Kirchhoff-Love shell theory based on tangential differential calculus
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The Kirchhoff-Love shell theory is recasted in the frame of the tangential differential calculus where differential operators on surfaces are formulated without the need for a parametrization, i.e., local coordinates. The governing equations are presented in strong and weak form including a detailed discussion of the boundary conditions and mechanical quantities such as moments, normal and shear forces. Although the parameter-free formulation leads to identical results than the classical formulation, it is more general as it applies also to shells whose geometry is implied by level-sets and, hence, no parametrization is available. Furthermore, it enables a different and unified view point on shell mechanics in general and leads to an elegant implementation. Numerical results are achieved based on isogeometric analysis for classical and new benchmark tests. Higher-order convergence rates in the residual errors are achieved when the physical fields are sufficiently smooth.
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