Finite elements for honeycomb sandwich plates and shells

pq-Adaptive solid finite elements for three-dimensional plates and shells

In this paper, novel finite elements that include an arbitrary number of additional nodes on each edge of a quadrilateral element are proposed to achieve compatible connection of neighboring nonmatching meshes in plate and shell analyses. The elements, termed variable-node plate elements, are based on two-dimensional variable-node elements with point interpolation and on the Mindlin---Reissner plate theory. Subsequently the flat shell elements, termed variable-node shell elements, are formulated by further extending the plate elements. To eliminate a transverse shear locking phenomenon, the assumed natural strain method is used for plate and shell analyses. Since the variable-node plate and shell elements allow an arbitrary number of additional nodes and overcome locking problems, they make it possible to connect two nonmatching meshes and to provide accurate solutions in local mesh refinement. In addition, the curvature and strain smoothing methods through smoothed integration are adopted to improve the element performance. Several numerical examples are presented to demonstrate the effectiveness of the elements in terms of the accuracy and efficiency of the analyses.

This paper addresses the problem of calculating sensitivity data by direct methods for isoparametric plate or shell elements. Sensitivity parameters of interest include intrinsic properties such as material modulus and plate thickness, as well as geometry variables which influence the size and shape of a structure. The sensitivity calculation therefore must consider the parametric mapping within an element, as well as the influence of geometric variables on the orientation of an element in space. The methods presented specialize directly to continuum elements, in which the co‐ordinate transformation is omitted, or to simple structural members situated arbitrarily in space. Numerical examples are presented which illustrate the accuracy of the proposed techniques, and the effect of discretization error on computed sensitivities.

The effect of the absolute nodal coordinate formulation (ANCF)–coupled deformation modes on the accuracy and efficiency when higher order three-dimensional beam and plate finite elements are used is investigated in this study. It is shown that while computational efficiency can be achieved in some applications by neglecting the effect of some of the ANCF-coupled deformation modes, such modes introduce geometric stiffening/softening effects that can be significant in the case of very flexible structures. As shown in previous publications, for stiff structures, the effect of the ANCF-coupled deformation modes can be neglected. For such stiff structures, the solution does not strongly depend on some of the ANCF-coupled deformation modes, and formulations that include these modes lead to numerical results that are in good agreement with formulations that exclude them. In the case of a very flexible structure, on the other hand, the inclusion of the ANCF-coupled deformation modes becomes necessary in order to obtain an accurate solution. In this case of very flexible structures, the use of the general continuum mechanics approach leads to an efficient solution algorithm and to more accurate numerical results. In order to examine the effect of the elastic force formulation on the efficiency and the coupling between different modes of deformation, three different models are used again to formulate the elastic forces in the absolute nodal coordinate formulation. These three methods are the general continuum mechanics approach, the elastic line (midsurface) approach, and the elastic line (midsurface) approach with the Hellinger–Reissner principle. Three-dimensional absolute nodal coordinate formulation beam and plate elements are used in this study. In the general continuum mechanics approach, the coupling between the cross section deformation and the beam centerline or plate midsurface displacement is considered, while in the approaches based on the elastic line and the Hellinger–Reissner principle, this coupling is neglected. In addition to the fully parametrized beam element used in this study, three different plate elements, two fully parametrized and one reduced order thin plate elements, are used. The numerical results obtained using different finite elements and elastic force formulations are compared in this study.

This chapter shows, through the example of the addition of a plate and shell element to freeware FEM-object, an object-oriented (C++) finite element program, how object-oriented approaches, as opposed to procedural approaches, make finite element codes more compact, more modular, and versatile but mainly more easily expandable, in order to improve the continuity and the compatibility between software of research and industrial software. The fundamental traits of object-oriented programming are first briefly reviewed, and it is shown how such an approach simplifies the coding process. Then, the isotropic shell and orthotropic plate formulations used are given and the discretized equations developed. Finally, the necessary additions to the FEM-object code are reviewed. Numerical examples using the newly created plate membrane plate element are shown.

Combining shell and GBT-based finite elements: Linear and bifurcation analysis

We present an approach for formulating efficient “3D-shell elements”, which are shell finite elements that feature the same external characteristics (geometry, shape functions) as standard 3D isoparametric elements. This makes the coupling with elements sharing the same outer surfaces straightforward. In addition, these 3D-shell elements can be used with a 3D variational formulation without modifying the constitutive equation, and they are much better adapted to large strain analysis than classical shell elements.

Analysis and Design Capabilities of STRUDL Program

The paper offers a new flat shell finite element. It results from the combination of a membrane and a bending elements, both founded on the strain based formulation. The used membrane element is the T43_Eq. It is a triangular element with four nodes, three nodes at the vertices and the fourth one at the barycenter. Each node has three degrees of freedom, two translations and one rotation around the normal. The coefficients related to the degrees of freedom at the internal node are subsequently removed from the element stiffness matrix by using the static condensation procedure. The interpolation functions of strain, displacements and stresses fields are developed from equilibrium conditions. Then, the plate element used for the construction of the shell element is a triangular four-node thin plate element based on: the deformation approach, the four fictitious node, the static condensation and the analytic integration. The shell element result of this combination is robust, competitive and efficient. The shell element result of this combination is robust, competitive and efficient.

A simplified implementation of the conventional extended finite element method (XFEM) for dynamic fracture in thin shells is presented. Though this implementation uses the same linear combination of the conventional XFEM, it allows for considerable simplifications of the discontinuous displacement and velocity fields in shell finite elements. The proposed method is implemented for the discrete Kirchhoff triangular (DKT) shell element, which is one of the most popular shell elements in engineering analysis. Numerical examples for dynamic failure of shells under impulsive loads including implosion and explosion are presented to demonstrate the effectiveness and robustness of the method.

Constrained finite element method with displacement mapping

Refined shell elements for the analysis of functionally graded structures

Curved beam, plate, and shell finite elements are commonly used in the finite element modeling of a wide range of civil and mechanical engineering structures. In civil engineering, curved elements are used to model tunnels, arch bridges, pipelines, and domes. Such structures provide a more efficient load transfer than their straight/flat counterparts due to the additional strength provided by their curved geometry. The load transfer is characterized by the bending, shear, and membrane actions. In this paper, a higher-order curved inverse beam element is developed for the inverse Finite Element Method (iFEM), which is aimed at reconstructing the deformed structural shapes based on real-time, in situ strain measurements. The proposed two-node inverse beam element is based on the quintic-degree polynomial shape functions that interpolate the kinematic variables. The element is C2 continuous and has rapid convergence characteristics. To assess the element predictive capabilities, several circular arch structures subjected to static loading are analyzed, under the assumption of linear elasticity and isotropic material behavior. Comparisons between direct FEM and iFEM results are presented. It is demonstrated that the present inverse beam finite element is both efficient and accurate, requiring only a few element subdivisions to reconstruct an accurate displacement field of shallow and deep curved beams.

The need for adding to the many existing rectangular plate elements is justified and the inclusion of the twist parameter, in the degrees of freedom selected, is shown to be essential. Using a rational choice of parameters to form the deflection functions for a simply supported plate element, a constant term, sixteen degrees of freedom rectangular element is developed which is shown to predict exactly the first mode frequency and mode shape when used in whole plate modelling. The properties of this ‘dynamic’ element are combined with the properties of an existing ‘static’ element to obtain the frequency dependent properties of a ‘blended’ element. It is demonstrated that in order to obtain high accuracy in eigenvalue determination it is necessary to use three separate modellings of the plate using a square element and two rectangular elements which are oriented orthogonally. From 3 × 3 and 2 × 5 modelling, it is shown that the frequencies of the first 20 modes of a simply supported square plate, resulting from matrix eigenvalue determinations are obtainable within one per cent of the exact values. Modes 11 and 18 are determined exactly. Mode shape distortions associated with frequency errors are examined and shown to be minimal for the first 20 modes.

Multilayered plate and shell finite elements usually have a constant shear distribution across the thickness. This causes a decrease of accuracy, especially for sandwich structures. The problem is overcome by using shear correction factors which are defined by energy considerations. In this paper a study on shear correction factors is presented as well as typical applications. These factors are defined by studying a crossply laminate without midplane symmetry in cylindrical bending. It is possible to define one factor for a given cross section or several ones, one factor per ply. The two ways are equivalent. Special cases are studied: a multilayered plate, a symmetrical sandwich and a structure formed by two plates glued to each other. The importance of shear correction factors is illustrated in the case of plate and shell applications; the results are obtained by using three‐dimensional degenerated shell finite elements.