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Aligning principal stress and curvature directions

Designing freeform architectural surfaces with due regard to economic and feasibility factors is a challenging task. Rationalizing such surfaces by means of quadrilateral meshes following principal curvature lines has proven to be beneficial for manufacturing reasons, such as planar cladding panels and simplified substructure connections. On the other hand, for structural efficiency, it is convenient to ensure static equilibrium in the load bearing structure through axial forces only. It turns out that both of these goals can be reached for surfaces in membrane equilibrium where principal stress and curvature directions coincide. In this paper, we present a method for the optimization of a given shape towards stress and curvature alignment, within a workflow for the design of principal meshes in equilibrium. Our method can be applied to shapes without any geometric or topological limitation.