Analytical sensitivity of interpolatory quadrature in force-based frame elements

Recent literature shows the choice of an integration method in the state determination of force-based frame finite elements has a significant influence on the computed element response. To assess the modeling uncertainty associated with integration methods in force-based elements, analytical sensitivity of one-dimensional interpolatory quadrature is developed via direct differentiation of the governing Vandermonde equations. Comparisons with finite difference calculations show that the combination of the Vandermonde equation sensitivity with equations that govern force-based element response sensitivity leads to an accurate approach to stand-alone response sensitivity analysis. Consistent with previous findings for material, load, and geometric parameters in finite element response sensitivity analysis, sensitivity with respect to parameters associated with the integration method in force-based elements improves the efficiency of gradient-based algorithms where the locations and/or weights of the integration method are treated as uncertain random variables. Copyright (C) 2009 John Wiley & Sons, Ltd.