The static bending and buckling behaviors of bi-directional functionally graded (BFG) plates with porosity are investigated in this paper. An improved first-order shear deformation theory with an ...assuming parabolic distribution shear stresses is developed to describe the displacement, strain, and stress fields of the plates. The significant novelty of the proposed theory is that the transverse shear stresses equal to zero at two free surfaces of the BFG plates. Therefore, no shear correction factor is required as in other first-order shear deformation theory. A four-node quadrilateral plate element (IMQ4) is developed based on the improved first-order shear deformation theory, mixed finite element method (FEM) and Hamilton's principle for analysis of BFG plates. Several comparison studies are provided to demonstrate the precision and robustness of the proposed plate element IMQ4. Then the proposed plate element, IMQ4, is employed to analyze the bending and buckling responses of the BFG plates. Some new numerical results on the flexural and buckling behaviors of BFG plates are achieved via a deep parametric study.
•A new mixed four-node quadrilateral plate element based on first-order shear deformation theory is established.•The proposed element is accuracy, robustness and good convergence.•The proposed element does not need any shear correction factors.•The bending and buckling behaviors of the bi-directional functionally graded with porosity are investigated.
Piezoelectric quasicrystals have a broad spectrum of promising applications and research value due to their unique atomic arrangement and multi-field coupling effects. This paper presents a ...mechanical analysis of the static bending and free vibration problems of two-dimensional multilayered decagonal piezoelectric quasicrystal laminated beams. Mechanical models of the beams are established, and the differential quadrature method in conjunction with the state-space method is utilized to obtain the solutions for the beams with mixed boundary conditions. We first investigated the static response and free vibration problem of quasicrystal laminated beams. By degrading them into crystalline materials, we verified the accuracy of the method by comparing the results with the existing ones. Then, the effects of different boundary conditions and slenderness ratios on the stresses, displacements, electric potentials, and electric displacements of quasicrystal laminated beams under normal mechanical loading and free vibration are investigated. Subsequently, the effects of different laying modes on the mechanical properties of the quasicrystal laminated beams when the material principal axis of the beam is changed are also analyzed.
•Analysis of the static bending and free vibration problems of multilayered 2D decagonal PQC beams is established.•Mixed boundary conditions are considered by using differential quadrature method and state-space method.•Orthogonal and diagonal laying modes are investigated by rotating the material stiffness matrixes.•Effects of different boundary conditions and slenderness ratios on the static bending and free vibration are analyzed.
This paper presents the elastic buckling and static bending analysis of shear deformable functionally graded (FG) porous beams based on the Timoshenko beam theory. The elasticity moduli and mass ...density of porous composites are assumed to be graded in the thickness direction according to two different distribution patterns. The open-cell metal foam provides a typical mechanical feature for this study to determine the relationship between coefficients of density and porosity. The partial differential equation system governing the buckling and bending behavior of porous beams is derived based on the Hamilton’s principle. The Ritz method is employed to obtain the critical buckling loads and transverse bending deflections, where the trial functions take the form of simple algebraic polynomials. Four different boundary conditions are considered in the paper. A parametric study is carried out to investigate the effects of porosity coefficient and slenderness ratio on the buckling and bending characteristics of porous beams. The influence of varying porosity distributions on the structural performance is highlighted to shed important insights into the porosity design to achieve improved buckling resistance and bending behavior.
A size-dependent inhomogeneous beam model, which accounts for the through-length power-law variation of a two-constituent axially functionally graded (FG) material, is deduced in the framework of the ...nonlocal strain gradient theory and the Euler–Bernoulli beam theory. By employing the Hamilton principle, the equations of motion and boundary conditions for size-dependent axially FG beams are deduced. A material length scale parameter and a nonlocal parameter are introduced in the axially FG beam model to consider the significance of strain gradient stress field and nonlocal elastic stress field, respectively. The bending, buckling and vibration problems of axially FG beams are solved by a generalized differential quadrature method. The influences of power-law variation and size-dependent parameters on the bending, buckling and vibration behaviors of axially FG beams are investigated. The mechanical behaviors can be affected by the through-length grading of the FG material and therefore may be controlled by choosing appropriate values of the power-law index. When considering concentrated and uniformly distributed loads, the maximum deflection decreases with increasing length scale parameter. The axially FG beam may exert a stiffness-softening effect or a stiffness-hardening effect on the critical buckling force and the natural frequencies depending on the values of the two size-dependent parameters.
This manuscript aims to examine and investigate the bending deflection and stress distribution of sandwich functionally graded nanoplates rested on variable Winkler elastic foundation based on new ...quasi 3D hyperbolic shear theory in conjoint with nonlocal strain gradient theory. The sandwich sigmoidal function graded material (SFGM) is proposed with three different configurations through thickness direction. New 3D hyperbolic shear theory is exploited to satisfy parabolic variation of shear through thickness direction and zero shear at the bottom and top surfaces. Modified continuum nonlocal strain gradient theory is used to include the material and geometrical nanosize length scales. Variable Winkler foundation model is proposed to the first time to include the variable elastic environmental under the nanoplate. The comprehensive model and governing equilibrium equations of SFG nanoplates is derived in detail with principle of virtual work and solved analytically by Galerkin method. The developed model is verified with previous work and parametric studies are presented to illustrate influences of the elastic foundation models, sigmoidal distribution index constant, configuration of sandwich plate, material and length nanoscales, boundary conditions on the static deflection and stress distributions of FG sigmodal nanoplate. The proposed model can be applied in design and analysis of NEMS structure under static load, such as nanocapacitor and nanoswitch.
For the first time, a numerical isogeometric numerical solution based on the nonlocal strain gradient elasticity theory for static bending, free vibration, and buckling of sigmoid functionally graded ...(S-FG) nanoplate is presented. Two configurations of S-FG sandwich material, including isotropic core and FG core, are considered. A parameter is proposed to define the location of the neutral axis through the cross-section. The simple Reissner-Mindlin plate theory, the nonlocal strain gradient theory, and Hamilton's principle are employed to establish the general equilibrium of S-FG nanoplate that contains two small size coefficients, including nonlocal and strain gradient parameters. The static bending, free vibration, and buckling responses of S-FG nanoplate are explored using isogeometric analysis with a NURBS basic function. The accuracy of the presented model is verified through the comparison with other solutions for nanoplate. As a result of numerical investigation studies, the static bending, free vibration, and buckling responses of S-FG are significantly affected by the material variation along the thickness direction, the neutral axis location, nonlocal parameter, strain gradient parameter, and material index.
The nonlinear static bending analysis of microplates resting on imperfect Pasternak elastic foundations is carried out in this paper. The finite element method based on the modified couple stress ...theory is used to derive the nonlinear finite element formulations. The present theory and mathematical model are validated by comparisons of this work’s results with those of other reputable publications, which show a very good agreement. The influences of length-scale parameter, nonlinearity, elastic foundation parameters, imperfect foundations, and boundary conditions on the nonlinear static bending response of microplates are then explored. The computed data of this study is very intriguing, particularly the interaction of the microplate with the imperfect elastic foundation, and this helps us better understand the mechanical behavior of this structure.
In this study, static bending response of single-walled carbon nanotubes (SWCNTs) embedded in an elastic medium is investigated on the basis of higher-order shear deformation microbeam models in ...conjunction with modified strain gradient theory. The governing differential equations and related boundary conditions are obtained by implementing a variational principle. The interactions between SWCNTs and surrounding elastic medium are simulated by Winkler elastic foundation model. The Navier-type solution is utilized to obtain an analytical solution for the bending problem of the simply supported embedded SWCNTs under uniform and sinusoidal loads. The influences of material length scale parameter-to-diameter ratio, slenderness ratio, loading type, shear correction factor and Winkler modulus on deflections of the embedded SWCNTs are discussed in detail. The present results illustrate that the bending behavior of SWCNTs is dependent on the small-size, stiffness of the elastic foundation and also effects of shear deformation, especially for smaller slenderness ratios.
•We model nonlinear electromechanical buckling of nanobridge.•We examine effect of van der Waals force on electromechanical buckling.•We study size effect by modified strain gradient theory.•We model clamped-guided functionally graded narrow nano-beam.•New model fills the gap between experimental results and classical theories.
•Post-blast residual static capacity determined on RC slabs.•Evaluation of retrofit systems on strength, stiffness and damage capacity.•All applied retrofit systems provided some level of blast ...mitigation.•Retrofitted RC slabs show an increase in residual ultimate load capacity.•Two layers of epoxy resin-impregnated glass mat had the highest contribution.
Laboratory static bending tests were carried out to determine post-blast residual load-bearing capacities of retrofitted and un-retrofitted RC slabs. Three different retrofit systems were previously devised to strengthen RC slabs on potential blast-induced damage. The retrofit systems consisted of impregnating epoxy resin with (1) one layer of glass woven fabric and (2) one and (3) two layers of chopped strand glass mat. The contribution to strength, stiffness, energy absorption and damage reduction of devised retrofit systems was evaluated during testing by measured deformations, displacements, and force capacities. The presented results indicate that all applied retrofit systems provided some blast mitigation level by enhancing RC slabs' residual strength and stiffness capacity. However, the retrofit system consisted of two layers of chopped-strand glass mat made the highest contribution to strength preservation.
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