Finite-element based program

These electrodes can be tested by appropriate software as SIMION [31] or other finite-element based programs. The suitability of the electrodes can be evaluated also by calculating their ability to store ions, in comparison with the ideal quadru-polar hyperboloidal geometry [32], to which the designers of micro traps aspire, and by dedicated experiment. 

Based on the shapes of the responses to step changes in controller output, and reasoning from the physical configuration of the extruder barrel, a reduced order dynamic model of the process was postulated. One can think of the Topaz program as order 80 (the number of nodes in the finite element subdivision), and the reduced model of order 4 (the number of dynamic variables). The figure below illustrates the model. 

The advantages of this type of system are obvious the pore space is of sufficient complexity to represent any natural or technical pore network. As the model objects are based on computer generated clusters, the pore spaces are well defined so that point-by-point data sets describing the pore space are available. Because these data sets are known, they can be fed directly into finite element or finite volume computational fluid dynamics (CFD) programs in order to simulate transport properties [7]. The percolation model objects are taken as a transport paradigm for any pore network of major complexity. 

The GRM using the generalized Maxwell-Stefan equations has no closed-form solutions. Numerical solutions were calculated using a computer program based on an implementation of the method of orthogonal collocation on finite elements [29,62,63]. The set of discretized ordinary differential equations was solved with the Adams-Moulton method, implemented in the VODE procedure [64]. The relative and absolute errors of the numerical calculations were 1 x 10 and 1 x 10 , respectively. 

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). 

There are a number of ray tracing programs available either based on geometry (e.g. Hubbard and Pantos (1983), Svensson and Nyholm (1985)) or including also finite element analysis routines to simulate thermal heating and distortion of optical elements (Gerritsen, pers. comm.). 

The numerical code used is the finite element program CODE BRlGHT. It is based on a mathematical formulation that combines an already existent thermo-hydro-mechanical formulation (Olivella et al., 1995) with the reactive transport equations in a fully coupled way (Guimaraes, 2002). 

The strength characteristics can be calculated with finite element methods (FEMs). Besides stress-strain analyses, thermodynamic and fluid dynamic tests can be carried out. Preprocessors enable automated net generation based on the initial geometric model. Most CAD systems have interfaces for common FEM programs (e.g., NASTRAN, ANSYS) or have their own equation solver for FEM tests. Based on the substantial data resulting from an FEM test, it is necessary for postprocessing of results. The results are then portrayed in deformation plots, color-coded presentations of the stress-strain process, or animations of the deformation. 

Since little damage was observed within the laminate in the course of the experiment, it was assumed that the diffusion process in the laminate essentially obeyed Tick s law given by equation [12.3]. A two-dimensional plane strain finite element model of the laminate was generated and the NOVA-3D finite element program was used to solve for the moisture uptake and stresses within the laminate. Based on characterization test data, the temperature dependent through-thickness diffusivity definition used in this analysis is given by ... 

The calculation methods described here have been somewhat simple it has however to be considered that, when a more accurate evaluation is warranted, finite element methods exist which are capable of modelling the behaviour of the soil-structure. The use of these programs has been proven essential when the economic burden due to the use of simpler and more conservative methods (e.g. those based on equivalent masses and springs) is not considered acceptable or when special effects have to be calculated, such as the mutual interaction between adjacent buildings. 

Software analysis programs based on stress-wave theory (Wang et al., 1990) or finite-element methods (Kalsi etal.,1987) can be used to predict and optimize jar placement in the drill string and physical performance measures. From jar input including size and overpuU, these programs can produce output on impact... 

---