Begell House Inc.
International Journal for Multiscale Computational Engineering
JMC
1543-1649
17
1
2019
MULTISCALE SEAMLESS-DOMAIN METHOD FOR NONPERIODIC FIELDS: NONLINEAR HEAT CONDUCTION ANALYSIS
1-28
Yoshiro
Suzuki
Tokyo Institute of Technology, Department of Mechanical Sciences and Engineering, Tokyo
152-8552, Japan
A multiscale numerical solver called the seamless-domain method (SDM) consists of macroscopic global analysis and
microscopic local analysis. Previous work presented a nonlinear solver using the SDM technique that does not couple these two analyses interactively. In addition, the practicality of this solver was verified only for use with periodic fields. In this work, we present another nonlinear SDM solver that couples the multiple scales completely interactively. We solve an example problem of a nonlinear heat conduction analysis of a nonperiodic field using the presented SDM, the standard finite difference method, and the conventional domain decomposition method (DDM). The target temperature field has thermal conductivity distribution that is nonuniform, nonperiodic, and has temperature dependency. This problem thus has material nonlinearity. The accuracy of the SDM solution is very high, and the root mean squared error in temperature is less than 0.044% of the maximum temperature in the field. In contrast, the error of the DDM is 0.10%–0.18%, which is larger than twice the error of the SDM. The finite difference method requires 7–36 times the computation time of the SDM to generate a solution as accurate as that of the SDM.
A FINITE-ELEMENT METHOD OF FLEXOELECTRIC EFFECTS ON NANOSCALE BEAM
29-43
Xu
Yang
School of Civil Engineering, Shandong University, Jinan, 250061, China
Yarong
Zhou
School of Civil Engineering, Shandong University, Jinan, 250061, China
Binglei
Wang
School of Civil Engineering, Shandong University, Jinan, 250061, China; State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi'an Jiaotong University, Xi'an 710049, China
Bo
Zhang
School of Civil Engineering, Shandong University, Jinan, 250061, China
Flexoelectricity is a linear coupling between the strain gradient and the electric polarization, which is present in all dielectric materials. Strain gradients cause flexoelectricity to be size-dependent, especially significant for nanoscale structures. However, strain gradients involve higher-order partial derivate of displacements which brings difficulties to the solution of flexoelectric problems. The effect of strain gradient elasticity was ignored in most previous works on
flexoelectricity. Thus, it is necessary to develop an effective numerical method that accounts for both strain gradient elasticity and flexoelectricity.We have developed a size-dependent finite-element model of a nanoscale Euler beam based on a reformulated strain gradient elasticity theory. The new model contains three independent material length scale parameters which capture the size effect. The developed C2 weak continuous element with two nodes has three degrees of freedom at each node. Using the Finite Element Method (FEM), with the Euler cantilever beam as an example, the effects of flexoelectricity and strain gradient elasticity on the beam have been investigated. The results were compared with those available in literature and an excellent agreement was achieved.
ASYMMETRIC NONLINEAR BENDING ANALYSIS OF POLYMERIC COMPOSITE ANNULAR PLATES REINFORCED WITH GRAPHENE NANOPLATELETS
45-63
R.
Gholami
Department of Mechanical Engineering, Lahijan Branch, Islamic Azad University, P.O. Box 1616, Lahijan, Iran
Reza
Ansari
Department of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran
This article reports the geometrically nonlinear bending response of polymeric composite annular plates reinforced with graphene platelets (GPLs) under transverse uniform and biharmonic loadings. The considered plates are embedded on
a Winkler-Pasternak elastic foundation. By considering a random orientation and a uniform dispersion for the GPL
nanofillers, four types of distribution patterns are assumed for the GPLs along the thickness of the plate. The modified
Halpin-Tsai (MHT) technique and the rule of mixture are adopted to obtain the effective material properties of GPL-reinforced polymeric nanocomposites (GPL-RPNCs). The discretized governing equations including the geometric
nonlinearity are expressed in their weak form using the principle of virtual work, variational differential quadrature (VDQ) method, and Reddy's plate theory. For the demonstration of the symmetric and asymmetric bending behaviors of GPL-RPNC annular plates and influence of different parameters, the pseudo-arc length algorithm is coupled with the modified Newton-Raphson approach to plot the maximum deflection of considered plate versus the amplitude of applied loading.
ENHANCEMENTS TO THE INHERENT STRAIN METHOD FOR ADDITIVE MANUFACTURING ANALYSIS
65-81
Qiukai
Lu
Altair Engineering, Austin, TX, 78757
Erwan
Beauchesne
Altair Engineering, Austin, TX, 78757
Tadeusz
Liszka
Altair Engineering, Austin, TX, 78757
Analysis of stress and deformation of parts produced during additive manufacturing (AM) process is critical to predict
potential defects during the process and quality of parts produced. However, the complex physics of the process and
vastly different scales of the analysis require long computations on powerful computers (including exa-scale computing), which makes accurate analysis impractical. Simplified approach in published literature typically utilizes extrapolation of inherent strain theory developed for analysis of welding processes, however, results are often unsatisfactory as the AM process and geometry of produced parts is much more complex. Here we present generalization of the inherent strain into a two-level method, where the fine model (so-called mesoscale analysis) provides a whole family of inherent strain models, and the coarse model (macroscale) uses different values for inherent strain varying with location, surrounding geometry, and parameters of AM process.
FREE-VIBRATION ANALYSIS OF HELICALLY COILED CARBON NANOTUBES CONSIDERING NONLOCAL EFFECT USING CURVED-BEAM ELEMENTS
83-97
Seyede Zahra
Mohammadi
Department of Mechanical Engineering, Shiraz University, Shiraz, Iran
Mehrdad
Farid
Department of Mechanical Engineering, Shiraz University, Shiraz, Iran
In this paper a numerical method is proposed to study the free vibration of helically coiled carbon nanotubes considering the nonlocal effects. In this method, the governing equations are obtained using the spatial curved-beam theory based on Washizu's static model. In the equations of motion all displacement functions are defined at the centroid axis and the effects of rotary inertia and transverse shear deformation are included. Moreover, nonlocal theory of elasticity is used in 3D curved-beam modeling. Therefore, six coupled equations including stresses and their second derivatives are obtained which should be combined with six coupled partial differential equations of motion of the system. Finite element method is used to solve the resulting equations, numerically. Curved elements with three nodes and six degrees of freedom per node are used in this method. In order to verify the developed MATLAB code, the results obtained from
the proposed method by neglecting nonlocal effects are compared with those of ANSYS simulation. Besides, the effects of different boundary conditions and various parameters including helix radius, pitch, number of turns, and nonlocal parameter are studied.