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Triangular virtual elements for Kirchhoff-Love shells
Paulo M. Pimenta, T. P. Wu
Polytechnic School at University of São Paulo, Brazil
It is aimed here to propose triangular shell elements for the Kirchhoff-Love shell theory and the virtual element method (VEM), geometrically and physically in the linear range. The domain’s discretization by triangles allows the direct approximation of the shell’s geometry (mid-surface) and consequently a mapping approach as in [3] is needless. Furthermore, no curvilinear coordinate system is used. The superposition of the membrane and plate bending behaviors is such that it is considered the lowest-order case for each, i.e. a linear ansatz and linear projection (equating the constant strain triangle) for the first, and a cubic ansatz and quadratic projection for the second. Together with the element’s geometry it may thus represents a starting point for the development of several virtual shell elements. For the convergence analysis of a static boundary value problem (BVP), numerical examples with result’s comparisons involving the (classical) stabilization of [1], energy stabilization [4] and finite shell elements are performed.
References [1] Franco Brezzi and L Donatella Marini. “Virtual element methods for plate bending problems”. In: Computer Methods in Applied Mechanics and Engineering 253 (2013), pp. 455–462. [2] L Beirao Da Veiga, Franco Brezzi, and L Donatella Marini. “Virtual elements for linear elasticity problems”. In: SIAM Journal on Numerical Analysis 51.2 (2013), pp. 794–812. [3] V Ivannikov, C Tiago, and PM Pimenta. “Meshless implementation of the geometrically exact Kirchhoff–Love shell theory”. In: International Journal for Numerical Methods in Engineering 100.1 (2014), pp. 1–39. [4] P Wriggers, B Hudobivnik, and Olivier Allix. “On two simple virtual Kirchhoff-Love plate elements for isotropic and anisotropic materials”. In: Computational Mechanics 69.2 (2022), pp. 615–637.
