Begell House Inc.
International Journal for Multiscale Computational Engineering
JMC
1543-1649
11
4
2013
NAVIER SOLUTION FOR STATIC ANALYSIS OF FUNCTIONALLY GRADED RECTANGULAR MICROPLATES
309-318
H.
Farahmand
Department of Mechanical Engineering, Islamic Azad University of Kerman Branch, Kerman, Iran
M.
Mohammadi
Young Researchers and Elites Club, Kerman Branch, Islamic Azad University, Kerman, Iran
In this paper, bending analysis of thin functionally graded (FG) rectangular microplates based on the strain gradient theory is presented. Relying on strain gradient theory, flexural microplate theory is utilized to obtain the governing equations for FG flexural microplates, which include higher-order terms. It is assumed that the material properties of FG microplates vary through the thickness according to a power law function. Also, it is supposed that the microplate is simply supported along all edges; hence, the Navier solution is used to find the deflection of the microplate. Finally, based on the obtained closed form solution, effects of length scale parameters, material properties, and dimensions on the static response of flexural microplates are investigated in detail.
PSEUDO-MULTI-SCALE FUNCTIONS FOR THE STABILIZATION OF CONVECTION-DIFFUSION EQUATIONS ON RECTANGULAR GRIDS
319-331
Ali I.
Nesliturk
Department of Mathematics, Izmir Institute of Technology, 35430, Izmir, Turkey
Onur
Baysal
Department of Mathematics, Izmir Institute of Technology, 35430, Izmir, Turkey
We propose a finite element method of Petrov-Galerkin type for a singularly perturbed convection diffusion problem on a discretization consisting of rectangular elements. The method is based on enriching the finite-element space with a combination of multiscale and residual-free bubble functions. These functions require the solution of the original differential problem, which makes the method quite expensive, especially in two dimensions. Therefore, we instead employ their cheap, yet efficient approximations, using only a few nodes in each element. Several numerical tests confirm the good performance of the corresponding numerical method.
SIMULATION OF TRANSIENT CONJUGATE HEAT TRANSFER VIA A TEMPORAL MULTISCALE APPROACH
333-345
Benedicte
Baque
Onera − The French Aerospace Lab, F-92322 Chatillon, France
Marc
Errera
Onera − The French Aerospace Lab, F-92322 Chatillon, France
Arjen
Roos
Onera − The French Aerospace Lab, F-92322 Chatillon, France
Frederic
Feyel
Onera − The French Aerospace Lab, F-92322 Chatillon, France
This paper describes a numerical investigation of the transient temperature field in a solid with a conjugate heat transfer method. The basic approach is based on the strong partitioned coupling of a finite-volume Navier-Stokes solver and a finite-element heat conduction solver. The numerical model employs a quasidynamic algorithm in which the transient thermal field in the solid is coupled with a sequence of steady states in the fluid. Experimental results from a simple test case are compared to numerical simulations and they are found to correspond to within the experimental uncertainties. This model represents a contribution to the field of real-time transient heat loads in solids.
STOCHASTIC MODELING OF MACROMOLECULAR MOTIONS THROUGH POST ARRAYS
347-358
Yun-Bo
Yi
Department of Mechanical and Materials Engineering, University of Denver, Denver, Colorado 80208, USA
The dynamic motions of macromolecules through a microfluidic postarray system are simulated using a three-dimensional stochastic finite element approach. The effects of molecular conformation on the time for a macromolecule to move across the system are investigated. The analyses are first performed on disklike geometries and then extended to a representative carbonic anhydrase (CA) macromolecule model consisting of elastically deformable beam networks. The model predicts that smaller molecules typically take less time to pass through the post array, and that for stiff materials the time inversely increases with the aspect ratio of molecules due to the conformational changes in collisions between the molecules and the obstacles. In addition, the dynamic responses of molecules are highly stochastic. The work has potential applications in designing functional microfluidic devices for separation and purification of macromolecules such as plasmid DNA.
GLOBAL SENSITIVITY ANALYSIS FOR A MICROPOLAR STOKES FLOW PROBLEM
359-368
Daniel
O'Malley
Department of Earth, Atmospheric, and Planetary Sciences, Purdue University West Lafayette, Indiana 47907, USA
John H.
Cushman
Purdue University West Lafayette Indiana UNITED STATES
L. M.
Flesch
Department of Earth, Atmospheric, and Planetary Sciences, Purdue University West Lafayette, Indiana 47907, USA
Micropolar field theories provide a systematic approach to modeling traditional materials like elastic bodies or viscous fluids that have microstructure. The downside to accounting for the behavior on the smaller scale is the introduction of many new parameters into the field equations. The difficulty of handling these new parameters can be mitigated by performing a sensitivity analysis to determine which parameters have the greatest impact on the solutions to the field equations. The sensitivity of an incompressible micropolar Stokes fluid to variations in the viscosity coefficients and boundary value of the microinertia is examined. This particular choice of field equations is motivated by an application of micropolar field theories to the deformation of the continental lithosphere, but the same approach can be used for other micropolar equations modeling solids or other types of fluids.
A NEW MULTISCALE FINITE ELEMENT METHOD FOR MECHANICAL ANALYSIS OF PERIODIC HETEROGENEOUS COSSERAT MATERIALS
369-387
Zhaoqian
Xie
State Key Laboratory for Structural Analysis of Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian 116024, P. R. China
Hongwu
Zhang
Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, P. R. China
A new multiscale finite element method is developed for mechanical analysis of periodic heterogeneous Cosserat materials. The main idea of the method is to numerically construct the multiscale base functions to capture the small-scale features of the coarse elements. Considering the existence of rotation in the Cosserat materials, specified boundary conditions of the base functions for extended multiscale finite element method (EMsFEM) are developed based on the relationship between transverse displacement and rotation (slope) of the two-node beam element, and the corresponding periodic boundary conditions are developed. By adopting both kinds of boundary conditions, the numerical base functions for displacement and rotation fields of Cosserat materials are constructed, respectively, to establish the relationship between the macroscopic deformation and the microscopic stress and strain. It is shown that the proposed method does not require the estimation of the overall material parameters of the heterogeneous Cosserat materials as the general homogenization methods. Numerical examples are carried out to verify the validity and efficiency of the developed multiscale finite element method.
BUCKLING OF FGM TIMOSHENKO MICROBEAMS UNDER IN-PLANE THERMAL LOADING BASED ON THE MODIFIED STRAIN GRADIENT THEORY
389-405
R.
Ansari
Department of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran
R.
Gholami
Department of Mechanical Engineering, Lahijan Branch, Islamic Azad University, P.O. Box 1616, Lahijan, Iran
M. Faghih
Shojaei
Department of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran
V.
Mohammadi
Department of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran
S.
Sahmani
Department of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran
According to the theory of thermal elasticity mechanics, thermal buckling characteristics of microbeams made of functionally graded materials (FGMs) are presented. The material properties of FGM microbeams are considered to be graded in the thickness direction on the basis of the MoriTanaka homogenization scheme. Based on the strain gradient elasticity theory, a size-dependent elastic beam model within the framework of the Timoshenko beam theory is developed containing three internal material length scale parameters to interpret size effect. By using Hamilton's principle, the higher-order governing differential equations of motion and related boundary conditions are derived. Afterward, the generalized differential quadrature (GDQ) method is employed to discretize the governing differential equations along various end supports and then the critical thermal buckling loads of FGM microbeams with three commonly used sets of boundary conditions are determined. The applicability of the present nonclassical beam model to predict thermal buckling behavior of FGM microbeams is established via various numerical results. It is found that the difference between thermal buckling of microbeams subjected to the uniform, linear, and nonlinear temperature distributions is more significant corresponding to the higher values of material property gradient index.