Finite element method, theoretical

Further details of the BB, sometimes referred to as Ladyzhenskaya-Babuska-Brezi (LBB) condition and its importance in the numerical solution of incompressible flow equations can be found in textbooks dealing with the theoretical aspects of the finite element method (e.g. see Reddy, 1986), In practice, the instability (or checker-boarding) of pressure in the U-V-P method can be avoided using a variety of strategies. 

Fig. 6.27 Comparison between experimental pressure profile for plasticized thermoplastic resin (34) and theoretical pressure profiles for n — 1 and n — 0.25 calculated by Kiparissides and Vlachopoulos (35). The theoretical curves were calculated both by finite element method and analytically by way of Gaskell type models, as discussed in this section, giving virtually identical results. [Reprinted by permission from C. Kiparissides and J. Vlachopoulos, Finite Element Analysis of Calendering, Polym. Eng. Set, 16, 712-719 (1976).]...

In this paper we shall explain how it is possible to determine theoretically y, ) giving a few technical details concerning a recently introduced method which exploits Monte Carlo within a Finite Element Methods approach (MC-FEM). After applying such MC-FEM method to intermixed Ge pyramids of different aspect ratios, we shall show how the steepness of the island facets influences the SiGe distribution. 

From the standpoint of the continuum simulation of processes in the mechanics of materials, modeling ultimately boils down to the solution of boundary value problems. What this means in particular is the search for solutions of the equations of continuum dynamics in conjunction with some constitutive model and boundary conditions of relevance to the problem at hand. In this section after setting down some of the key theoretical tools used in continuum modeling, we set ourselves the task of striking a balance between the analytic and numerical tools that have been set forth for solving boundary value problems. In particular, we will examine Green function techniques in the setting of linear elasticity as well as the use of the finite element method as the basis for numerical solutions. 

The theoretical prediction of the leakage current requires the solution of Laplace s equation and a closed-form solution for an arbitrary geometry is not straight-forward. The finite-element method (1 0) can be used to obtain a numerical solution to Laplace s... 

At about the same time, another detailed theoretical study was presented with intended applications to the acceptor spectrum in germanium and GaAs up to relatively large values of B parallel to the three main crystal orientations [128]. Considering the VB s-o splitting in these crystals, the ITV VB was disregarded so that the calculations cannot be transposed to acceptors in silicon. The numerical method (the matrix method ) used to determine the eigenvalues in this study is non-variational and different from the finite-element method of Said et al. (ref. 51 in Chap 5). The results of these calculations will also be compared later with the experimental observations. 

The role of resonances was in some sense verified by a study prototype three-body scattering reaction F + H2 — HF(v, J) + H problem[8]. Recent experimental as well as theoretical results indicate that resonances play a very important role in this reaction [9]. We have previously developed methods by which scattering cross sections can be computed from the properties associated with resonant states[19, 28, 29, 30]. Problems like the fluorine hydrogen collision encourage us to come back and combine these methods with our current 3-D finite element method in order to study the influence of intermediate resonant states FH2 (v, J, K) in... 

Fujinawa, K. 1991. Theoretical studies on two-phase heat conduction in saturated porous media using the finite element method - studies on heat transfer in porous media (/). Trans. JSIDRE 152 pp.83-90. 

The validity conditions for the reduced method are currently rather vague and a theoretical framework outlining the exact validity conditions is missing. Despite this uncertainty, the reduced method offers a huge advantage over the full finite element method considering the enormous difficulties and cost in obtaining the full constitutive laws. 

ABSTRACT We are working on non-destructive evaluation of metal quality by the electric conductivity. We use contactless method with eddy currents to probe the metal piece. Here we are testing and verifying the theoretical methods for later use in practical algorithms in fast metal conductivity evaluation. In this particular work we compare the basic eddy current theory of coil impedance with the same scenario modeled with Finite Element Method (FEM). We foimd very good correlation between the theory and Finite Element Method below 2 kHz. 

These results allow us to use the theory for practical applications in a very wide frequency range in the infinite plate scenario, where the measured metal sample is much larger than the coil. For smaller coil-size metal samples we can safely use the theoretical results only on lower frequencies below 2 kHz. For higher frequencies the theoretical methods as well as the model in Finite Element Method have to be investigated and possible reasons for divergence found before proper confidence in these methods can be attained. 

In their theoretical studies, Bogen et al (1980) assumed an initially spherical membrane model for the infarcted LV. Employing a finite element method, it was possible to obtain end diastolic and end systolic pressure-volume curves. From these P-V curves, the effects of infarct size and infarct stiffness on the... 

The experimental and theoretical studies are completed by the application of the finite element method (FEM) for numerical analysis of fracture processes. By that approach the region surrounding the crack tip can be approximately represented by an equivalent system of discrete elements. A simple example shown in Figure 10.8 is partly based on work published by Petersson (1981). The density of the mesh for finite elements, their shape (e.g. 

A good understanding of the process of adhesion from the mechanics viewpoint and the predictive capability for structural failures associated with adhesive bonding requires realistic theoretical analysis methods to determine stress distributions in the joint. The finite-element method is the most powerful analysis tool that can be used to determine stress and displacement fields in complicated structures. 

A review of the literature reveals that previous finite-element analyses of adhesive joints were either based on simplified theoretical models or the analyses themselves did not exploit the full potential of the finite-element method. Also, several investigations involving finite-element analyses of the same adhesive joint have reported apparent contradictory conclusions about the variations of stresses in the joint.(24,36) while the computer program VISTA looks promising (see Table 1), its nonlinear viscoelastic capability is limited to Knauss and Emri.(28) Recently, Reddy and Roy(E2) (see also References 37 and 38) developed a computer program, called NOVA, based on the updated Lagrangian formulation of the kinematics of deformation of a two-dimensional continuum and Schapery s(26) nonlinear viscoelastic model. The free-volume model of Knauss and Emri(28) can be obtained as a degenerate model from Schapery s model. 

At present, research on polymers modified with inorganic whiskers focuses mainly on mechanical performance analysis and further theoretical analysis is relatively rare. In recent years, the finite element method has been widely used in such studies, which can provide a necessary theoretical basis for the micro-structure design of material and macro performance improvement. 

Jia et al. analyzed the influence of SiC whiskers with different L/D ratios on the stress distribution of a SiC resin composite material under a certain SiC whisker volume ratio by using the finite element method on the basis of the axisymmetric model of a resin matrix composite material reinforced by single orientation whiskers, and provided a theoretical basis for the optimal design of a whisker-reinforced composite material. 

The analysis was performed using the finite-element method. The results obtained by this technique are compared with the results for the same problem solved by a theoretical analysis based on classical method. 

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