Sensitivity analysis of structural response to position of external applied load: in plane stress condition

Abstract

Procedures for sensitivity analysis of the structural responses, i.e., nodal displacement, mean compliance and local stresses within an element, with respect to the location of an external applied load are developed. This is mainly because the external loads are often of some freedom to change their application positions in the structural preliminary design. Apart from the structural response evaluation, the finite element method is employed in this work for the sensitivity analysis implementation of a plane stress continuum structure. First, an external load is transformed into the equivalent nodal forces such that the influence of an external load shift is represented completely by the magnitude variation of the associated nodal forces, upon which the first- and second-order derivatives of an external load to its location change are performed respectively in a closed form by the aid of the features of the element shape functions. Then, the relevant sensitivities of the structural responses aforementioned are formulated readily with the discrete method. Finally, two typical examples are provided to demonstrate the validity of the sensitivity formulations presented, and the numerical results show a perfect accuracy of calculation of the response sensitivity.