An efficient isostatic mixed shell element for coarse mesh solution

Abstract

A novel mixed shell finite element (FE) is presented. The element is obtained from the Hellinger-Reissner variational principle and it is based on an elastic solution of the generalized stress field, which is ruled by the minimum number of variables. As such, the new FE is isostatic because the number of stress parameters is equal to the number of kinematical parameters minus the number of rigid body motions. We name this new FE MISS-8. MISS-8 has generalized displacements and rotations interpolated along its contour and drilling rotation is also considered as degree of freedom. The element is integrated exactly on its contour, it does not suffer from rank defectiveness and it is locking-free. Furthermore, it is efficient for recovering both stress and displacement fields when coarse meshes are used. The numerical investigation on its performance confirms the suitability, accuracy, and efficiency to recover elastic solutions of thick-and thin-walled beam-like structures. Numerical results obtained with the proposed FE are also compared with those obtained with isogeometric high-performance solutions. Finally, numerical results show a rate of convergence between h 2 and h 4 .

A corotational mixed flat shell finite element for the efficient geometrically nonlinear analysis of laminated composite structures

“…An eigenvalue analysis of the stiffness matrix of one MISS‐4c element is performed. We refer to Madeo et al 37 for the details on the stability analysis. The eigenvalue analysis is conducted for a regular and for distorted geometries.…”

“…The capability of MISS‐4c to recover constant stress fields is herein tested 32 . A rectangular plate discretized by three different meshes is analyzed, whose geometry is given in Madeo et al 37 Three values of the thickness are considered, namely 4, 0.4, and 0.04. The plate is subjected to in‐plane and out‐of‐plane loading conditions 37,39 .…”

“…In fact, it has been employed, among the others, to model crack problems, 33 heat transfer, 34 Helmholtz problems 35 and to general hyperbolic boundary value problems 36 with possible applications to electromagnetism, acoustic wave propagation and other branches of physics. Based on this technique, a mixed FE for the linear‐elastic analysis of isotropic shell structures has been recently proposed 37 . This element, named MISS‐8, is characterized by accuracy for coarse meshes, high convergence rate, and insensitivity to mesh distortion.…”

An Isogeometric Solid-Shell Model for Postbuckling Optimisation Strategies

“…When a mixed format is adopted the configuration variables u collect both displacement and stress fields. (17) where Ω e is the element domain and a numerical integration is usually adopted.…”

“…In the Koiter analysis this phenomenon is much more evident because the equilibrium path is directly extrapolated using the ROM, and an equilibrium error is not corrected by an iterative scheme, so affecting the accuracy of the method. On the contrary mixed formulations [17] avoid this drawback because the stresses are directly extrapolated.…”