• Structural Engineering and Mechanics
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• v.78 no.4
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• pp.439-453
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• 2021

In this work, quasi three-dimensional (quasi-3D) shear deformation theory is presented for bending and dynamic analysis of functionally graded (FG) plates. The effect of varying material properties and volume fraction of the constituent on dynamic and bending behavior of the FG plate is discussed. The benefit of this model over other contributions is that a number of variables is diminished. The developed model considers nonlinear displacements through the thickness and ensures the free boundary conditions at top and bottom faces of the plate without using any shear correction factors. The basic equations that account for the effects of transverse and normal shear stresses are derived from Hamilton's principle. The analytical solutions are determined via the Navier procedure. The accuracy of the proposed formulation is proved by comparisons with the different 2D, 3D and quasi-3D solutions found in the literature.

• Journal of the Earthquake Engineering Society of Korea
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• v.1 no.4
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• pp.59-68
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• 1997

In analysis of underground structures, the effects of artificial boundary conditions are considered as one of the major reasons for differences from experimental results. These phenomena can be overcome by using the boundary elements which satisfy the multi-layered half space conditions. The fundamental solutions of multi-layered half-space for boundary element method is formulated satisfying the transmission and reflection of waves at each layer interface and radiation conditions at bottom layer. The governing equations can be obtained from the displacements at each layer which are expressed in terms of harmonic functions. All types of waves can be included using the complete response from semi-infinite integrals with respect to horizontal wavenumbers using expansion of Fourier series and Hankel transformation. Two dimensional Green's functions are derived from cylindrical Navier equations and potentials performing infinite integration in y-direction. In this case, it is effective to transform into two dimensional problem using semi-analytical integration and sinusoidal Bessel function. Some verifications are given to show the accuracy and efficiency of the developed method, and numerical examples to demonstrate the dynamic behavior of underground with various properties.

• Steel and Composite Structures
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• v.41 no.6
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• pp.899-910
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• 2021

A 4-unknown shear deformation theory is applied to investigate the vibration of functionally graded plates under thermal environment. The plate is fabricated from a functionally graded material mixed of ceramic and metal with continuously varying material properties through the plate thickness. Three types of thermal loadings, uniform, linear and nonlinear temperature rises along the plate thickness are taken into account. The present theory contains four unknown functions as against five or more in other higher order shear deformation theories. The through-the-thickness distributions of transverse shear stresses of the plate are considered to vary parabolically and vanish at upper and lower surfaces. The present model does not require any problem dependent shear correction factor. Analytical solutions for the free vibration analysis are derived based on Fourier series that satisfy the boundary conditions (Navier's method). Benchmark solutions are firstly considered to evaluate the accuracy of the proposed model. Comparisons with the solutions available in literature revealed the good capabilities of the present model for the simulations of vibration responses of FG plates. Some parametric studies are carried out for the frequency analysis by varying the volume fraction profile and the temperature distribution across the plate thickness.

• Journal of the Korean Society of Hazard Mitigation
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• v.7 no.5
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• pp.61-71
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• 2007

Navier's and Finite element solutions based on the first-order shear deformation theory are presented for the analysis of through-thickness functionally graded plates and shells. The functionally graded materials are considered: a sigmoid function is utilized for the mechanical properties through the thickness of the isotropic structure which varies smoothly through the plate and shell thickness. The formulation of a nonlinear 9-node Element-based Lagrangian shell element is presented for the geometrically nonlinear analysis. Natural-coordinate-based strains are used in present shell element. Numerical results of the linear and nonlinear analysis are presented to show the effect of the different top/bottom elastic modulus, loading conditions, aspect ratios and side-to-thickness ratios on the mechanical behaviors. Besides, the result according to the variation of the power-law index of isotropic functionally graded structures is investigated.

• Geomechanics and Engineering
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• v.34 no.3
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• pp.233-250
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• 2023

This paper investigates the flexural analysis of isotropic, transversely isotropic, and laminated composite plates using a new higher-order normal and shear deformation theory. In the present theory, only five unknown functions are involved compared to six or more unknowns used in the other similar theories. The developed theory does not need a shear correction factor. It can satisfy the zero traction boundary conditions on the top and the bottom surfaces of the plate as well as account for sufficient distribution of the transverse shear strains. The thickness stretching effect is considered in the computation. A simply supported was considered on all edges of the plate. The plate is subjected to uniform and sinusoidal distributed load in the static analysis. Laminated composite, isotropic, and transversely isotropic plates are considered. The governing equations are obtained utilizing the virtual work principle. The differential equations are solved via Navier's procedure. The results obtained from the developed theory are compared with other higher-order theories considered in the previous studies and 3D elasticity solutions. The results showed that the proposed theory accurately and effectively predicts the bidirectional bending responses of laminated composite plates. Several parametric studies are presented to illustrate the various parameters influencing the static response of the laminated composite plates.

• Journal of computational fluids engineering
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• v.13 no.2
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• pp.8-13
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• 2008

A supersonic viscous flow over a five-degree half-angle cone is studied computationally with three-dimensional Navier-Stokes equations. Steady asymmetric solutions show that the asymmetric flow separation is caused by convective instability. The effects of angle of attacks, Reynolds numbers, and Mach numbers have been investigated and it is found that those factors affect the generation of the side force. The side force has the maximum value at ${\alpha}=22^{\circ}$, while over ${\alpha}=22^{\circ}$, asymmetric vortex becomes transient, which results in the unsteady shedding. At the angle of attack of 22 degrees, the side force increases with Reynolds number and decreases with Mach number. The increase of the side force stops over the critical Reynolds number for the present configuration.

• Steel and Composite Structures
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• v.18 no.1
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• pp.91-120
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• 2015

A refined higher-order shear deformation theory for bending, vibration and buckling analysis of functionally graded sandwich plates is presented in this paper. It contains only four unknowns, accounts for a hyperbolic distribution of transverse shear stress and satisfies the traction free boundary conditions. Equations of motion are derived from Hamilton's principle. The Navier-type and finite element solutions are derived for plate with simply-supported and various boundary conditions, respectively. Numerical examples are presented for functionally graded sandwich plates with homogeneous hardcore and softcore to verify the validity of the developed theory. It is observed that the present theory with four unknowns predicts the response accurately and efficiently.

• Journal of computational fluids engineering
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• v.3 no.1
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• pp.30-36
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• 1998

The three dimensional Navier-Stokes equations in rotational coordinate are solved using a multigrid algorithm for the calculations of turbulent flows in centrifugal compressor impellers. Some numerical studies are made in applying the multigrid algorithm for the turbulent flow calculations with the standard κ-ε equations. The present method is used to calculate the flow fields of Mizuki's B-type and Niigata Ms. 350 centrifugal compressor impellers. Fast convergent steady-state solutions are carefully examined, comparing the static pressure distributions along the impeller flow passage and also in the diffuser with experimental data. Performance of a centrifugal compressor system is also numerically validated by comparing the performances of the impeller and the diffuser individually.

• 한국전산유체공학회:학술대회논문집
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• 2007.10a
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• pp.171-176
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• 2007

Supersonic viscous flow over a 5 degree half angle cone studied computationally with three-dimensional Navier-Stokes equations. Steady asymmetric solutions of 5-deg half angle cone show that the asymmetric flow separation is caused by convective instability. The angle of attack, Reynolds number, and Mach number affected the side force variation that is caused by asymmetric vortical flow.

• Journal of computational fluids engineering
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• v.3 no.2
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• pp.17-26
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• 1998

The three-dimensional incompressible Navier-Stokes equations have been solved by a node-centered finite volume method with unstructured hybrid grids. The pressure-velocity coupling is handled by the artificial compressibility algorithm and convective fluxes are obtained by Roe's flux difference splitting scheme with linear reconstruction of the solutions. Euler implicit method with Jacobi matrix solver is used for the time-integration. The viscous terms are discretised in a manner to handle any kind of grids such as tetragedra, prisms, pyramids, hexahedra, or mixed-element grid. Inviscid bump flow is solved to check the accuracy of high order convective flux discretisation. And viscous flows around a circular cylinder and a sphere are studied to show the efficiency and accuracy of the solver.