An improved quadrilateral flat element with drilling degrees of freedom for shell structural analysis

This paper reports the development of a simple and efficient 4-node flat shell element with six degrees of freedom per node for the analysis of arbitrary shell structures. The element is developed by incorporating a strain smoothing technique into a flat shell finite element approach. The membrane part is formulated by applying the smoothing operation on a quadrilateral membrane element using Allman-type interpolation functions with drilling DOFs. The plate-bending component is established by a combination of the smoothed curvature and the substitute shear strain fields. As a result, the bending and a part of membrane stiffness matrices are computed on the boundaries of smoothing cells which leads to very accurate solutions, even with distorted meshes, and possible reduction in computational cost. The performance of the proposed element is validated and demonstrated through several numerical benchmark problems. Convergence studies and comparison with other existing solutions in the literature suggest that the present element is efficient, accurate and free of lockings

Orthotropic rotation-free thin shell elements

A method to simulate orthotropic behaviour in thin shell finite elements is proposed. The approach is based on the transformation of shape function derivatives, resulting in a new orthogonal basis aligned to a specified preferred direction for all elements. This transformation is carried out solely in the undeformed state leaving minimal additional impact on the computational effort expended to simulate orthotropic materials compared to isotropic, resulting in a straightforward and highly efficient implementation. This method is implemented for rotation-free triangular shells using the finite element framework built on the Kirchhoff--Love theory employing subdivision surfaces. The accuracy of this approach is demonstrated using the deformation of a pinched hemispherical shell (with a 18{\deg} hole) standard benchmark. To showcase the efficiency of this implementation, the wrinkling of orthotropic sheets under shear displacement is analyzed. It is found that orthotropic subdivision shells are able to capture the wrinkling behavior of sheets accurately for coarse meshes without the use of an additional wrinkling model.Comment: 10 pages, 8 figure

Phase-field modeling of brittle fracture with multi-level hp-FEM and the finite cell method

The difficulties in dealing with discontinuities related to a sharp crack are overcome in the phase-field approach for fracture by modeling the crack as a diffusive object being described by a continuous field having high gradients. The discrete crack limit case is approached for a small length-scale parameter that controls the width of the transition region between the fully broken and the undamaged phases. From a computational standpoint, this necessitates fine meshes, at least locally, in order to accurately resolve the phase-field profile. In the classical approach, phase-field models are computed on a fixed mesh that is a priori refined in the areas where the crack is expected to propagate. This on the other hand curbs the convenience of using phase-field models for unknown crack paths and its ability to handle complex crack propagation patterns. In this work, we overcome this issue by employing the multi-level hp-refinement technique that enables a dynamically changing mesh which in turn allows the refinement to remain local at singularities and high gradients without problems of hanging nodes. Yet, in case of complex geometries, mesh generation and in particular local refinement becomes non-trivial. We address this issue by integrating a two-dimensional phase-field framework for brittle fracture with the finite cell method (FCM). The FCM based on high-order finite elements is a non-geometry-conforming discretization technique wherein the physical domain is embedded into a larger fictitious domain of simple geometry that can be easily discretized. This facilitates mesh generation for complex geometries and supports local refinement. Numerical examples including a comparison to a validation experiment illustrate the applicability of the multi-level hp-refinement and the FCM in the context of phase-field simulations

A volume-averaged nodal projection method for the Reissner-Mindlin plate model

We introduce a novel meshfree Galerkin method for the solution of Reissner-Mindlin plate problems that is written in terms of the primitive variables only (i.e., rotations and transverse displacement) and is devoid of shear-locking. The proposed approach uses linear maximum-entropy approximations and is built variationally on a two-field potential energy functional wherein the shear strain, written in terms of the primitive variables, is computed via a volume-averaged nodal projection operator that is constructed from the Kirchhoff constraint of the three-field mixed weak form. The stability of the method is rendered by adding bubble-like enrichment to the rotation degrees of freedom. Some benchmark problems are presented to demonstrate the accuracy and performance of the proposed method for a wide range of plate thicknesses