Finite element -based simulation methods

Adhikari S (2011) A reduced spectral function approach for the stochastic finite element analysis. Comput Methods Appl Mech Eng 200 1804-1821 Au SK, Beck JL (2001) Estimation of small failure probabilities in high dimensions by subset simulation. Probab Eng Mech 16 263-277 Au SK, Beck JL (2003) Subset simulatimi and its application to seismic risk based on dynamic analysis. J Eng Mech (ASCE) 129 901-917... 

Numerical simulations on the parison formation can minimize machine setup times and tooling costs. Several research teams modeled the parison formation stage to predict the parison dimensions [1-6]. The results showed that the finite-element-based numerical simulation method can predict the parison dimensions with certain precision. Huang et al. [7, 8] utilized the artifieial neural networks (ANN) method to predict the diameter and thickness swell of the parison and showed that the ANN method can predict the parison dimensions with a high degree of precision. However, the parison formation simulations and... 

While most authors have used the finite-difference method, the finite element method has also been used—e.g., a two-dimensional finite element model incorporating shrinkable subdomains was used to de.scribe interroot competition to simulate the uptake of N from the rhizosphere (36). It included a nitrification submodel and found good agreement between ob.served and predicted uptake by onion on a range of soil types. However, while a different method of solution was used, the assumptions and the equations solved were still based on the Barber-Cushman model. 

Numerical micromagnetics, which may be based either on the finite difference or finite element method, resolve the local arrangement of the magnetization which arises from the interaction between intrinsic magnetic properties such as the magnetocrystalline anisotropy and the physical and chemical microstructure of the material. The numerical solution of the equation of motion also provides information on how the magnetization evolves in time. The time and space resolution of numerical micromagnetic simulations is in the order of nanometers and nanoseconds, respectively. 

Simulations of diffusion propagators based on a finite element method. J. Magn. Res., 161, 138-147. 

The pairwise Brownian dynamics method has several advantages over numerical methods based on Smoluchowski s [9] approach (e.g., finite element method), and we discuss these here. The primary advantage of the method is the ease of mathematical formulation even for cases involving complex reaction site geometries, hydrodynamic interactions, charge effects, anisotropic diffusion and flow fields. Furthermore the method obviates the need to solve complex diffusion equations to obtain the concentration field from which the rate constant is calculated in the Smoluchowski method. In contrast, the rate constant is obtained directly in the pairwise Brownian dynamics method. The effective rate constants for different reaction conditions may be obtained from a single simulation this is not possible using the finite element method. 

For the coarse estimation of extruder size and screw speed, simple mass and energy balances based on a fixed output rate can be used. For the more detailed design of a twin-screw extruder configuration it is necessary to combine implicit experience knowledge with simulation techniques. Theses simulation techniques cover a broad range from specialized programs based on very simple models up to detailed Computational Fluid Dynamics (CFD) driven by Finite Element Analysis (FEA) or Boundary Element Method (BEM). 

Hagslatt, H., Jonsson, B., Nyden, M., and Soderman, O. Predictions of pulsed field gradient NMR echo-decays for molecules diffusing in various restrictive geometries. Simulations of diffusion propagators based on a finite element method, /. Magn. Reson., 161,138, 2003. 

In the 1980s, a large number of laboratories developed Laplace equation solvers for use in current-distribution simulations. These procedures are normally based on boundary-element methods (BEM), finite-difference methods (FDM), or finite-element methods (FEM). For Laplace s equation, it is not clear that any particular method has an overwhelming advantage over the others. It is, however, clear that a large number of current distributions caimot be described by Laplace s equation. 

The methods developed in this book can also provide input parameters for calculations using techniques such as mean field theory and mesoscale simulations to predict the morphologies of multiphase materials (Chapter 19), and to calculations based on composite theory to predict the thermoelastic and transport properties of such materials in terms of material properties and phase morphology (Chapter 20). Material properties calculated by the correlations presented in this book can also be used as input parameters in computationally-intensive continuum mechanical simulations (for example, by finite element analysis) for the properties of composite materials and/or of finished parts with diverse sizes, shapes and configurations. The work presented in this book therefore constitutes a "bridge" from the molecular structure and fundamental material properties to the performance of finished parts. 

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