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Analytical and FE Modeling of FG Beams Based on A Refined Shear Deformable Beam Theory for Static and Dynamic Analyses of FG BeamsWith Thermoelastic Coupling
Get PDFThe static and dynamic thermoelastic analyses of the beams made of functionally graded materials (FGMs) are presented in this paper. Based on the refined third-order shear deformation beam theory proposed by the senior author and the variational principle, the governing equations of FG beams are deduced. The influence of temperature on Young’s modulus and coefficients of thermal expansion is taken into account when FG beams are subjected to thermal loading. The resulting governing equations are a system of the eighth-order differential equations in terms of displacement variables, and the thermoelastic coupling is included in the equations. An accurate and reliable two-noded beam element is developed for the bending and free vibration analysis of FG beams by employing the refined thirdorder shear deformation beam theory and the quasi-conforming element technique. Several typical examples of FG beams are solved using the present FG beam element to show the effects of the material distribution and thermal loading on the defections, stresses and natural frequencies of FG beams. The accuracy of both the analytical solutions and numerical results given by the proposed models are validated against the results reported in the literature or the 2D finite element results solved by the authors. The results show that the present models are capable of yielding not only accurate displacements but also accurate stresses and higher-order frequencies of free vibration for the FG beams with thermoelastic coupling
Hierarchal Decomposition for the Structure-Fluid-Electrostatic Interaction in a Microelectromechanical System
Get PDFIn this study, a hierarchal decomposition is proposed to solve the structure- fluid-electrostatic interaction in a microelectromechanical system (MEMS). In the proposed decomposition, the structure-fluid-electrostatic interaction is partitioned into the structure-fluid interaction and the electrostatic field using the iteratively staggered method, and the structure-fluid interaction is split into the structurefluid velocity field and the fluid pressure field using the projection method. The proposed decomposition is applied to a micro cantilever beam actuated by the electrostatic force in air. It follows from the comparisons among the numerical and experimental results that the proposed method can predict the MEMS vibration characteristics accurately
A New Hybrid Uncertain Analysis Method and its Application to Acoustic Field with Random and Interval Parameters
Get PDFThis paper presents a new hybrid Chebyshev-perturbation method (HCPM) for the prediction of acoustic field with random and interval parameters. In HCPM, the perturbation method based on the first-order Taylor series that accounts for the random uncertainty is organically integrated with the first-order Chebyshev polynomials that deal with the interval uncertainty; specifically, a random interval function is firstly expanded with the first-order Taylor series by treating the interval variables as constants, and the expressions of the expectation and variance can be obtained by using the random moment method; then the expectation and variance of the function are approximated by using the first-order Chebyshev polynomials; the bounds of the expectation and variance are finally obtained by using the Monte Carlo method. Numerical results on two acoustic models verify that the accuracy of HCPM is better than that of the hybrid perturbation method (HPM)
The Finite Points Approximation to the PDE Problems in Multi-Asset Options
Get PDFIn this paper we present a meshless collocation method based on the moving least squares (MLS) approximation for numerical solution of the multiasset (d-dimensional) American option in financial mathematics. This problem is modeled by the Black-Scholes equation with moving boundary conditions. A penalty approach is applied to convert the original problem to one in a fixed domain. In finite parts, boundary conditions satisfy in associated (d-1)-dimensional Black-Scholes equations while in infinity they approach to zero. All equations are treated by the proposed meshless approximation method where the method of lines is employed for handling the time variable. Numerical examples for single- and two-asset options are illustrated
Aerodynamic Performance of DragonflyWing with Well-designed Corrugated Section in Gliding Flight
Get PDFDragonflies possess the highly corrugated wings which distinguish from the ordinary airfoils. To unlock the secrets of the dramatic flight ability of dragonflies, it will be of great significance to investigate the aerodynamic contribution of the corrugations. In this paper, a group of corrugated airfoils were specially designed based on the geometrical characteristics of a typical dragonfly wing. The two-dimensional Navier-Stokes equations were solved using the finite volume method, and the coefficients of lift and drag of the studied airfoils were calculated and compared with those of a flat airfoil and a NACA0008 airfoil. The obtained numerical results illustrated that well-designed corrugated airfoils can enhance the lift-drag ratio in the condition of steady flow and maintain the steadiness of the flow field at low Reynolds numbers (500-12000). To approach the optimized state, corrugation amplitude could be considered as a key parameter to describe the irregularities of the corrugated wings. These results will inspire the design of MAVs
Active Cancellation Stealth Analysis Based on Cancellaty
Get PDFActive cancellation stealth is a significant developing direction in modern stealth technology field. In this paper, according to characteristics of linear frequency modulated (LFM) signal and nonlinear frequency modulated (NLFM) signal, the cancellation signal was designed. An important parameter called cancellaty which is used to measure the effect of cancellation is proposed. The basic theory of active cancellation stealth is introduced. Based on radar target fluctuation models, the formulas of the radar detection probability are given. Combining the definition of cancellaty with radar detection probability, the effective scope of the cancellaty is ensured. Simulation results show the effectiveness and the practicability of active cancellation
Lattice Boltzmann Simulation of MHD Double Dispersion Natural Convection in a C-shaped Enclosure in the Presence of a Nanofluid
No full textMHD double-diffusive natural convective flow in a C-shaped enclosure filled with a Cu/Water nanofluid is investigated numerically using the Lattice Boltzmann Method (LBM). Much care is devoted to the validation of the numerical code. The effects exerted on the flow, concentration and temperature fields by different parameters such as the Rayleigh number (103−106), the nanoparticle volume concentration (0−0,1), the Lewis number (1-5), the Hartmann number (0−30) and different types of nanoparticles (Cu, Ag, Al2O3 and TiO3 are assessed in detail. Results for stream function, Nusselt and Sherwood numbers are presented and discussed for various parametric conditions. Results indicate that the average Nusselt number increases with an increase in the Rayleigh number and particle volume concentration but it decrease with the Hartman number. Increasing the Lewis number leads to an enhancement of mass transfer but it reduces the heat transfer rate. The type of nanofluid is a key factor for heat transfer enhancement. The highest values are obtained when Ag nanoparticles are used. Mass transfer enhancement is obtained when TiO3 nanoparticles are used
Fracture Mechanics Approach to Estimate Fatigue Lives of Welded Lap-Shear Specimens
Get PDFA full range of stress intensity factor solutions for a kinked crack with finite length is developed as a function of weld width and the sheet thickness. When used with the main crack solutions (global stress intensity factors) in terms of the applied load and the specimen geometric parameters, the fatigue lives of the kinked crack can be estimated for the laser-welded lap-shear specimens. The predicted curve for the load range-fatigue life passes through the cluster of experimental data and is in good agreement. A classical solution associated with an infinitesimal kink is also employed. However, its life prediction tends to overestimate the actual fatigue life. In addition, the traditional fatigue life estimation based on structural stress is performed for completeness. This non-fracture mechanics approach only agrees well with the experimental data under high cyclic load conditions
Three-Dimensional Free Vibration Analysis of Sandwich FGM Cylinders with Combinations of Simply-Supported and Clamped Edges and Using the Multiple Time Scale and Meshless Methods
No full textAn asymptotic meshless method using the differential reproducing kernel (DRK) interpolation and multiple time scale methods is developed for the three-dimensional (3D) free vibration analysis of sandwich functionally graded material (FGM) circular hollow cylinders with combinations of simply-supported and clamped edge conditions. In the formulation, we perform the mathematical processes of nondimensionalization, asymptotic expansion and successive integration to obtain recurrent sets of motion equations for various order problems. Classical shell theory (CST) is derived as a first-order approximation of the 3D elasticity theory, and the motion equations for higher-order problems retain the same differential operators as those of CST, although with different nonhomogeneous terms. Expanding the primary field variables of each order as the Fourier series functions in the circumferential direction, and interpolating these in the axial direction using the DRK interpolation, we can obtain the leading-order solutions of this analysis. The higher-order modifications can be obtained in a systematic manner, in which the solvability and normality conditions are used to eliminate secular terms and uniquely determine these modifications. Some 3D solutions of the natural frequencies of sandwich FGM cylinders and their corresponding through-thickness distributions of modal variables are given to demonstrate the performance of the asymptotic DRK-based meshless method
Finite Element Multi-mode Approach to Thermal Postbuckling of Functionally Graded Plates
Get PDFPostbuckling analysis of functionally graded ceramic-metal plates under temperature field is presented using finite element multi-mode method. The three-node triangular element based on the Mindlin plate theory is employed to account for the transverse shear strains, and the von-Karman nonlinear strain-displacement relation is utilized considering the geometric nonlinearity. The effective material properties are assumed to vary through the thickness direction according to the power law distribution of the volume fraction of constituents. The temperature distribution along the thickness is determined by one dimensional Fourier equations of heat conduction. The buckling mode shape solved from eigen-buckling analysis is adopted as the assumed mode function to reduce the degrees of freedom of nonlinear postbuckling equilibrium equations. The postbuckling response is obtained by solving the nonlinear equilibrium equations, and compared with the Newton- Raphson numerical results. The effects of boundary conditions, material gradient index and temperature distribution on postbuckling behavior are examined