Theoretical Analysis Of Pipe Bend
The current state of knowledge in the area of pipe bend design is reviewed in this chapter. However, the literature on pipe bend design requires the details in the following area. Theoretical analysis of pipe bend Mathematical modelling Experimental investigation of the behaviour of pipe bends Numerical analysis of pipe bends Limit load analysis Piping bending methods STUDIES RELATED TO THEORETICAL ANALySIS OF PIPE BEND Systematic investigation in pipe bends was demonstrated experimentally by Bantlin (1910) that a curved pipe behaves differently under load than predicted by simple beam theory. The phenomenon of ovalization in pipe bend was observed and reported on the fact that it leads to greater flexibility than straight pipes …show more content…
The different approaches aim at providing more accurate estimate of these correction factors, in a form that can adequately be simplified, to become readily useable in design contexts. By comparing experimental and theoretical results, Gross (1952) detected a logical inconsistency in the way the circumferential membrane force is treated theoretically. He demonstrated that a correction for transverse compression was needed to maintain static equilibrium in the structure. He developed an expression that yields a more accurate estimate of the circumferential membrane force, based on the assumption that Von Karman’s analysis gives a correct estimate of the axial membrane …show more content…
For the flexibility factor, analytical solutions are presented in the case where a bend is approximated by a rigid restraint on both ends. To verify the analytical solution and its applicability limits, two numerical procedures are developed, which are based on the finite difference method and the reduction to the Kochi problem by the expansion of the unknowns in the Fourier series over the circumferential coordinate. The authors compared the results obtained with data from the literature, discussed the advantages and disadvantages of the methods, and presented recommendations for their practical application. Man Gyun Na el al. (2006) estimated the collapse moment due to wall thinned defects was estimated through fuzzy model identification. A subtractive clustering method was used as the basis of a fast and robust algorithm for identifying the fuzzy model which was optimized by a genetic algorithm combined with least square method. Principal component analysis was used to pre-process the input signals in to the fuzzy model to reduce the sensitivity to the input change and fuzzy model were trained by using the data set prepared for training and verified by using another data set different from training
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443 Words | 2 PagesThe knowledge base consists of a collection of fuzzy if-then rules of the following form: $R^{l}$: if $x_1$ is $F_1^{l}$ and $x_2$ is $F_2^{l}$ and $ldots$ and $x_n$ is $F_n^{l}$, then is $G^{l},~l=1,2, cdots ,n$, where $x=[x_1,cdots,x_i]^{T}$ and $y$ are the FLS input and output, respectively. Fuzzy sets $F_i^{l}$ and $G^{l}$, associated with the fuzzy functions $mu_{{F_i}^{l}}(x_i)$ and $mu_{{G}^{l}}(y)$, respectively. $N$ is the rules inference number. \Through singleton function, center average defuzzification and product inference cite{shaocheng2000fuzzy}, the FLS can be expressed as: For any continuous function $f(x)$ defined on a compact set $Omegain R^n$, there exists a fuzzy system $y(x) = heta ^T
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