Sensitivity analysis of structural response to position of external applied load in plate flexural condition

Abstract

Procedures for discrete sensitivity analyses of the static responses of a structure, i.e., nodal displacements, mean compliance, local bending moments and stresses, are respectively developed for a plate or shell structure with regard to the position of an external load mainly because of the uncertainties related to the application point of a load in the preliminary design of an engineering structure. With the sensitivities developed herein, those responses can be estimated quickly and accurately by using the Taylor expansions after a position disturbance of the external load.Based on the classical theory of the finite element analysis, the shift influences of a point or distributed load are firstly transformed into the associated value variation of the equivalent nodal forces. As a result of this transformation, the first- and second-order derivatives of the external load to its movement are constituted readily in a regularized formulation. Subsequently, the relevant sensitivities of the structural responses aforementioned are developed upon the essential concepts of the discrete approach. Finally, two typical examples are provided to illustrate the implementation of the sensitivity analyses derived and their applications in a quick estimate of the structural response variation. The numerical results show a high accuracy of the response sensitivity calculation.