Stiffness-matrix condition number and shape sensitivity errors

This paper derives an error magnification index for assessing the sensitivity of the displacement field to errors in the load vector. It is shown that the error magnification index is less conservative than the stiffness-matrix condition number and that, for some cases, no error magnification occurs even when the condition number is very high. The proposed index was used to calculate the derivatives of beam response to changes in the beam structural parameters, using a semianalytical method. It is shown that the proposed index discriminates well between the calculation of the derivative with respect to length, which is very sensitive to errors, and the calculation of the derivative with respect to cross-sectional height, which is not sensitive.