• Advances in aircraft and spacecraft science
• /
• v.7 no.1
• /
• pp.19-40
• /
• 2020

In the present study, a fifth-order shear and normal deformation theory using a polynomial function in the displacement field is developed and employed for the static analysis of laminated composite and sandwich simply supported spherical shells subjected to sinusoidal load. The significant feature of the present theory is that it considers the effect of transverse normal strain in the displacement field which is eliminated in classical, first-order and many higher-order shell theories, while predicting the bending behavior of the shell. The present theory satisfies the zero transverse shear stress conditions at the top and bottom surfaces of the shell. The governing equations and boundary conditions are derived using the principle of virtual work. To solve the governing equations, the Navier solution procedure is employed. The obtained results are compared with Reddy's and Mindlin's theory for the validation of the present theory.

• 한국전산유체공학회:학술대회논문집
• /
• 2011.05a
• /
• pp.278-285
• /
• 2011

In the present study, the numerical prediction of the oil amount leaked from the hole of a damaged tank is investigated using the improved MPS (Moving Particle Semi-implicit) method, which was originally proposed by Koshizuka and Oka (1996) for incompressible flow. The governing equations, which consist of the continuity and Navier-Stokes equations, are solved by Lagrangian moving particles, and all terms expressed by differential operators should be replaced by the particle interaction models based on a Kernel function. The simulation results are validated though the comparison with the analytic solution based on Torricelli's equilibrium relation. Furthermore, a series of numerical simulations under the various conditions are performed in order to estimate more accurately the initial amount of leaked oil.

• Steel and Composite Structures
• /
• v.48 no.3
• /
• pp.263-273
• /
• 2023

This paper investigates dynamic characteristics of a graphene nanoplatelets reinforced composite (GNPRC) sandwich doubly curved shell based on the first-order shear deformation theory (FSDT) and Hamilton's principle. The sandwich doubly curved shell is fabricated from a core made of honeycomb materials sandwiched by composite GNPs reinforced face-sheets. Effective materials properties of composite face-sheets are assumed to vary based on Halpin-Tsai micromechanical models and rule of mixture. Furthermore, the material properties of honeycomb core are estimated using Gibson's formula. The fundamental frequencies of the shell are computed with changes of main geometrical and material properties such as amount and distribution type of graphene nanoplatelets, side length ratio, thickness to length ratio of and side length ratio of honeycomb. The Navier's technique is presented to obtain responses. Accuracy and trueness of the present model and analytical solution is confirmed through comparison of the results with available results in literature. It is concluded that an increase in thickness to length ratio yields a softer core with lower natural frequencies. Furthermore, increase in height to length ratio leads to significant decrease in natural frequencies.

• Coupled systems mechanics
• /
• v.13 no.4
• /
• pp.337-357
• /
• 2024

This paper studies, the analysis of nonlinear thermal vibration of fluid-infiltrated FG nanobeam with voids. The effect of nonlinear thermal in a FG ceramic-metal nanobeam is determined using Murnaghan's model. Here the influence of fluids in the pores is investigated using the Skempton coefficient. Hamilton's principle is used to find the equation of motion of functionally graded nanobeam with the effect of refined higher-order state space strain gradient theory (SSSGT). Numerical solutions of the FG nanobeam are employed using Navier's solution. These solutions are validated against the impact of various parameters, including imperfection ratio, fluid viscosity, fluid velocity, amplitude, and piezoelectric strain, on the behavior of the fluid-infiltrated porous FG nanobeam.

• Journal of computational fluids engineering
• /
• v.19 no.4
• /
• pp.20-28
• /
• 2014

An efficient solution algorithm for simulating free surface problem is presented. Navier-Stokes equations for variable density incompressible flow are employed as the governing equation on Cartesian meshes. In order to describe the free surface motion efficiently, VOF(Volume Of Fluid) method utilizing THINC(Tangent of Hyperbola for Interface Capturing) scheme is employed. The most time-consuming part of the current free surface flow simulations is the solution step of the linear system, derived by the pressure Poisson equation. To solve a pressure Poisson equation efficiently, the PCG(Preconditioned Conjugate Gradient) method is utilized. This study showed that the proper application of the preconditioner is the key for the efficient solution of the free surface flow when its pressure Poisson equation is solved by the CG method. To demonstrate the efficiency of the current approach, we compared the convergence histories of different algorithms for solving the pressure Poisson equation.

• Wind and Structures
• /
• v.26 no.4
• /
• pp.205-214
• /
• 2018

In this paper, the thermo-mechanical buckling characteristics of functionally graded (FG) size-dependent Timoshenko nanobeams subjected to an in-plane thermal loading are investigated by presenting a Navier type solution for the first time. Material properties of FG nanobeam are supposed to vary continuously along the thickness according to the power-law form and the material properties are assumed to be temperature-dependent. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The nonlocal governing equations are derived based on Timoshenko beam theory through Hamilton's principle and they are solved applying analytical solution. According to the numerical results, it is revealed that the proposed modeling can provide accurate critical buckling temperature results of the FG nanobeams as compared to some cases in the 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 material distribution profile, small scale effects and aspect ratio on the critical buckling temperature of the FG nanobeams in detail. It is explicitly shown that the thermal buckling of a FG nanobeams is significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FG nanobeams.

• Structural Engineering and Mechanics
• /
• v.17 no.5
• /
• pp.641-654
• /
• 2004

This paper presents a theoretic model of a smart structure, a transversely isotropic piezoelectric thick square plate constructed with three laminas, piezoelectric-elastic-piezoelectric layer, by adopting the first order shear deformation plate theory and piezoelectric theory. This model assumes that the transverse displacements through thickness are linear, and the in-plane displacements in the mid-plane of the plate are not taken to be account. By using Fourier's series expansion, an exact Navier typed analytical solution for deflection and electric potential of the simply supported smart plate is obtained. The electric boundary conditions are being grounded along four vertical edges. The external voltage and non-external voltage applied on the surfaces of piezoelectric layers are all considered. The convergence of the present approach is carefully studied. Comparison studies are also made for verifying the accuracy and the applicability of the present method. Then some new results of the electric potentials and displacements are provided. Numerical results show that the electrostatic voltage is approximately linear in the thickness direction, while parabolic in the plate in-plane directions, for both the deflection and the electric voltage. These results are very useful for distributed sensing and finite element verification.

• Journal of Korea Water Resources Association
• /
• v.48 no.4
• /
• pp.291-298
• /
• 2015

The aim of this study is that a theoretical formula for estimating the one-dimensional longitudinal dispersion coefficient is derived based on a transverse distribution equation for the depth averaged stream-wise velocity in open channel. In "Part I. Theoretical equation for stream-wise velocity" which is the former volume of this article, the velocity distribution equation is derived analytically based on the Shiono-Knight Model (SKM). And then incorporating the velocity distribution equation into a triple integral formula which was proposed by Fischer (1968), the one-dimensional longitudinal dispersion coefficient can be derived theoretically in "Part II. Longitudinal dispersion coefficient" which is the latter volume of this article. SKM has presented an analytical solution to the Navier-Stokes equation to describe the transverse variations, and originally been applied to straight and nearly straight compound channel. In order to use SKM in modeling non-prismatic and meandering channels, the shape of cross-section is regarded as a triangle in this study. The analytical solution for the velocity distribution is verified using Manning's equation and applied to velocity data measured at natural streams. Although the velocity equation developed in this study do not agree well with measured data case by case, the equation has a merit that the velocity distribution can be calculated only using geometric data including Manning's roughness coefficient without any measured velocity data.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
• /
• v.8 no.2
• /
• pp.267-278
• /
• 1996

Steady, laminar, forced convection flow and heat transfer in the entrance region of an internally finned circular duct with a finite thermal conductivity has been analyzed numerically. The problem under investigation is a three-dimensional boundary layer problem, and is solved by employing a marching-type procedure which involves solution of a series of 2-dimensional elliptic problems in the cross-stream plane. Two types of inlet hydrodynamic conditions are considered : (a) uniform velocity flow and (b) fully developed flow. From the above inlet conditions, the effects of the fin height(h), fin number(N) and conductivity ratio($k_r$) on the flow and thermal characteristics are investigated. The numerical results show that the height and number of fins, and ratio of the solid to fluid thermal conductivity have pronounced effect on the solution. Considering pressure drop, optimized dimensionless fin height is 0.4.

• Advances in nano research
• /
• v.4 no.3
• /
• pp.197-228
• /
• 2016

In the present study, thermo-electro-mechanical vibration characteristics of functionally graded piezoelectric (FGP) Timoshenko nanobeams subjected to in-plane thermal loads and applied electric voltage are carried out by presenting a Navier type solution for the first time. Three kinds of thermal loading, namely, uniform, linear and non-linear temperature rises through the thickness direction are considered. Thermo-electro-mechanical properties of FGP nanobeam are supposed to vary smoothly and continuously throughout the thickness based on power-law model. Eringen's nonlocal elasticity theory is exploited to describe the size dependency of nanobeam. Using Hamilton's principle, the nonlocal equations of motion together with corresponding boundary conditions based on Timoshenko beam theory are obtained for the free vibration analysis of graded piezoelectric nanobeams including size effect and they are solved applying analytical solution. According to the numerical results, it is revealed that the proposed modeling can provide accurate frequency results of the FGP nanobeams as compared to some cases in the literature. In following a parametric study is accompanied to examine the effects of several parameters such as various temperature distributions, external electric voltage, power-law index, nonlocal parameter and mode number on the natural frequencies of the size-dependent FGP nanobeams in detail. It is found that the small scale effect and thermo-electrical loading have a significant effect on natural frequencies of FGP nanobeams.