A Consistent Finite Element Formulation of the Geometrically Non-linear Reissner-Mindlin Shell Model

Abstract We present an objective, singularity-free, path independent, numerically robust and efficient geometrically non-linear Reissner-Mindlin shell finite element formulation. The formulation is especially suitable for higher order ansatz spaces. utilizes geometric elements presented by Sander [74] Grohs [34] the interpolation on manifolds. proposed method objective free from artificial singularities spurious dependence. Due to fact that director field lives unit sphere, a special linearization procedure required obtain stiffness matrix. Here, we use simple constructions of Absil et al. [2, 3], which yields easy way correct tangent operator potential energy. Additionally, compare three different schemes can be found in literature, where one them applied first time model. Furthermore, exponential map radial return normalization as update nodal directors conclude superiority latter, terms fewer load steps. also investigate construction consistent base scheme. Path independence, efficiency objectivity are verified via set numerical examples.