• Structural Engineering and Mechanics
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• v.6 no.7
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• pp.727-746
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• 1998

Finite element models and numerical results are presented for bending and natural vibration using the unified third-order plate theory developed in Part 1 of this paper. The unified third-order theory contains the classical, first-order, and other third-order plate theories as special cases. Analytical solutions are developed using the Navier and L$\acute{e}$vy solution procedures (see Part 1 of the paper). Displacement finite element models of the unified third-order theory are developed herein. The finite element models are based on $C^0$ interpolation of the inplane displacements and rotation functions and $C^1$ interpolation of the transverse deflection. Numerical results of bending and natural vibration are presented to evaluate the accuracy of various plate theories.

• Advances in aircraft and spacecraft science
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• v.5 no.4
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• pp.445-458
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• 2018

Turbulent airflow in channels of rectangular cross section with symmetric centerbodies is studied numerically. Shock wave configurations formed in the channel and in front of the entrance are examined. Solutions of the unsteady Reynolds-averaged Navier-Stokes equations are obtained with finite-volume solvers of second-order accuracy. The solutions demonstrate an expulsion/swallowing of the shocks with variations of the free-stream Mach number or angle of attack. Effects of the centerbody length and thickness on the shock wave stability and flow bifurcation are examined. Bands of the Mach number and angle of attack, in which there exist non-unique flow fields, are identified.

• Geomechanics and Engineering
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• v.11 no.2
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• pp.289-307
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• 2016

A simple hyperbolic shear deformation theory taking into account transverse shear deformation effects is proposed for the free flexural vibration analysis of thick functionally graded plates resting on elastic foundations. By considering further supposition, the present formulation introduces only four unknowns and its governing equations are therefore reduced. Hamilton's principle is employed to obtain equations of motion and Navier-type analytical solutions for simply-supported plates are compared with the available solutions in literature to check the accuracy of the proposed theory. Numerical results are computed to examine the effects of the power-law index and side-to-thickness ratio on the natural frequencies.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.8
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• pp.1921-1930
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• 1993

In order to evaluate the inlet pressure correctly, the full Navier-Stokes equations are solved numerically for the computational domain which covers the cavity region between pads as well as the bearing film. A nonuiform grid system is adopted to reduce the number of grid points, and the numerical solutions are obtained for a wide range of Reynolds number in laminar regime with various values of the distance between pads. The numerical results show that the inlet pressure is significantly affected by Reynolds number and the distance between pads. An expression for the loss coefficient in terms of Reynolds number and non-dimensional distance between pads is obtained on the basis of the numerical results. It is found that the inlet pressure over the whole range of numerical solutions can be fairly accurately estimated by applying the formula for the loss coefficient to the extended Bernoulli equation.

• The KSFM Journal of Fluid Machinery
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• v.8 no.3 s.30
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• pp.7-15
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• 2005

A Navier-Stokes code has been developed to simulate the flow through a cross flow fan. It is based on an unstructured finite volume method and uses moving grid technique to model the rotation of the fan. A low Reynolds number turbulence model is used to calculate eddy viscosity. The basic algorithm is SIMPLE. Numerical simulations over a wide range of flow rate aye carried out to validate the code. Comparison of all numerical solutions with experimental data confirms the validity of the present code. Present numerical solutions show a noticeable improvement over a previous numerical method which is based on a model of body force to simulate the rotation of the impeller.

• Smart Structures and Systems
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• v.25 no.4
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• pp.447-457
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• 2020

In this study, a simple two-dimensional shear deformation model is employed for buckling analysis of functionally graded (FG) plates. The proposed theory has a kinematic with integral terms which considers the influence of shear deformation without using "shear correction factors". The impact of varying material properties and volume fraction of the constituent on buckling response of the FG plate is examined and discussed. The benefit of this theory over other contributions is that a number of variables is reduced. The basic equations that consider the influence of transverse shear stresses are derived from the principle of virtual displacements. The analytical solutions are obtained utilizing the "Navier method". The accuracy of the proposed theory is proved by comparisons with the different solutions found in the literature.

• Steel and Composite Structures
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• v.16 no.5
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• pp.507-519
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• 2014

In this paper, a higher order shear deformation beam theory is developed for static and free vibration analysis of functionally graded beams. The theory account for higher-order variation of transverse shear strain through the depth of the beam and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. The material properties of the functionally graded beam are assumed to vary according to power law distribution of the volume fraction of the constituents. Based on the present higher-order shear deformation beam theory, the equations of motion are derived from Hamilton's principle. Navier type solution method was used to obtain frequencies. Different higher order shear deformation theories and classical beam theories were used in the analysis. A static and free vibration frequency is given for different material properties. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.

• Steel and Composite Structures
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• v.25 no.4
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• pp.389-401
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• 2017

In this work, a new higher shear deformation theory (HSDT) is developed for the free vibration and buckling of functionally graded (FG) sandwich plates. The proposed theory presents a new displacement field by using undetermined integral terms. Only four unknowns are employed in this theory, which is less than the classical first shear deformation theory (FSDT) and others HSDTs. Equations of motion are obtained via Hamilton's principle. The analytical solutions of FG sandwich plates are determined by employing the Navier method. A good agreement between the computed results and the available solutions of existing HSDTs is found to prove the accuracy of the developed theory.

• The KSFM Journal of Fluid Machinery
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• v.9 no.4 s.37
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• pp.27-35
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• 2006

A Navier-Stokes code has been developed to simulate the flow through a cross flow fan. It is based on an unstructured finite volume method and uses moving grid technique to model the rotation of the fan. A low Reynolds number turbulence model is used to calculate eddy viscosity. The basic algorithm is SIMPLE. Numerical simulations over a wide range of flow rate are carried out to validate the code. Comparison of all numerical solutions with experimental data confirms the validity of the present code. Present numerical solutions show a noticeable improvement over a previous numerical method which is based on a model of body force to simulate the rotation of the impeller.

• Advances in aircraft and spacecraft science
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• v.6 no.1
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• pp.19-30
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• 2019

Two- and three-dimensional turbulent airflows in a 9-degrees-bent channel are studied numerically. The inner surfaces of upper and lower walls are parallel to each other upstream and downstream of the bend section. The free stream is supersonic, whereas the flow at the channel exit is either supersonic or subsonic depending on the given backpressure. Solutions of the Reynolds-averaged Navier-Stokes equations are obtained with a finite-volume solver ANSYS CFX. The solutions reveal instability of formed shock waves and a flow hysteresis in considerable bands of the free-stream Mach number at zero and negative angles of attack. The instability is caused by an interaction of shocks with the expansion flow formed over the convex bend of lower wall.