sec5-10 - Errors in FE Modelling (Section 5.10) Modelling...

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1 Errors in FE Modelling (Section 5.10) Modelling error : arises because physical reality is replaced by a mathematical model. Example: A beam that can resist both axial and transverse loads being modelled as one with bending resistance only ignoring the axial resistance. Discretization error : arises because a mathematical model is implemented in a piecewise manner. Example: Perimeter, p, of a circle being computed with a finite number of straight segments. θ =2 π /n ; b=2r sin ( θ /2) ; p=nb=2nr sin ( π /n) (p/r) exact = 2 π . (p/r) n=6 =6 (4.5 %) and (p/r) n=12 =6.212 (1.1 %) (Error shown in parentheses. No modelling error here) θ b r
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Round-off error and ill-conditioning Numerical (round-off) error : arises because a computer uses a finite number of significant digits to represent a number. Such error may cause problem in ill-conditioned systems. Ill-conditioned system : small changes in structural parameters or loading (i.e., in matrix entries) produce large changes in the solution and the solution may be inaccurate. Example
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sec5-10 - Errors in FE Modelling (Section 5.10) Modelling...

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