Analytical expressions of sensitivities for shape variables in second order bending systems

Abstract

Due to the variety of its uses, sensitivity analysis is a very interesting field in structural engineering. However, the computational effort to obtain the analytical values for such sensitivities is a formidable task. Hence, it has generally been avoided when bending systems are considered; instead, approaches based on finite differences have been used. Nevertheless, using the latter method to carry out sensitivity analyses leads to considerable error, especially with shape variables, as many authors have pointed out. In this paper, the analytical expressions of sensitivity analyses with respect to shape variables are carried out for bending systems in second order theory. The first step is to evaluate the sensitivity analyses of the nodal movements by performing the loading vector along with the elastic and geometric stiffness matrix sensitivity analyses. Then, the sensitivity analyses of the maximum normal stresses are evaluated. Thereafter, there is an explanation of structural examples in which the previous analytical sensitivities are evaluated. The results are contrasted with those obtained by finite difference methods. There is also an example where the analytical sensitivities are used to carry out the optimisation of a portal structure. Finally, conclusions drawn from this work are presented.