Computer simulation finite-element method

Mechanical properties of PNCs can also be estimated by using computer modeling and simulation methods at a wide range of length and time scales. Seamless movement from one scale to another, for example, from the molecular scale (e.g., MD) and microscale (e.g., Halphin-Tsai) to macroscale (e.g., finite element method, FEM), and the combination of scales (or the so-called multiscale methods) is the most important prerequisite for the efficient transfer and extrapolation of calculated parameters, properties, and numerical information across length scales. 

See Ref. 1 in Chap. 3. Typical papers from Annual Reviews include A. Leonard, Computing three-dimensional incompressible flows with vortex elements, Annu. Rev. Fluid Mech. 17, 523-59 (1985) M. Y. Hussaini and T. A. Zang, Spectral methods in fluid dynamics, Annu. Rev. Fluid Mech. 19, 339-67 (1987) R. Glowinski and O. Pironneau, Finite element methods forNavier-Stokes equations, Annu. Rev. Fluid Mech. 24, 167-204 (1992) R. Scardovelli and S. Zaleski, Dierect numerical simulation of free-surface and interfacial flow, Annu. Rev. Fluid Mech. 31, 567-603 (1999). 

Zhang X.Y.2001. Some Problem on Simulation of Casing damage by Finite Element Method. Natural Gas Industry. 21(1) pp.62-65 Lian Z.H., Zhao G.Z., Zhang X.P. 1998. A Study on Computer Emulation Software for Casing Failure. Natural Gas Industry. 18(2) pp.35-38... 

The use of numerical finite element methods to simulate the dynamic behaviour of structures used to be mostly the provision of academic researchers. However, the very considerable increase in cheap computing power has resulted in wide-scale industrial use, quite often as a design tool. Dynamic FE codes have also become user-friendly and very sophisticated in modelling complex geometries and material... 

With the recent advance in computational technology, efforts have also been devoted to numerical simulations of drag reduction, such as for viscoelastic polymers via constitutive equations and finite element methods [Dimitropoulos et al., 1998 Fullerton and McComb, 1999 Mitsoulis, 1999 Beris et al., 2000 Yu and Kawaguchi, 2004] and for DR flow with surfactant additives via second-order finite-difference direct numerical simulation (DNS) studies [Yu and Kawaguchi, 2003, 2006]. 

Geometric tolerances are also used in design to limit the form deviations. Classical tolerance models are not yet satisfactory in simulating the effect of the form deviations on part geometry. The modal tolerancing method allows to decompose any real defects of any discretized feature in the natural mode shapes with an unambiguous mathematical language. The finite element method is used to compute those shapes, and... 

Numerical methods are a family of mathematical techniques for solving complicated problems approximately by the repetition of the elementary mathematical operations (+, —, x, H-). In the past, numerical solution of a PDE was extremely time consuming, requiring many man-hours of tedious calculation. However the utility of numerical methods has greatly increased since the advent of programmable computers. In the field of electrochemistry, two main techniques are used for simulation purposes the finite difference method and the finite element method, though the former is by far the more popular and will be used exclusively throughout this book. 

Computational fluid dynamics (CFD) based on the continuum Navier-Stokes equations Eq. 2 has long been successfully used in fundamental research and engineering design in different fluid related areas. Namrally, it becomes the first choice for the simulation of microfluidic phenomena in Lab-on-a-Chip devices and is still the most popular simulation model to date. Due to the nonlinearity arising from the convention term, Eq. 2 must be solved numerically by different discretization schemes, such as finite element method, finite difference method, finite volume method, or boundary element method. Besides, there are a variety of commercially available CFD packages that can be less or more adapted to model microfluidic processes (e.g., COMSOL (http //www.femlab.com), CFD-ACE+ (http // www.cfdrc.com), Coventor (http //www. coventor.com), Fluent (http //www.fluent.com), and Ansys CFX (http //www.ansys.com). For majority of the microfluidic flows, Re number is... 

Kamiadakis and Beskok [6] developed a code H Flow with implementation of spectral element methods. They employed both the Navier-Stokes (incompressible and compressible) and energy equations in order to compute the relative effects of compressibility and rarefaction in gas microflow simulations. In addition, they also considered the velocity slip, temperature jump, and thermal creeping boundary conditions in the code Flow. The spatial discretization of fi Flow was based on spectral element methods, which are similar to the hp version of finite-element methods. A typical mesh for simulation of flow in a rough micro-channel with different types of roughness is shown in Fig. 1. The two-dimensional domain is broken up into elements, similar to finite elements, but each element employs high-order interpolants based on... 

FIGURE 1.5 Multiscale modeling in computational pharmaceutical solid-state chemistry. Here DEM and FEM are discrete and finite element methods MC, Monte Carlo simulation MD, molecular dynamics MM, molecular mechanics QM, quantum mechanics, respectively statistical approaches include knowledge-based models based on database analysis (e.g., Cambridge Structure Database [32]) and quantitative structure property relationships (e.g., group contributions models [33a]). 

Mesoscale models have predominately utilized the finite-difference and (for advection), the semi-Lagrangian approaches. A few groups have applied the finite-element method, but its additional computational cost has limited its use. The spectral method, which is most valuable for models without boundaries and for simulation without sharp spatial gradients, has not generally been used since mesoscale models have lateral boundaries. 

Ke Twords computer aided engineering (CAE), computer simulation, fiber orientation prediction, fiber orientation modelling, fiber reinforced thermoplastics, finite difference method, finite element method (FEM), flow, glass fiber reinforcement, injection molding, mold filling analysis, warpage. 

Ten Thije, R., Akkerman, R., Huetink, J., 2007. Large deformation simulation of anisotropic material using an updated Lagrangian finite element method. Comput. Methods Appl. Mech. Eng. 196, 3141-3150. 

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