By Zhi Zong
The publication used to be very fascinating for me as my PhD thesis are hooked up with differential quadrature (DQ). It includes rather new informations approximately improveing of the DQM. It base on authors articles from numerous final years. The unfavourable is that the articles are shorten, so occasionally you need to search for them within the booklet info base to discover info. occasionally it isn't so transparent clarify from the place the autors receive there formulation [there will be extra references to literature] - occasionally it really is attainable to discover theorems that healthy even beter to the topic. besides i'm more than pleased to have this e-book because it supplies me much convenient informations approximately instructions of the DQ thought advance.
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Additional info for Advanced Differential Quadrature Methods (Chapman & Hall/CRC Applied Mathematics & Nonlinear Science)
39). Substituting Eq. 6: Euler beam under uniform loading. elimination or other methods. We will elaborate this point through the following example. 5 Bending of Euler beam A uniform Euler beam under pure bending shown in Fig. 49) where EI is the flexural rigidity of the beam, f (x) the external distributed load, and L the length of the beam. 49) may be further transformed to a dimensionless form for the convenience of calculation. 50) where X = x/L, W = w/a, a = f0 L/EI, F (x) = f (x)/f0 , f0 is a constant for non-dimensionalisation.
49) may be further transformed to a dimensionless form for the convenience of calculation. 50) where X = x/L, W = w/a, a = f0 L/EI, F (x) = f (x)/f0 , f0 is a constant for non-dimensionalisation. As shown in Fig. 6 the beam is clamped at the left end and simply supported at the right end. 51b) 1 The exact solution to this problem is W (X) = 48 X 2 (5X − 2X 2 − 3). Divide the beam domain 0 ≤ X ≤ 1 into N = 21 nodes distributed in the form of Eq. 48). Writing the deflection W (x) in the form of Eq.
21). The worst case, however, can be as bad as divergent as specified by Eq. 16). Therefore, the above analysis outlines the accuracy we are able to obtain if polynomial interpolation is employed. 22) on an interval of [-1, 1]. 1. 1: The 5th-order interpolating polynomial vs exact function. 03846 On plotting the fifth-order interpolating polynomial and the given function in Fig. 1, we immediately conclude that the two sets of results do not match well. Except at the six given points, the interpolating polynomial is far away from the true values.
Advanced Differential Quadrature Methods (Chapman & Hall/CRC Applied Mathematics & Nonlinear Science) by Zhi Zong