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

• Transactions of Materials Processing
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• v.7 no.3
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• pp.233-245
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• 1998

A new approach has been proposed for the incremental analysis of the nonsteady state large deformation of planar anisotropic elastic-plastic sheet forming. A mathematical brief review of a constitutive law for the incremental deformation theory has been presented from flow theory using the minimum plastic work path for elastic-plastic material. Since the material embedded coordinate system(Lagrangian quantity) is used in the proposed theory the stress integration procedure is completely objective. A new return mapping algorithm has been also developed from the general midpoint rule so as to achieve numerically large strain increment by successive control of yield function residuals. Some numerical tests for the return mapping algorithm were performed using Barlat's six component anisotropic stress potential. Performance of the proposed algorithm was shown to be good and stable for a large strain increment, For planar anisotropic sheet forming updating algorithm of planar anisotropic axes has been newly proposed. In order to show the effectiveness and validity of the present formulation earing simulation for a cylindrical cup drawing and front fender stamping analysis are performed. From the results it has been shown that the present formulation can provide a good basis for analysis for analysis of elastic-plastic sheet metal forming processes.

• Steel and Composite Structures
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• v.34 no.5
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• pp.657-670
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• 2020

In this paper, vibration analysis of functionally graded nanoshell is studied based on the sinusoidal higher-order shear and normal deformation theory to account thickness stretching effect. To account size-dependency, Eringen nonlocal elasticity theory is used. For more accurate modeling the problem and corresponding numerical results, sinusoidal higher-order shear and normal deformation theory including out of plane normal strain is employed in this paper. The radial displacement is decomposed into three terms to show variation along the thickness direction. Governing differential equations of motion are derived using Hamilton's principle. It is assumed that the cylindrical shell is made of an arbitrary composition of metal and ceramic in which the local material properties are measured based on power law distribution. To justify trueness and necessity of this work, a comprehensive comparison with some lower order and lower dimension works and also some 3D works is presented. After presentation of comparative study, full numerical results are presented in terms of significant parameters of the problem such as small scale parameter, length to radius ratio, thickness to radius ratio, and number of modes.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.6
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• pp.1365-1381
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• 1990

A $C^{0}$ continuous displacement finite element method based on a higher-order shear deformation theory is employed in the prediction of the transient response of laminated composite plates subjected to low-velocity impact. A modified contact law was applied to calculate the contact force during impact. The discrete element chosen is a nine-noded quadrilateral with 5 degree-of-freedom per node. The Wilson-.theta. time integration algorithm is used for solving the time dependent equations of the impactor and the central difference method was adopted to perform time integration of the plate. Numerical results, including the contact force history, deflection, and velocity history, are presented. Comparisons of numerical results using a higher order theory and a first-order theory show that using a higher order theory provides more accurate results. Effects of boundary condition, impact velocity, and mass of the impactors are also discussed.d.

• Structural Engineering and Mechanics
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• v.57 no.4
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• pp.617-639
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• 2016

In this work, an analytical formulation based on both hyperbolic shear deformation theory and stress function, is presented to study the nonlinear post-buckling response of symmetric functionally graded plates supported by elastic foundations and subjected to in-plane compressive, thermal and thermo-mechanical loads. Elastic properties of material are based on sigmoid power law and varying across the thickness of the plate (S-FGM). In the present formulation, Von Karman nonlinearity and initial geometrical imperfection of plate are also taken into account. By utilizing Galerkin procedure, closed-form expressions of buckling loads and post-buckling equilibrium paths for simply supported plates are obtained. The effects of different parameters such as material and geometrical characteristics, temperature, boundary conditions, foundation stiffness and imperfection on the mechanical and thermal buckling and post-buckling loading capacity of the S-FGM plates are investigated.

• Coupled systems mechanics
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• v.6 no.3
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• pp.251-272
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• 2017

In this paper, the thermo-mechanical vibration characteristics of functionally graded (FG) nanobeams subjected to three types of thermal loading including uniform, linear and non-linear temperature change are investigated in the framework of third-order shear deformation beam theory which captures both the microstructural and shear deformation effects without the need for any shear correction factors. Material properties of FG nanobeam are assumed to be temperature-dependent and vary gradually along the thickness according to the power-law form. Hence, applying a third-order shear deformation beam theory (TSDBT) with more rigorous kinetics of displacements to anticipate the behaviors of FG nanobeams is more appropriate than using other theories. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The nonlocal equations of motion are derived through Hamilton's principle and they are solved applying analytical solution. The obtained results are compared with those predicted by the nonlocal Euler-Bernoulli beam theory and nonlocal Timoshenko beam theory and it is revealed that the proposed modeling can accurately predict the vibration responses of FG nanobeams. The obtained results are presented for the thermo-mechanical vibration analysis of the FG nanobeams such as the effects of material graduation, nonlocal parameter, mode number, slenderness ratio and thermal loading in detail. The present study is associated to aerospace, mechanical and nuclear engineering structures which are under thermal loads.

• Structural Engineering and Mechanics
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• v.60 no.4
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• pp.547-565
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• 2016

In this work a new 3-unknown non-polynomial shear deformation theory for the buckling and vibration analyses of functionally graded material (FGM) sandwich plates is presented. The present theory accounts for non-linear in plane displacement and constant transverse displacement through the plate thickness, complies with plate surface boundary conditions, and in this manner a shear correction factor is not required. The main advantage of this theory is that, in addition to including the shear deformation effect, the displacement field is modelled with only 3 unknowns as the case of the classical plate theory (CPT) and which is even less than the first order shear deformation theory (FSDT). The plate properties are assumed to vary according to a power law distribution of the volume fraction of the constituents. Equations of motion are derived from the Hamilton's principle. Analytical solutions of natural frequency and critical buckling load for functionally graded sandwich plates are obtained using the Navier solution. The results obtained for plate with various thickness ratios using the present non-polynomial plate theory are not only substantially more accurate than those obtained using the classical plate theory, but are almost comparable to those obtained using higher order theories with more number of unknown functions.

• Steel and Composite Structures
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• v.22 no.1
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• pp.91-112
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• 2016

In this paper, post-buckling behavior of sandwich plates with functionally graded (FG) face sheets under uniform temperature rise loading is examined based on both sinusoidal shear deformation theory and stress function. It is supposed that the sandwich plate is in contact with an elastic foundation during deformation, which acts in both compression and tension. Thermo-elastic non-homogeneous properties of FG layers change smoothly by the variation of power law within the thickness, and temperature dependency of material constituents is considered in the formulation. In the present development, Von Karman nonlinearity and initial geometrical imperfection of sandwich plate are also taken into account. By employing Galerkin method, analytical solutions of thermal buckling and post-buckling equilibrium paths for simply supported plates are determined. Numerical examples presented in the present study discuss the effects of gradient index, sandwich plate geometry, geometrical imperfection, temperature dependency, and the elastic foundation parameters.

• Geomechanics and Engineering
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• v.22 no.4
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• pp.349-359
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• 2020

Quantification of the influence of the fracture of thick magmatic rock (TMR) on the behavior of its overlying strata is a prerequisite to the understanding of the deformation behavior of the earth's surface in deep mining. A three-dimensional numerical model of a special geological mining condition of overlying TMR was developed to investigate the overburden movement and fracture law, and compare the influence of the occurrence horizon of TMR. The research results show that the movement of overlying rock was greatly affected by the TMR. Before the fracture of TMR, the TMR had shielding and controlling effects on the overlying strata, the maximum vertical and horizontal displacement values of overlying strata were 0.68 m and 0.062 m. After the fracture, the vertical and horizontal displacements suddenly increased to 3.06 m and 0.105 m, with an increase of 350% and 69.4%, respectively, and the higher the occurrence of TMR, the smaller the settlement of the overlying strata, but the wider the settlement span, the smaller the corresponding deformation value of the basin edge (the more difficult the surface to crack). These results are of tremendous importance for the control of rock strata and the revealing of surface deformation mechanism under TMR mining conditions in mines.

• Computers and Concrete
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• v.26 no.1
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• pp.63-74
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• 2020

In this investigation, study of the bending response of functionally graded (FG) porous plates is presented using a cubic shear deformation theory. The properties of the FG-plate vary according to a power-law distribution which is modified to approximate material characteristics for considering the effect of porosities. The equilibrium equations are derived by using the principle of virtual work and solved by using Navier's procedure. Various numerical results are discussed to demonstrate the influence of the variation of the power index, the porosity parameter and the geometric ratios on the bending response of FG porous plates.