• Coupled systems mechanics
• /
• v.9 no.3
• /
• pp.265-280
• /
• 2020

In this paper, a new refined hyperbolic shear deformation beam theory for the free vibration analysis of functionally graded beam is presented. The theory accounts for hyperbolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the functionally graded beam without using shear correction factors. In addition, the effect of different micromechanical models on the free vibration response of these beams is studied. Various micromechanical models are used to evaluate the mechanical characteristics of the FG beams whose properties vary continuously across the thickness according to a simple power law. Based on the present theory, the equations of motion are derived from the Hamilton's principle. Navier type solution method was used to obtain frequencies, and the numerical results are compared with those available in the literature. A detailed parametric study is presented to show the effect of different micromechanical models on the free vibration response of a simply supported FG beams.

• Structural Engineering and Mechanics
• /
• v.74 no.2
• /
• pp.175-187
• /
• 2020

The theories having been developed thus far account for higher-order variation of transverse shear strain through the depth of the beam and satisfy the stress-free boundary conditions on the top and bottom surfaces of the beam. A shear correction factor, therefore, is not required. In this paper, the effect of surface on the axial buckling and free vibration of nanobeams is studied using various refined higher-order shear deformation beam theories. Furthermore, these theories have strong similarities with Euler-Bernoulli beam theory in aspects such as equations of motion, boundary conditions, and expressions of the resultant stress. The equations of motion and boundary conditions were derived from Hamilton's principle. The resultant system of ordinary differential equations was solved analytically. The effects of the nanobeam length-to-thickness ratio, thickness, and modes on the buckling and free vibration of the nanobeams were also investigated. Finally, it was found that the buckling and free vibration behavior of a nanobeam is size-dependent and that surface effects and surface energy produce significant effects by increasing the ratio of surface area to bulk at nano-scale. The results indicated that surface effects influence the buckling and free vibration performance of nanobeams and that increasing the length-to-thickness increases the buckling and free vibration in various higher-order shear deformation beam theories. This study can assist in measuring the mechanical properties of nanobeams accurately and designing nanobeam-based devices and systems.

• Steel and Composite Structures
• /
• v.20 no.5
• /
• pp.1043-1066
• /
• 2016

A new analytical solution based on a third order shear deformation theory for the problem of static analysis of cross-ply doubly-curved shells is presented. The boundary-discontinuous generalized double Fourier series method is used to solve highly coupled linear partial differential equations with the mixed type simply supported boundary conditions prescribed on the edges. The complementary boundary constraints are introduced through boundary discontinuities generated by the selected boundary conditions for the derivation of the complementary solution. The numerical accuracy of the solution is compared by studying the comparisons of deflections, stresses and moments of symmetric and anti-symmetric laminated shells with finite element results using commercially available software under uniformly distributed load. Results are in good agreement with finite element counterparts. Additional results of the symmetric and anti-symmetric laminated and sandwich shells under single point load at the center and pressure load, are presented to provide data for the unsolved boundary conditions, benchmark comparisons and verifications.

• Structural Engineering and Mechanics
• /
• v.31 no.5
• /
• pp.587-603
• /
• 2009

We performed a free vibration analysis of skew composite laminates with or without cutout based on the high-order shear deformation plate theory (HSDT). The effects of skew angles and ply orientations on the natural frequencies for various boundary conditions are studied using a nonlinear high-order finite element program developed for this study. The numerical results are in good agreement with those reported by other investigators for simple test cases, and the new results reported in this paper show the interactions between the skew angle, layup sequence and cutout size on the free vibration of the laminate. The findings highlight the importance of skew angles when analyzing laminated composite skew plates with cutout or without cutout.

• Earthquakes and Structures
• /
• v.13 no.5
• /
• pp.509-518
• /
• 2017

The objective of the present paper is to investigate the bending behavior with stretching effect of carbon nanotube-reinforced composite (CNTRC) beams. The beams resting on the Pasternak elastic foundation, including a shear layer and Winkler spring, are considered. The single-walled carbon nanotubes (SWCNTs) are aligned and distributed in polymeric matrix with different patterns of reinforcement. The material properties of the CNTRC beams are estimated by using the rule of mixture. The significant feature of this model is that, in addition to including the shear deformation effect and stretching effect it deals with only 4 unknowns without including a shear correction factor. The single-walled carbon nanotubes (SWCNTs) are aligned and distributed in polymeric matrix with different patterns of reinforcement. The material properties of the CNTRC beams are assessed by employing the rule of mixture. The equilibrium equations have been obtained using the principle of virtual displacements. The mathematical models provided in this paper are numerically validated by comparison with some available results. New results of bending analyses of CNTRC beams based on the present theory with stretching effect is presented and discussed in details. the effects of different parameters of the beam on the bending responses of CNTRC beam are discussed.

• Coupled systems mechanics
• /
• v.9 no.6
• /
• pp.575-597
• /
• 2020

Equilibrium equations of a porous FG plate resting on Winkler-Pasternak foundations with various boundary conditions are derived using a new refined shear deformation theory. Different types of porosity distribution rate are considered. Governing equations are obtained including the plate-foundation interaction. This new model meets the nullity of the transverse shear stress at the upper and lower surfaces of the plate. The novel rule of mixture is proposed to describe and approximate material properties of the FG plates with different distribution case of porosity. The validity of this theory is studied by comparing some of the present results with other higher-order theories reported in the literature. Effects of variation of porosity distribution rate, boundary conditions, foundation parameter, power law index, plate aspect ratio, side-to-thickness ratio on the deflections and stresses are all discussed.

• Advances in nano research
• /
• v.17 no.4
• /
• pp.335-350
• /
• 2024

This paper investigates the mechanical behavior of a new type of functionally graded graphene-reinforced nanocomposite (FG-GRNC) doubly-curved laminated shells, referred to as cosine FG-GRNC. The study employs a refined higher-order shear deformation shell theory combined with a modified continuum nonlocal strain gradient theory. The effective Young's modulus of the GRNC shell in the thickness direction is determined using the modified Halpin-Tsai model, while Poisson's ratio and mass density are calculated using the rule of mixtures. The analysis includes two graphene-reinforced distribution patterns-FG-A CNRCs and FG-B CNRCs-along with uniform UD CNRCs. An enhanced Galerkin method is used to solve the governing equilibrium equations for the GRNC nanoshell, yielding closed-form solutions for bending deflection and critical buckling loads. The nanoshell is supported by an orthotropic elastic foundation characterized by three parameters. A detailed parametric analysis is performed to evaluate how factors such as the length scale parameter, nonlocal parameter, distribution pattern, GPL weight fraction, shell thickness, and shell geometry influence deflections and critical buckling loads.

• Wind and Structures
• /
• v.27 no.6
• /
• pp.369-380
• /
• 2018

In this research work, nonlinear thermal buckling behavior of functionally graded (FG) plates is explored based a new higher-order shear deformation theory (HSDT). The present model has just four unknowns, by using a new supposition of the displacement field which enforces undetermined integral variables. A shear correction factor is, thus, not necessary. A power law distribution is employed to express the disparity of volume fraction of material distributions. Three kinds of thermal loading, namely, uniform, linear, and nonlinear and temperature rises over z-axis direction are examined. The non-linear governing equations are resolved for plates subjected to simply supported boundary conditions at the edges. The results are approved with those existing in the literature. Impacts of various parameters such as aspect and thickness ratios, gradient index, type of thermal load rising, on the non-dimensional thermal buckling load are all examined.

• Advances in concrete construction
• /
• v.14 no.3
• /
• pp.169-183
• /
• 2022

In this article, vibrational behavior and wave propagation characteristics in (FG) functionally graded plates resting on Kerr foundation with three parameters is studied using a 2D dimensional (HSDT) higher shear deformation theory. The new 2D higher shear deformation theory has only four variables in field's displacement, which means has few numbers of unknowns compared with others theories. The shape function used in this theory satisfies the nullity conditions of the shear stresses on the two surfaces of the FG plate without using shear correction factors. The FG plates are considered to rest on the Kerr layer, which is interconnected with a Pasternak-Kerr shear layer. The FG plate is materially inhomogeneous. The material properties are supposed to vary smoothly according to the thickness of the plate by a Voigt's power mixing law of the volume fraction. The equations of motion due to the dynamics of the plate resting on a three-parameter foundation are derived using the principle of minimization of energies; which are then solved analytically by the Navier technique to find the vibratory characteristics of a simply supported plate, and the wave propagation results are derived by using the dispersion relations. Perceivable numerical results are fulfilled to evaluate the vibratory and the wave propagation characteristics in functionally graded plates and some parameters such wave number, thickness ratio, power index and foundation parameters are discussed in detail.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.11 no.12
• /
• pp.5199-5206
• /
• 2010

In this paper, we investigate the buckling analysis of laminated composite plates, using a improved assumed natural strain shell element. In order to overcome membrane and shear locking phenomena, the assumed natural strain method is used. The eigenvalues of the laminated composite plates are calculated by varying the width-thickness ratio and angle of fiber. To improve an shell element for buckling analysis, the new combination of sampling points for assumed natural strain method was applied and the refined first-order shear deformation theory which allows the shear deformation without shear correction factor. In order to validate the present solutions, the reference solutions are used and discussed. The results of laminated composite plates under the in-plane shear loading may be the benchmark test for the buckling analysis.