Variable continuous versus discrete

Continuous versus Discrete Models The preceding discussion has focused on systems where variables change continuously with... 

Note that if Bn is zero, then T13 and T23 are also zero, so Equation (5.81) reduces to the specially orthotropic plate solution. Equation (5.65), if D11 =D22- Because Tn, T12, and T22 are functions of both m and n, no simple conclusion can be drawn about the value of n at buckling as could be done for specially orthotropic laminated plates where n was determined to be one. Instead, Equation (5.81) is a complicated function of both m and n. At this point, recall the discussion in Section 3.5.3 about the difference between finding a minimum of a function of discrete variables versus a function of continuous variables. We have already seen that plates buckle with a small number of buckles. Consequently, the lowest buckling load must be found in Equation (5.81) by a searching procedure due to Jones involving integer values of m and n [5-20] and not by equating to zero the first partial derivatives of N with respect to m and n. 

Continuous scans of modulus versus temperature utilizing the DuPont Dynamic Mechanical Analyzer (DMA) has provided a comparison of the high temperature service capabilities of radiation-cured experimental formulations of a vinyl-modified epoxy resin. Shell Epocryl-12. These scans were compared to data obtained when the same materials were applied as adhesives on aluminum test panels, radiation-cured with an electron beam, and lap shear strength tested at discrete temperatures. The DMA instrument utilizes a thin rectangular specimen for the analysis, so specimens can be cut from blocks or from flat sheets. In this case the specimens were cured as sheets of resin-saturated graphite-fibers. The same order of high temperature stability was obtained by each method. However, the DMA method provided a more complete characterization of temperature performance in a much shorter test time and thus, it can be very useful for quick analyses of formulation and processing variables in many types of materials optimization studies. The paper will present details of this study with illustrations of the comparisons. 

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