aeroelastic static response of flexible wings with arbitrary cross-section geometry via a coupled CUF-XFLR5 approach is presented. Refined structural one-dimensional (1D) models, with a variable order of expansion for the displacement field, are developed on the basis of the Carrera Unified Formulation (CUF), taking into account cross-sectional deformability. A three-dimensional (3D) Panel Method is employed for the aerodynamic analysis, providing more accuracy with respect to the Vortex Lattice Method (VLM). A straight wing with an airfoil cross-section is modeled as a clamped beam, by means of the finite element method (FEM). Numerical results present the variation of wing aerodynamic parameters, and the equilibrium aeroelastic response is evaluated in terms of displacements and in-plane cross-section deformation. Aeroelastic coupled analyses are based on an iterative procedure, as well as a linear coupling approach for different free stream velocities. A convergent trend of displacements and aerodynamic coefficients is achieved as the structural model accuracy increases. Comparisons with 3D finite element solutions prove that an accurate description of the in-plane cross-section deformation is provided by the proposed 1D CUF model, through a significant reduction in computational cost.

• Computers and Concrete
• /
• v.32 no.4
• /
• pp.411-423
• /
• 2023

The rapid development of road transport has increased the number of bridges that require widening. A critical issue in the construction of bridge widening is the influence of vibrations of the old bridge on the casting of wet joint concrete between the old and new bridges owing to the running traffic. Typically, the bridge is closed to traffic during the pouring of wet joint concrete, which negatively affects the existing transportation network. In this study, a newly developed microscopic traffic load modeling approach and the vehicle-bridge interaction theory are incorporated to develop a refined numerical framework for the analysis of random traffic-bridge coupled dynamics. This framework was used to investigate traffic-induced vibrations at the wet joint of a widened bridge. Based on an experimental study on the vibration resistance of wet joint concrete, traffic control strategies were proposed to ensure the construction performance of cast-in-site wet joint concrete under random traffic without interruption. The results show that the vibration displacement and frequency of the old bridge, estimated by the proposed framework, were comparable with those obtained from field measurements. Based on the target peak particle velocity and vibration amplitude of the wet joint concrete, it was found that traffic control measures, such as limiting vehicle gross weight and limiting traffic volume by closing an additional traffic lane, could ensure the construction performance of the wet joint concrete.

• Structural Engineering and Mechanics
• /
• v.67 no.5
• /
• pp.527-544
• /
• 2018

In this paper, the effect of homogenization models on stress analysis is presented for functionally graded plates (FGMs). The derivation of the effective elastic proprieties of the FGMs, which are a combination of both ceramic and metallic phase materials, is of most of importance. The majority of studies in the last decade, the Voigt homogenization model explored to derive the effective elastic proprieties of FGMs at macroscopic-scale in order to study their mechanical responses. In this work, various homogenization models were used to derive the effective elastic proprieties of FGMs. The effect of these models on the stress analysis have also been presented and discussed through a comparative study. So as to show this effect, a refined plate theory is formulated and evaluated, the number of unknowns and governing equations were reduced by dividing the transverse displacement into both bending and shear parts. Based on sinusoidal variation of displacement field trough the thickness, the shear stresses on top and bottom surfaces of plate were vanished and the shear correction factor was avoided. Governing equations of equilibrium were derived from the principle of virtual displacements. Analytical solutions of the stress analysis were obtained for simply supported FGM plates. The obtained results of the displacements and stresses were compared with those predicted by other plate theories available in the literature. This study demonstrates the sensitivity of the obtained results to different homogenization models and that the results generated may vary considerably from one theory to another. Finally, this study offers benchmark results for the multi-scale analysis of functionally graded plates.

• Geomechanics and Engineering
• /
• v.16 no.3
• /
• pp.257-271
• /
• 2018

In this paper, the effect of the homogenization models on buckling and free vibration is presented for simply supported functionally graded plates (FGM) resting on elastic foundation. The majority of investigations developed in the last decade, explored the Voigt homogenization model to predict the effective proprieties of functionally graded materials at the macroscopic-scale for FGM mechanical behavior. For this reason, various models have been used to derive the effective proprieties of FGMs and simulate thereby their effects on the buckling and free vibration of FGM plates based on comparative studies that may differ in terms of several parameters. The refined plate theory, as used in this paper, is based on dividing the transverse displacement into both bending and shear components. This leads to a reduction in the number of unknowns and governing equations. Furthermore the present formulation utilizes a sinusoidal variation of displacement field 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. Equations of motion are derived from Hamilton's principle. Analytical solutions for the buckling and free vibration analysis are obtained for simply supported plates. The obtained results are compared with those predicted by other plate theories. This study shows the sensitivity of the obtained results to different homogenization models and that the results generated may vary considerably from one theory to another. Comprehensive visualization of results is provided. The analysis is relevant to aerospace, nuclear, civil and other structures.

• Composites Research
• /
• v.36 no.2
• /
• pp.117-125
• /
• 2023

This paper proposes a new finite element formulation based on enhanced first-order shear deformation theory including the transverse normal strain effect via the mixed formulation (EFSDTM-TN) for the effective thermo-mechanical analysis of laminated composite structures. The main objective of the EFSDTM-TN is to provide an accurate and efficient solution in describing the thermo-mechanical behavior of laminated composite structures by systematically establishing the relationship between two independent fields (displacement and transverse stress fields) via the mixed formulation. Another key feature is to consider the thermal strain effect without additional unknown variables by introducing a refined transverse displacement field. In the finite element formulation, an eight-node isoparametric plate element is newly developed to implement the advantage of the EFSDTM-TN. Numerical solutions for the thermo-mechanical behavior of laminated composite structures are compared with those available in the open literature to demonstrate the numerical performance of the proposed finite element model.

• Steel and Composite Structures
• /
• v.44 no.5
• /
• pp.721-740
• /
• 2022

In this paper, an accurate kinematic model has been developed to study the mechanical response of functionally graded (FG) sandwich beams, mainly covering the bending, buckling and free vibration problems. The studied structure with homogeneous hardcore and softcore is considered to be simply supported in the edges. The present model uses a new refined shear deformation beam theory (RSDBT) in which the displacement field is improved over the other existing high-order shear deformation beam theories (HSDBTs). The present model provides good accuracy and considers a nonlinear transverse shear deformation shape function, since it is constructed with only two unknown variables as the Euler-Bernoulli beam theory but complies with the shear stress-free boundary conditions on the upper and lower surfaces of the beam without employing shear correction factors. The sandwich beams are composed of two FG skins and a homogeneous core wherein the material properties of the skins are assumed to vary gradually and continuously in the thickness direction according to the power-law distribution of volume fraction of the constituents. The governing equations are drawn by implementing Hamilton's principle and solved by means of the Navier's technique. Numerical computations in the non-dimensional terms of transverse displacement, stresses, critical buckling load and natural frequencies obtained by using the proposed model are compared with those predicted by other beam theories to confirm the performance of the proposed theory and to verify the accuracy of the kinematic model.

• Wind and Structures
• /
• v.27 no.4
• /
• pp.269-282
• /
• 2018

In this paper, a new displacement field based on quasi-3D hybrid-type higher order shear deformation theory is developed to analyze the static and dynamic response of exponential (E), power-law (P) and sigmoïd (S) functionally graded beams. Novelty of this theory is that involve just three unknowns with including stretching effect, as opposed to four or even greater numbers in other shear and normal deformation theories. It also accounts for a parabolic distribution of the transverse shear stresses across the thickness, and satisfies the zero traction boundary conditions at beams surfaces without introducing a shear correction factor. The beam governing equations and boundary conditions are determined by employing the Hamilton's principle. Navier-type analytical solutions of bending and free vibration analysis are provided for simply supported beams subjected to uniform distribution loads. The effect of the sigmoid, exponent and power-law volume fraction, the thickness stretching and the material length scale parameter on the deflection, stresses and natural frequencies are discussed in tabular and graphical forms. The obtained results are compared with previously published results to verify the performance of this theory. It was clearly shown that this theory is not only accurate and efficient but almost comparable to other higher order shear deformation theories that contain more number of unknowns.