• Structural Engineering and Mechanics
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• v.64 no.5
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• pp.527-541
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• 2017

In this work, a new hyperbolic shear deformation beam theory is proposed based on a modified couple stress theory (MCST) to investigate the bending and free vibration responses of functionally graded (FG) micro beam made of porous material. This non-classical micro-beam model introduces the material length scale coefficient which can capture the size influence. The non-classical beam model reduces to the classical beam model when the material length scale coefficient is set to zero. The mechanical material properties of the FG micro-beam are assumed to vary in the thickness direction and are estimated through the classical rule of mixture which is modified to approximate the porous material properties with even and uneven distributions of porosities phases. Effects of several important parameters such as power-law exponents, porosity distributions, porosity volume fractions, the material length scale parameter and slenderness ratios on bending and dynamic responses of FG micro-beams are investigated and discussed in detail. It is concluded that these effects play significant role in the mechanical behavior of porous FG micro-beams.

• Computers and Concrete
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• v.26 no.5
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• pp.439-450
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• 2020

In this research, bending and buckling analyses of porous functionally graded (FG) plate under mechanical load are presented. The properties of the FG plate vary gradually across the thickness according to power-law and exponential functions. The material imperfection is considered to vary depending to a logarithmic function. The plate is modeled by a refined trigonometric shear deformation theory where the use of the shear correction factor is unnecessary. The governing equations of the FG plate are derived via virtual work principle and resolved via Navier solutions. The accuracy of the present model is checked by comparing the obtained results with those found in the literature. The various effects influencing the stresses, displacements and critical buckling loads of the plate are also examined and discussed in detail.

• Steel and Composite Structures
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• v.28 no.3
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• pp.349-362
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• 2018

This paper presents a semi-analytical solution for the creep analysis and life assessment of 304L austenitic stainless steel thick truncated conical shells using multilayered method based on the first order shear deformation theory (FSDT). The cone is subjected to the non-uniform internal pressure and temperature gradient. Damages are obtained in thick truncated conical shell using Robinson's linear life fraction damage rule, and time to rupture and remaining life assessment is determined by Larson-Miller Parameter (LMP). The creep response of the material is described by Norton's law. In the multilayer method, the truncated cone is divided into n homogeneous disks, and n sets of differential equations with constant coefficients. This set of equations is solved analytically by applying boundary and continuity conditions between the layers. The results obtained analytically have been compared with the numerical results of the finite element method. The results show that the multilayered method based on FSDT has an acceptable amount of accuracy when one wants to obtain radial displacement, radial, circumferential and shear stresses. It is shown that non-uniform pressure has significant influences on the creep damages and remaining life of the truncated cone.

• Smart Structures and Systems
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• v.26 no.5
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• pp.641-656
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• 2020

The finite element solutions of thermal buckling load values of the graded sandwich curved shell structure are reported in this research using a higher-order kinematic model including the shear deformation effect. The numerical buckling temperature has been computed using an in-house specialized code (MATLAB environment) prepared in the framework of the current mathematical formulation. In addition, the mathematical model includes the excess structural distortion under the influence of elevated environment via Green-Lagrange nonlinear strain. The corresponding eigenvalue equation has been solved to predict the critical buckling temperature of the graded sandwich structure. The numerical stability and the accuracy of the current solution have been confirmed by comparing with the available published results. Thereafter, the model is extended to bring out the influences of structural parameters i.e. the curvature ratio, core-face thickness ratio, support conditions, power-law indices and sandwich types on the thermal buckling behavior of graded sandwich curved shell panels.

• 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.20 no.1
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• pp.205-225
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• 2016

In this study the finite element method is utilized to predict the deflection and vibration characteristics of rectangular plates made of saturated porous functionally graded materials (PFGM) within the framework of the third order shear deformation plate theory. Material properties of PFGM plate are supposed to vary continuously along the thickness direction according to the power-law form and the porous plate is assumed of the form where pores are saturated with fluid. Various edge conditions of the plate are analyzed. The governing equations of motion are derived through energy method, using calculus of variations while the finite element model is derived based on the constitutive equation of the porous material. According to the numerical results, it is revealed that the proposed modeling and finite element approach can provide accurate deflection and frequency results of the PFGM plates as compared to the previously published results in literature. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as porosity volume fraction, material distribution profile, mode number and boundary conditions on the natural frequencies and deflection of the PFGM plates in detail. It is explicitly shown that the deflection and vibration behaviour of porous FGM plates are significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FGM plates with porosity phases.

• Geomechanics and Engineering
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• v.9 no.3
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• pp.275-286
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• 2015

A new method is presented to recover missing deformation data of lateral walls of foundation pit when the monitoring is interrupted; the method is called Dynamic Mathematical Model - Parameter Interpolation. The deformation of lateral walls of foundation pit is mainly affected by the type of supporting structure and the situation of constraints, therefore, this paper mainly studies the two different kinds of variation law of deep horizontal displacement when the lateral walls are constrained or not, proposes two dynamic curve models of normal distribution type and logarithmic type, deals with model parameters by interpolating and obtains the parameters of missing data, then missing monitoring data could be Figured out by these parameters. Compared with the result from the common average method which is used to recover missing data, in the upper 2/3 of the inclinometer tube, the result by using this method is closer to the actual monitoring data, in the lower 1/3 part of the inclinometer tube, the result from the common average method is closer to the actual monitoring data.

• Structural Engineering and Mechanics
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• v.62 no.4
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• pp.401-415
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• 2017

A new higher shear deformation theory (HSDT) is presented for the thermal buckling behavior of functionally graded (FG) sandwich plates. It uses only four unknowns, which is even less than the first shear deformation theory (FSDT) and the conventional HSDTs. The theory considers a hyperbolic variation of transverse shear stress, respects the traction free boundary conditions and contrary to the conventional HSDTs, the present one presents a new displacement field which includes undetermined integral terms. Material characteristics and thermal expansion coefficient of the sandwich plate faces are considered to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic material. The thermal loads are supposed as uniform, linear and non-linear temperature rises within the thickness direction. An energy based variational principle is used to derive the governing equations as an eigenvalue problem. The validation of the present work is carried out with the available results in the literature. Numerical results are presented to demonstrate the influences of variations of volume fraction index, length-thickness ratio, loading type and functionally graded layers thickness on nondimensional thermal buckling loads.

• Geomechanics and Engineering
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• v.13 no.6
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• pp.1027-1044
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• 2017

Membrane penetration is the most important factor influencing the measurement of volume change for triaxial consolidated-drained shear test for coarse-grained soil. The effective pressure p, average particle size $d_{50}$, thickness $t_m$ and elastic modulus $E_m$ of membrane, contact area between membrane and soil $A_m$ as well as the initial void ratio e are the major factors influencing membrane penetration. According to the membrane deformation model given by Kramer and Sivaneswaran, an analytical solution of the membrane penetration considering the initial void ratio is deduced using the energy conservation law. The basic equations from theory of plates and shells and the elastic mechanics are employed during the derivation. To verify the presented solution, isotropic consolidation tests of a coarse-grained soil are performed by using the method of embedding different diameter of iron rods in the triaxial samples, and volume changes due to membrane penetration are obtained. The predictions from presented solution and previous analytical solutions are compared with the test results. It is found that the prediction from presented analytical solution agrees well with the test results.

• Steel and Composite Structures
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• v.39 no.3
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• pp.275-290
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• 2021

The main purpose of this research work is to investigate the critical buckling load of functionally graded (FG) porous plates with graphene platelets (GPLs) reinforcement using generalized differential quadrature (GDQ) method at thermal condition. It is supposed that the GPL nanofillers and the porosity coefficient vary continuously along the plate thickness direction. Generally, the thermal distribution is considered to be nonlinear and the temperature changing continuously through the thickness of the nanocomposite plates according to the power-law distribution. To model closed cell FG porous material reinforced with GPLs, Halpin-Tsai micromechanical modeling in conjunction with Gaussian-Random field scheme are used, through which mechanical properties of the structures can be extracted. Based on the third order shear deformation theory (TSDT) and the Hamilton's principle, the equations of motion are established and solved for various boundary conditions (B.Cs). The fast rate of convergence and accuracy of the method are investigated through the different solved examples and validity of the present study is evaluated by comparing its numerical results with those available in the literature. A special attention is drawn to the role of GPLs weight fraction, GPLs patterns through the thickness, porosity coefficient and distribution of porosity on critical buckling load. Results reveal that the importance of thermal condition on of the critical load of FGP-GPL reinforced nanocomposite plates.