Finite element analysis description

The above problems of fabrication and performance present a challenging task of identification of the governing material mechanisms. Use of nonlinear finite element analysis enables close simulation of actual thermal and mechanical loading conditions when combined with measurable geometrical and material parameters. As we continue to investigate real phenomena, we need to incorporate non-linearities in behavior into carefully refined models in order to achieve useful descriptions of structural responses. 

We present the major results established in the description of crazing and the recent developments in this field. Crazing has been investigated within continuum or discrete approaches (e.g., spring networks or molecular dynamics calculations to model the craze fibrils), which have provided phenomenological or physically based descriptions. Both are included in the presentation of the crazing process, since they will provide the basis for the recent cohesive surface model used to represent crazing in a finite element analysis [20-22],... 

R. L. Williamson, B. H. Rabin and J. T. Drake, "Finite Element Analysis of Thermal Residual Stresses at Graded Ceramic-Metal Interfaces, Part I Model Description and Geometrical Effects," /. Appl. Phys., 74 [2] 1310-1320 (1993). 

The models used for Eq. 4.3 may range from simple to complicated. Most of these functions are already known from system design and from the detailed design of the sensing element (see Section 4.1.3). If there are no analytical models available or if the physical relationships are too complicated for analytical description, finite element analysis, network-type analysis, or empirical studies need to be used to obtain the relationships summarized in Eq. 4.3. 

The final example involves fracture mechanics-finite element analysis of the double cantilever beam (nontapered) specimen (see Fig. 10 as well as the figures and descriptions in ASTM D-3433). The finite element analysis was very much as outlined above, leading to Eqs. (8) through (11). These results were compared with the equations in Section 11.1.1 of D-3433 (Eq. (7) in this chapter). Except for the longest cracks (i.e., very large a in Fig. 10), the FEM-determined ERR differed appreciably from the Gc value determined from Eq. (7). These differences might be attributed to the fact that the derivation of Eq. (7), similar to that for Eq. (5), assumes ideal cantilever boundary conditions at the point x = a. 

Figure 2 (a) Schematic compressive stress-strain curves for PP foam, (b) Schematic description of the numerical foam model, (c) Loading and imloading behavior of the foetm skeleton, (d) Comparison of experimental data and finite-element analysis result. 

The chapter includes brief descriptions of the analysis modules, ZEUS-NL and Vec-Tor2, as well as the simulation coordinator program UI-SIMCOR (Kwon et ah, 2005), that was used to combine these analysis tools. The modeling details for the 54-story dnal-system high-rise structure used as the reference implementation are presented including the techniques used to model the interface between the two structural models. The influence of different interface assumptions on predicted response is also examined. Using the selected interface boundary conditions, comprehensive comparisons between and discussions of the predicted static and dynamic responses by the MDFEA and by a conventional finite element analysis are presented. 

For analyzing real heart geometry, the finite element models are definitely the best tools. The accuracy of the computed results by the finite element analysis is only limited by (1) the geometric description of the heart, (2) the loading and boundary conditions, (3) material properties of the cardiac components, and (4) the available computer hardware and software for finite element calculations. 

The underlying Finite Volume Method divides the system geometry into small (linked) partial volumes of the same magnitude analog to the well-known finite elements in FEA (Finite Element Analysis). The differential equations that describe the flow are converted in this way into difference equations (integrals to be summed). These can then be solved as a linear equation system using a high performance Solver. If this calculation is repeated for each time step, the result is a description of the time-dependent transient flow. 

With the increased computational power of today s computers, more detailed simulations are possible. Thus, complex equations such as the Navier—Stokes equation can be solved in multiple dimensions, yielding accurate descriptions of such phenomena as heat and mass transfer and fluid and two-phase flow throughout the fuel cell. The type of models that do this analysis are based on a finite-element framework and are termed CFD models. CFD models are widely available through commercial packages, some of which include an electrochemistry module. As mentioned above, almost all of the CFD models are based on the Bernardi and Verbrugge model. That is to say that the incorporated electrochemical effects stem from their equations, such as their kinetic source terms in the catalyst layers and the use of Schlogl s equation for water transport in the membrane. 

Numerical Calculation of Two-Dimensional Equilibrium Shapes. To go beyond the relative simplicity of the set of shapes considered in the analysis presented above it is necessary to resort to numerical procedures. As a preliminary to the numerical results that will be considered below and which are required when facing the full complexity of both arbitrary shape variations and full elastic anisotropy, we note a series of finite-element calculations that have been done (Jog et al. 2000) for a wider class of geometries than those considered by Johnson and Cahn. The analysis presented above was predicated on the ability to extract analytic descriptions of both the interfacial and elastic energies for a restricted class of geometries. More general geometries resist analytic description, and thus the elastic part of the problem (at the very least) must be solved by recourse to numerical methods. 

CODE BRIGHT is a finite element code for the simulation of THM problems in geological media. It was initially developed for the analysis of those problems in saline media (Olivella et al, 1996), but it has been extended to cope with THM behaviour of other tnaterials. In fact that code has been used in recent years to analyse THM problems in the context of radioactive waste disposal (Gens et al, 1995 Gens et al, 1998 Gens Olivella, 2000). A brief description of the main features of the code is included here for consistency. 

The analysis method used in the SASSI computer program is the flexible volume method. This method is formulated in the frequency domain using the complex frequency response method and the finite element technique. The following list represents a brief description of the features available in the SASSI computer program ... 

For static and (structural) dynamic analysis, for determination of eigenfre-quencies and eigenmodes, several different commercial tools exist such as NASTRAN, ABAQUS or ANSYS. Some of them are also able to handle actuators and piezoelectric materials, and also to carry out some types of model reduction techniques. Nevertheless, specific techniques might have to be established by the user via accessing the modal data base. These data are then also used to set up a modal or otherwise condensed state-space representation possibly including specific actuator and sensor models. A description of the transformation of finite-element models from ANSYS to dynamic models in state space form in MATLAB can be found in [20]. 

The methods discussed earlier are applied to the seat-occupant-restraint system of an aircraft. A description of a computer-aided analysis environment, including a multibody model of the occupant and a nonlinear finite element model of the seat, is provided, which can be used to re-construct variety of crash scenarios. These detailed models are useful in studies of the potential human injuries in a crash environment, injuries to the head, the upper spinal column, and the lumbar area, and also structural behavior of the seat. The problem of reducing head injuries to an occupant in case of a head contact with the surroundings (bulkhead, interior walls, or instrument panels), is then considered. The head impact scenario is re-constructed using a nonlinear visco-elastic type contact force model. A measure of the optimal values for the bulkhead compliance and displacement requirements is obtained in order to keep the possibility of a head injury as little as possible. This information could in turn be used in the selection of suitable materials for the bulkhead, instrument panels, or interior walls of an aircraft. The developed analysis tool also allows aircraft designers/engineers to simulate a variety of crash events in order to obtain information on mechanisms of crash protection, designs of seats and safety features, and biodynamic responses of the occupants as related to possible injuries. 

A similar process can be applied to all the other aspects associated with the design environment until an adequate taxonometric description of the Real World Problem is achieved. At this stage we are ready to enter the threads analysis of the next section which addresses the real decomposition of the finite element process. 

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