Elasticity analysis

The theory relating stress, strain, time and temperature of viscoelastic materials is complex. For many practical purposes it is often better to use an ad hoc system known as the pseudo-elastic design approach. This approach uses classical elastic analysis but employs time- and temperature-dependent data obtained from creep curves and their derivatives. In outline the procedure consists of the following steps ... 

The appropriate formula is selected from classical elastic analysis. 

The appropriate formula from classical elastic analysis is... 

When required, combined with the use of computers, the finite element analysis (FEA) method can greatly enhanced the capability of the structural analyst to calculate displacement and stress-strain values in complicated structures subjected to arbitrary loading conditions. In its fundamental form, the FEA technique is limited to static, linear elastic analysis. However, there are advanced FEA computer programs that can treat highly nonlinear dynamic problems efficiently. 

Resistance-Deflection Function. The resistance-deflection function establishes the dynamic resistance of the trial cross-section. Figure 4a shows a typical design resistance-deflection function with elastic stiffness, Kg (psi/in), elastic deflection limit, Xg (in) and ultimate resistance, r.. (psi). The stiffness is determined from a static elastic analysis using the average moment of inertia of a cracked and uncracked cross-section. (For design... 

The spot demand elasticity analysis algorithm has also been analyzed and presented in the sales model (see table 24). Two products in two sales locations with a significant number of customers are analyzed with respect to spot sales elasticity customer demands are ranked by price and the price-quantity function of cumulated spot sales quantities. The average price is determined over 12 periods. Fig. 83 shows the results of the elasticity analysis. 

Without having conducted a full elasticity analysis across the entire portfolio, the analysis helps to prove market perceptions such as a higher elasticity exist in one market compared to another market or comparing elasticity between products being perceived to have a different elasticity. The statistical quality of the linear regression analysis in selected months is considered as good in terms of the number of customers involved and the R-squared value proving the applicability of the approach. 

Elasticity analysis algorithm as pragmatic approach to determine average price elasticity of aggregated demand forecasts that analyzes underlying customer price-quantity demand. 

Pavia H, Toth GB, Aberg P (2002) Optimal defense theory elasticity analysis as a tool to predict intraplant variation in defenses. Ecology 83 891-897 Peckol P, Krane JM, Yates JL (1996) Interactive effects of inducible defence and resource availability on pholorotannins in the North Atlantic brown alga Fucus vesiculosus. Mar Ecol Prog Ser 138 209-217... 

Whitney, J.M. (1985). Elasticity analysis of orthotropic beams under concentrated loads. Composites Sci. Technol. 22, 167-184,... 

The density of chemicaUy-blown LDPE foam was altered by varying the amount of blowing agent, degree of crosslinking of the polymer, and the foam expansion temperature. A theory was proposed for the equilibrium density, based on the gas pressures in a Kelvin foam structure, and a rubber-elastic analysis of the biaxial stretching of the cell faces. 20 refs. 

S.4.3.2 Strength of Laminate Composites. The strength of angle-ply laminates can be calculated using the same type of elastic analysis as for modulus in the previous section. The strains produced in the laminate by a given set of applied stresses are first calculated, using the computed laminate moduli. Stresses corresponding to these strains are then calculated for each layer of the laminate. These stresses are then expressed in terms of stresses parallel and normal to the fibers, and the combination of stresses... 

Gerbal, F., Chaikin, P., Rabin, Y., and Prost, J. (2000a). An elastic analysis of Listeria monocytogenes propulsion. Biophys.J. 79, 2259-2275. 

Consider an elliptical hole characterized by a semimajor axis of length la and semiminor axis of length lb. The result of a detailed elastic analysis of a plane strain geometry with remote loading parallel to the semiminor axis (call this direction y) is an enhancement of the local stresses well above the remote value of (To- The key point that emerges from an analysis of the stresses associated with an elliptical hole are summarized in schematic form in fig. 2.12. In particular, the maximum value of the stress Oyy is given by... 

The residual stress effect is considered by the separate analysis model and unified analysis model, and the results are shown in figures 3(a) and (b). Figure 3(a) corresponds to the elastic analysis and it is seen that the separate analysis model and unified analysis model give the same resultant stress Figure 3(b) corresponds to the eltistic-plastic analysis tmd it is seen that the resultant stresses found from the two models are different. This is because in the elastic analysis the two responses in phase I and phase II are both linear and the resultant response can be obtained from a direct superposition of the two separate ones. In the elastic-plastic analysis, however, the two separate responses are both nonlinear and the separate analysis model based on the direct superposition of the two separate responses is no longer suitable. 

In the elastic analysis, the separate analysis model and the unified analysis model give the same result because the two responses of the cooling and working phases are both linear. In this case, the direct superimposition is suitable. 

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