Enforcement of Traction Boundary Conditions to Improve Shape Sensitivity of Plate Response

Continuum sensitivity analysis provides an analytical framework to obtain shape derivatives of fluid and structural responses of a system. Previous work has shown that the accuracy of continuum sensitivity analysis is highly dependent on the quality of the spatial gradient reconstruction. In two dimensions, traction and equilibrium enforcement have both been shown to significantly improve spatial gradient reconstruction results for in-plane membrane stresses. The current work expands this to two-dimensional plate elements subject to out-of-plane bending. A numerical example illustrates the degree to which traction-enforced spatial gradient reconstruction improves the gradient accuracy, and the resulting effect on sensitivity values.