A triangular virtual element for thin shells

Resumo

We propose a low-order triangular element for Kirchhoff-Love shells by the virtual element method, for use in the kinematically linear range. The shell domain discretization by flat triangles enables no use of a predefined mapping approach and curvilinear coordinates system. The displacements and deflection gradient locally defined at the triangle vertices are the local degrees of freedom, corresponding to the lowest-order cases for conforming in-plane and out-of-plane displacement approximations. Accordingly, their respective projections from the finite-dimensional space to linear and quadratic polynomials over the element, supplied by a stabilization, allow defining a (projected) constant strain and curvature virtual element. Numerical examples including stabilization and element geometry extension to quadrilateral for cylindrical shells are used as an illustration of our results.