Modeling approaches stiffness

Despite its success, the embedded model approach still requires repeated solution of the process model (and sensitivities). For large processes or for processes that require the solution of rigorous underlying procedures, this approach can become expensive. Moreover, for stiff or otherwise difficult systems, this approach is only as reliable as the ODE solver. The embedded model approach also offers only indirect ways of handling time-dependent constraints. Finally, the optimal solution of this approach is only as good as its control variable parameterization, which often can only be improved by a priori information about the specific problem. Consequently, we now consider the simultaneous approach to (16) as an alternative to solution methods for (17). 

Based on these preliminary results, important questions on how filopodia interact with stiff topography and how the deformation of a filopodium occurs near the surface features have raised. To answer these questions, computational and modeling approaches become more powerful and effective in providing better visualization... 

Overall, other than underestimation of compressive strains, the MVLEM proves to be an effective modeling approach for the flexural response prediction of slender RC walls, as the model provides good predictions of the experimentally observed global and local responses, including wall lateral load capacity and lateral stiffness at varying drift levels, yield point, cyclic properties of the load-displacement response, rotations (average over the region of inelastic deformations), position of the neutral axis and tensile strains. 

Z. M. Huang, S. Ramakrishna (2000) Micromechanical modelling approaches for the stiffness and strength of knitted fabric composites A review and comparative study. Composites A 31,479. 

Ultrasound reflects from a layer of oil between two bearing surfaces. The response of the oil film can be modelled using a quasi-static spring model. The proportion of the wave reflected depends on the stiffness of the oil film and its acoustic properties. Experiments have shown this spring model approach to be valid for the thickness of oil films typically encountered in the operation of hydrodynamic bearings. 

In a real chain segment-segment correlations extend beyond nearest neighbour distances. The standard model to treat the local statistics of a chain, which includes the local stiffness, would be the rotational isomeric state (RIS) [211] formalism. For a mode description as required for an evaluation of the chain motion it is more appropriate to consider the so-called all-rotational state (ARS) model [212], which describes the chain statistics in terms of orthogonal Rouse modes. It can be shown that both approaches are formally equivalent and only differ in the choice of the orthonormal basis for the representation of statistical weights. In the ARS approach the characteristic ratio of the RIS-model becomes mode dependent. 

A theoretical approach is applied to elucidate the molecular conformations, associated flexibility, and dynamics of polylp-hydroxybenzoic acid) esters, pHB. Properties such as the radius of gyration and persistence length which are characteristic for the stiffness of a macromolecule are calculated on the basis of two different theoretical methods (a) Molecular dynamics and (b) the RIS model augmented by the more recent scheme for the matrix computations. The analysis of the results obtained by the latter method reflects a strong dependence on the choice of the structural parameters of the system. 

As an example, if only quasi-steady flow elements are used with volume pressure elements, a model s smallest volume size (for equal flows) will define the timescale of interest. Thus, if the modeler inserts a volume pressure element that has a timescale of one second, the modeler is implying that events which happen on this timescale are important. A set of differential equations and their solution are considered stiff or rigid when the final approach to the steady-state solution is rapid, compared to the entire transient period. In part, numerical aspects of the model will determine this, but also the size of the perturbation will have a significant impact on the stiffness of the problem. It is well known that implicit numerical methods are better suited towards solving a stiff problem. (Note, however, that The Mathwork s software for real-time hardware applications, Real-Time Workshop , requires an explicit method presumably in order to better guarantee consistent solution times.)... 

These relationships show that (i) if the copolymer approach is considered as a correct model, this means that the Fox-Loshaek relationship is only valid at low crosslink densities (as effectively found experimentally) (ii) The Fox-Loshaek constant is an increasing function of Tgi, e.g., of the chain stiffness, as effectively found. KFl varies from 6-10 K kg mol-1 for fully aliphatic to 50-60 K kg mol-1 for highly aromatic systems. Thus, it appears that both chain stiffness and crosslinking effects cannot be considered independent. The effect of crosslinking, represented for instance by (Tg—Tgi) in the Fox-Loshaek equation, is an increasing function of the chain stiffness. This dependence is taken into account in the approach based on the theory of conformational entropy (Di Marzio, 1964) and leads to... 

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