• Steel and Composite Structures
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• v.39 no.1
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• pp.51-64
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• 2021

This paper presents a high-order shear and normal deformation theory for the bending of FGM plates. The number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. Unlike any other theory, the number of unknown functions involved in displacement field is only four, as against five or more in the case of other shear and normal deformation theories. Based on the novel shear and normal deformation theory, the position of neutral surface is determined and the governing equilibrium equations based on neutral surface are derived. There is no stretching-bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. Navier-type analytical solution is obtained for functionally graded plate subjected to transverse load for simply supported boundary conditions. The accuracy of the present theory is verified by comparing the obtained results with other quasi-3D higher-order theories reported in the literature. Other numerical examples are also presented to show the influences of the volume fraction distribution, geometrical parameters and power law index on the bending responses of the FGM plates are studied.

• Advances in materials Research
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• v.8 no.3
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• pp.155-177
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• 2019

In this paper, a new displacement based high-order shear deformation theory is introduced for the static response of functionally graded sandwich plate with new definition of porosity distribution taking into account composition and the scheme of the sandwich plate. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, has strong similarity with classical plate theory in many aspects, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. Material properties of FGM layers are assumed to vary continuously across the plate thickness according to either power-law or sigmoid function in terms of the volume fractions of the constituents. The face layers are considered to be FG across each face thickness while the core is made of a ceramic homogeneous layer. Governing equations are derived from the principle of virtual displacements. The closed-form solution of a simply supported rectangular plate subjected to sinusoidal loading has been obtained by using the Navier method. Numerical results are presented to show the effect of the material distribution, the sandwich plate geometry and the porosity on the deflections and stresses of FG sandwich plates. The validity of the present theory is investigated by comparing some of the present results with other published results.

• Steel and Composite Structures
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• v.29 no.1
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• pp.53-66
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• 2018

A high-order nonlocal strain gradient model is developed for wave propagation analysis of porous FG nanoplates resting on a gradient hybrid foundation in thermal environment, for the first time. Material properties are assumed to be temperature-dependent and graded in the nanoplate thickness direction. To consider the thermal effects, uniform, linear, nonlinear, exponential, and sinusoidal temperature distributions are considered for temperature-dependent FG material properties. On the basis of the refined-higher order shear deformation plate theory (R-HSDT) in conjunction with the bi-Helmholtz nonlocal strain gradient theory (B-H NSGT), Hamilton's principle is used to derive the equations of wave motion. Then the dispersion relation between frequency and wave number is solved analytically. The influences of various parameters (such as temperature rise, volume fraction index, porosity volume fraction, lower and higher order nonlocal parameters, material characteristic parameter, foundations components, and wave number) on the wave propagation behaviors of porous FG nanoplates are investigated in detail.

• Structural Engineering and Mechanics
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• v.69 no.5
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• pp.511-525
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• 2019

This paper presents an analytical study of wave propagation in simply supported graduated functional plates resting on a two-parameter elastic foundation (Pasternak model) using a new theory of high order shear strain. Unlike other higher order theories, the number of unknowns and governing equations of the present theory is only four unknown displacement functions, which is even lower than the theory of first order shear deformation (FSDT). Unlike other elements, the present work includes a new field of motion, which introduces indeterminate integral variables. The properties of the materials are assumed to be ordered in the thickness direction according to the two power law distributions in terms of volume fractions of the constituents. The wave propagation equations in FG plates are derived using the principle of virtual displacements. The analytical dispersion relation of the FG plate is obtained by solving an eigenvalue problem. Numerical examples selected from the literature are illustrated. A good agreement is obtained between the numerical results of the current theory and those of reference. A parametric study is presented to examine the effect of material gradation, thickness ratio and elastic foundation on the free vibration and phase velocity of the FG plate.

• Steel and Composite Structures
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• v.38 no.3
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• pp.281-291
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• 2021

An equivalent single-layer theory (EST) is put forward for analyzing free vibrations of steel-concrete composite beams (SCCB) based on a higher-order beam theory. In the EST, the effect of partial interaction between sub-beams and the transverse shear deformation are taken into account. After using the interlaminar shear force continuity condition and the shear stress free conditions at the top and bottom surface, the displacement function of the EST does not contain the first derivatives of transverse displacement. Therefore, the C0 interpolation functions are just demanded during its finite element implementation. Finally, the EST is validated by comparing the results of two simply-supported steel-concrete composite beams which are tested in laboratory and calculated by ANSYS software. Then, the influencing factors for free vibrations of SCCB are analyzed, such as, different boundary conditions, depth to span ratio, high-order shear terms, and interfacial shear connector stiffness.

• Wind and Structures
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• v.28 no.1
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• pp.19-30
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• 2019

This article present the free vibration analysis of simply supported perfect and imperfect (porous) FG beams using a high order trigonometric deformation theory. It is assumed that the material properties of the porous beam vary across the thickness. Unlike other theories, the number of unknown is only three. This theory has a parabolic shear deformation distribution across the thickness. So it is useless to use the shear correction factors. The Hamilton's principle will be used herein to determine the equations of motion. Since, the beams are simply supported the Navier's procedure will be retained. To show the precision of this model, several comparisons have been made between the present results and those of existing theories in the literature.

• Structural Engineering and Mechanics
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• v.69 no.4
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• pp.427-437
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• 2019

In this study, an alternative solution procedure presented by using variational methods for analysis of shear deformable functionally graded material (FGM) beams with mixed formulation. By using the advantages of $G{\hat{a}}teaux$ differential approaches, a refined complex general functional and boundary conditions which comprises seven independent variables such as displacement, rotation, bending moment and higher-order bending moment, shear force and higher-order shear force, is derived for general thick-thin FGM beams via shear deformation beam theories. The mixed-finite element method (FEM) is employed to obtain a beam element which have a 2-nodes and total fourteen degrees-of-freedoms. A computer program is written to execute the analyses for the present study. The numerical results of analyses obtained for different boundary conditions are presented and compared with results available in the literature.

• Journal of Korean Society of Steel Construction
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• v.10 no.2 s.35
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• pp.201-209
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• 1998

The presence of elevated temperature can alter significantly the structural response of fibre-reinforced laminated composites. A thermal environment causes degradation in both strength and constitutive properties, particularly in the case of fibre-reinforced polymeric composites. Furthermore, associated thermal expansion, either alone or in combination with mechanically induced deformation, can result in buckling, large deflections, and excessively high stress levels. Consequently, it is often imperative to consider environmental effects in the analysis and design of laminated systems. Exact analytical solutions of higher-order shear deformation theory is developed to study the thermal buckling of cross-ply and antisymmetric angle-ply rectangular plates. The buckling behavior of moderately thick cross-ply and antisymmetric angle-ply laminates that are simply supported and subject to a uniform temperature rise is analyzed. Numerical results are presented for fiber-reinforced laminates and show the effects of ply orientation, number of layers, plate thickness, and aspects ratio on the critical buckling temperature and compared with those obtained using the classical and first-order shear deformation theory.

• Advances in concrete construction
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• v.17 no.2
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• pp.75-92
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• 2024

High Strength steel reinforced Reactive Powder Concrete (RPC) Beam is a new type of beams which has evident advantages than the conventional concrete beams. However, there is limited research on the shear bearing capacity of high-strength steel reinforced RPC structures, and there is a lack of theoretical support for structural design. In order to promote the application of high-strength steel reinforced RPC structures in engineering, it is necessary to select a shear model and derive applicable calculation methods. By considering the shear span ratio, steel fiber volume ratio, longitudinal reinforcement ratio, stirrup ratio, section shape, horizontal web reinforcement ratio, stirrup configuration angle and other variables in the shear test of 32 high-strength steel reinforced RPC beams, the applicability of three theoretical methods to the shear bearing capacity of high-strength steel reinforced RPC beams was explored. The plasticity theory adopts the RPC200 biaxial failure criterion, establishes an equilibrium equation based on the principle of virtual work, and derives the calculation formula for the shear bearing capacity of high-strength steel reinforced RPC beams; Based on the Strut and Tie Theory, considering the softening phenomenon of RPC, a failure criterion is established, and the balance equation and deformation coordination condition of the combined force are combined to derive the calculation formula for the shear bearing capacity of high-strength reinforced RPC beams; Based on the Rankine theory and Rankine failure criterion, taking into account the influence of size effects, a calculation formula for the shear bearing capacity of high-strength reinforced RPC beams is derived. Experimental data is used for verification, and the results are in good agreement with a small coefficient of variation.

• Advances in nano research
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• v.10 no.4
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• pp.313-325
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• 2021

This paper is concerned with the buckling behavior of 2D and quasi-3D problem of functionally graded nanobeam founded on high order shear deformation beams theory and made by two different types of porous distribution materials in Nano- and micro-scales. The used Quasi-3D formulation takes into account the transverse shear effect and uses only three variables. Both formulations do not include the correction factor that is required in the first shear deformation theory proposed by Timoshenko. Governing equations are derived using the principle of virtual work. Analytical resolutions for buckling of FG nanobeam are introduced under tow different boundary conditions, and the results obtained are compared to those proposed in literatures.