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

A new locking-free polygonal plate element for thin and thick plates based on Reissner-Mindlin plate theory and assumed shear strain fields

A new $n-$ noded polygonal plate element is proposed for the analysis of plate structures comprising of thin and thick members. The formulation is based on the discrete Kirchhoff Mindlin theory. On each side of the polygonal element, discrete shear constraints are considered to relate the kinematical and the independent shear strains. The proposed element: (a) has proper rank; (b) passes patch test for both thin and thick plates; (c) is free from shear locking and (d) yields optimal convergence rates in $L^2-$norm and $H^1-$semi-norm. The accuracy and the convergence properties are demonstrated with a few benchmark examples

Strategies for using cellular automata to locate constrained layer damping on vibrating structures

It is often hard to optimise constrained layer damping (CLD) for structures more complicated than simple beams and plates as its performance depends on its location, the shape of the applied patch, the mode shapes of the structure and the material properties. This paper considers the use of cellular automata (CA) in conjunction with finite element analysis to obtain an efficient coverage of CLD on structures. The effectiveness of several different sets of local rules governing the CA are compared against each other for a structure with known optimum coverage-namely a plate. The algorithm which attempts to replicate most closely known optimal configurations is considered the most successful. This algorithm is then used to generate an efficient CLD treatment that targets several modes of a curved composite panel. To validate the modelling approaches used, results are also presented of a comparison between theoretical and experimentally obtained modal properties of the damped curved panel

Macro-mechanical modelling and simulation of textile fabric and clothing with S-FEM

Tese de Doutoramento Programa Doutoral em Engenharia TêxtilEsta tese propõe um método de elementos finitos, designado por S-FEM (Smoothed Finite Element Method), para modelação e análise mecânica de estruturas têxteis planas. Neste enquadramento teórico, supõe-se que a estrutura têxtil não-tecida é um material isotrópico elástico, enquanto a estrutura têxtil tecida é um material elástico com anisotropia ortotrópica, para os quais as leis constitutivas utilizam propriedades mecânicas de baixa pressão (low stress) com base na Medição Objetiva de Tecidos (FOM - Fabric Objective Measurement). As formulações de elementos finitos de baixa ordem baseadas em deslocamento quando aplicadas a elementos finitos de placas (plate/shell) quadriláteras de 4 nós, incluindo campos de tensão de cisalhamento transversal, baseiam-se nas contribuições de Raymond Mindlin e por Eric Reissner, no que agora se designa teoria de deformação por cisalhamento de primeira ordem (first-order shear deformation, do inglês, ou FSDT de forma abreviada), ou simplesmente teoria de Mindlin-Reissner, e nas abordagens MITC (Mixed Interpolation of Tensorial Components), são nesta tese combinadas com a técnica de suavização do/da gradiente/tensão nos termos dos modelos S-FEM por forma a mitigar problemas como são o caso da distorção de elementos finitos, da granularidade grosseira da malha, bem como dos bem conhecidos fenómenos de bloqueio. As malhas de quadriláteros são utilizadas nesta tese devido à sua capacidade de representar geometrias complexas de tecidos em resultado de deformações mecânicas como são os casos da recuperação face à pressão planar, flexão, deformação, vibração, drapejamento, etc. Refira-se que foi desenvolvido e implementado em Matlab um software para os novos modelos de elementos finitos, em grande medida devido à inexistência de modelos S-FEM em softwares de análise de elementos finitos (finite element analysis ou FEA), lacuna esta que ocorre quer em softwares comerciais, quer não comerciais, e até em códigos abertos. Exemplos numéricos para as aplicações básicas de engenharia no que respeita à modelação mecânica de folhas de tecido fino e de folhas de tecido de espessura média em estudos de casos típicos, como é o caso da recuperação face a pressão planar, flexão, deformação e comportamento livre de vibrações, indicam que os elementos finitos (plate/shell) desenvolvidos com a técnica de suavização de tensão e MITC acabam por aliviar os efeitos de distorção dos elementos, a granularidade grosseira da malha e efeito de bloqueio na modelação e análise mecânica de tecidos muito finos e até mesmo de tecidos de espessura média. Os modelos de elementos finitos de placas (plate/shell) desenvolvidos durante o trajeto desta tese, bem como as suas propriedades mecânicas de baixa tensão em termos de FOM, são, portanto, bem adaptados à modelação e análise numérica de deformação macro-mecânica de folhas de tecido muito fino e de folhas de tecido de espessura média, incluindo ao mesmo tempo análise de deformação mecânica simples e complexa.An S-FEM (Smoothed Finite Element Method) for mechanical analysis and modelling of the textile fabrics is proposed. In this theoretical framework, one assumes that the non-woven fabric is an elastic isotropic material, while the woven fabric is an elastic with orthotropic anisotropy for which the constitutive laws formulated are using low-stress mechanical properties based on FOM (Fabric Objective Measurement). The displacement-based low-order finite element formulations for four-node quadrilateral plate/shell finite element, including assumed transverse shear strain fields, are based on the contributions of Raymond Mindlin and by Eric Reissner as FSDT (first-order shear deformation theory and so-called the Mindlin-Reissner theory) together with MITC (Mixed Interpolation of Tensorial Components) approaches, which are combined with the gradient/strain smoothing technique in terms of S-FEM models contributed by G. R. Liu et al. in order to mitigate problems as element distortion, mesh coarseness as well as the well-known locking phenomena. Quadrilateral meshes are used due to ability to represent complicated geometries of complex mechanical deformation of the fabric such as plane stress recovery, bending, buckling, vibration, draping behavior, etc. The finite element computer codes were developed in MATLAB for the new formulated plate/shell finite element models due to the lack of FEM (Finite Element Method) packages for S-FEM models in both commercial and non-commercial FEA (Finite Element Analysis) computer applications, and even from open-source platforms. Numerical examples for the basic engineering applications of mechanical modelling of thin to moderately thick fabric sheet in the typical case studies such as in-plane stress recovery, bending, buckling and free-vibration behavior, indicate that the developed plate/shell finite elements with assumed strain smoothing technique and MITC, do alleviate element distortion, mesh coarseness, and locking effect even for mechanical analysis and modelling very thin to moderately thick fabric. The developed plate/shell finite element models and low-stress mechanic properties in terms of FOM are, therefore, well adapted for numerical analysis and modelling of macro-mechanical deformation of the thin to moderately thick fabric sheet including both simple and complex mechanical deformation analysis.EMECW L12 MOBILITY GRANT AWARD CONTRACT BTG_559 Grant agreement n 2009/1661-001 001EC

Isogeometric analysis based on rational splines over hierarchical T-mesh and alpha finite element method for structural analysis

This thesis presents two new methods in finite elements and isogeometric analysis for structural analysis. The first method proposes an alternative alpha finite element method using triangular elements. In this method, the piecewise constant strain field of linear triangular finite element method models is enhanced by additional strain terms with an adjustable parameter a, which results in an effectively softer stiffness formulation compared to a linear triangular element. In order to avoid the transverse shear locking of Reissner-Mindlin plates analysis the alpha finite element method is coupled with a discrete shear gap technique for triangular elements to significantly improve the accuracy of the standard triangular finite elements. The basic idea behind this element formulation is to approximate displacements and rotations as in the standard finite element method, but to construct the bending, geometrical and shear strains using node-based smoothing domains. Several numerical examples are presented and show that the alpha FEM gives a good agreement compared to several other methods in the literature. Second method, isogeometric analysis based on rational splines over hierarchical T-meshes (RHT-splines) is proposed. The RHT-splines are a generalization of Non-Uniform Rational B-splines (NURBS) over hierarchical T-meshes, which is a piecewise bicubic polynomial over a hierarchical T-mesh. The RHT-splines basis functions not only inherit all the properties of NURBS such as non-negativity, local support and partition of unity but also more importantly as the capability of joining geometric objects without gaps, preserving higher order continuity everywhere and allow local refinement and adaptivity. In order to drive the adaptive refinement, an efficient recovery-based error estimator is employed. For this problem an imaginary surface is defined. The imaginary surface is basically constructed by RHT-splines basis functions which is used for approximation and interpolation functions as well as the construction of the recovered stress components. Numerical investigations prove that the proposed method is capable to obtain results with higher accuracy and convergence rate than NURBS results

About the edge-based smoothed finite element method for the Reissner-Mindlin plate-bending problem

The paper further develops the edge-based smoothed finite element method (ES-FEM) for analysis of Reissner-Mindlin plates using triangular meshes. The bending and shearing stiffness matrices are obtained using strain smoothing technique over the smoothing domains associated with edges of elements. Transverse shear locking can be avoided with help of the discrete shear gap (DSG) method. The numerical examples show that the present ES-FEM-DSG method obtains very accurate results compared to the exact solution and other existing elements

A monolithic fluid-structure interaction formulation for solid and liquid membranes including free-surface contact

A unified fluid-structure interaction (FSI) formulation is presented for solid, liquid and mixed membranes. Nonlinear finite elements (FE) and the generalized-alpha scheme are used for the spatial and temporal discretization. The membrane discretization is based on curvilinear surface elements that can describe large deformations and rotations, and also provide a straightforward description for contact. The fluid is described by the incompressible Navier-Stokes equations, and its discretization is based on stabilized Petrov-Galerkin FE. The coupling between fluid and structure uses a conforming sharp interface discretization, and the resulting non-linear FE equations are solved monolithically within the Newton-Raphson scheme. An arbitrary Lagrangian-Eulerian formulation is used for the fluid in order to account for the mesh motion around the structure. The formulation is very general and admits diverse applications that include contact at free surfaces. This is demonstrated by two analytical and three numerical examples exhibiting strong coupling between fluid and structure. The examples include balloon inflation, droplet rolling and flapping flags. They span a Reynolds-number range from 0.001 to 2000. One of the examples considers the extension to rotation-free shells using isogeometric FE.Comment: 38 pages, 17 figure

Strain smoothing for compressible and nearly-incompressible finite elasticity

We present a robust and efficient form of the smoothed finite element method (S-FEM) to simulate hyperelastic bodies with compressible and nearly-incompressible neo-Hookean behaviour. The resulting method is stable, free from volumetric locking and robust on highly distorted meshes. To ensure inf-sup stability of our method we add a cubic bubble function to each element. The weak form for the smoothed hyperelastic problem is derived analogously to that of smoothed linear elastic problem. Smoothed strains and smoothed deformation gradients are evaluated on sub-domains selected by either edge information (edge-based S-FEM, ES-FEM) or nodal information (node-based S-FEM, NS-FEM). Numerical examples are shown that demonstrate the efficiency and reliability of the proposed approach in the nearly-incompressible limit and on highly distorted meshes. We conclude that, strain smoothing is at least as accurate and stable, as the MINI element, for an equivalent problem size

Co-rotational shell element for numerical analysis of laminated piezoelectric composite structures

Laminated composite structures consisting of load-carrying and multifunctional materials represent a rather powerful material system. The passive, load-carrying layers can be made of isotropic material or fiber-reinforced composites, while piezoelectric materials represent the most common choice of multifunctional materials for active layers. The multifunctionality of piezoelectric layers is provided by their inherent property to couple mechanical and electric fields. The property can thus be used to sense deformations or produce actuating forces. A highly efficient 3-node shell element is developed for modeling piezoelectric laminated composite shells. The equivalent single-layer approach and Mindlin-Reissner kinematics are used in the element formulation together with the discrete shear gap (DSG) technique to resolve the shear locking and strain smoothing technique to improve the performance. Piezoelectric layers are assumed to be polarized in the thickness direction thus coupling the in-plane strains with the electric field oriented in the thickness direction. The co-rotational FE formulation is used to account for geometrically nonlinear effects. Numerical examples cover linear and geometrically nonlinear static and dynamic cases with piezoelectric layers used as actuators and sensors

Multiscale simulation methodology for the forming behavior of biaxial weft-knitted fabrics

Trotz der guten Drapierbarkeit ist das Formen von flachen Mehrlagen-Gestricken (MLG) zu 3D-Preforms für schalenartige Faser-Kunststoff-Verbund (FKV) Bauteile immer noch eine Herausforderung, da einige Defekte wie Falten, Gassenbildung oder Faserschäden nicht vollständig vermieden werden können. Daher ist vor der Massenproduktion eine Optimierung erforderlich. Die virtuelle Optimierung des Umformprozesses mit Hilfe von Finite-Element-Methode (FEM) Modellen ist ein attraktiver Ansatz, da die Rechenkosten immer geringer werden. Dazu wurde ein auf Kontinuumsmechanik basierendes Makromodell erfolgreich für MLG implementiert. Der makroskalige Modellierungsansatz bietet angemessene Rechenkosten und kann gängige Defekte wie Faltenbildung vorhersagen. Weitere Defekte wie Faserversatz, ondulierte Fasern, Knicken von Fasern, Faserschädigung und Gassenbildung können jedoch mit dem Makromodell nicht vorhergesagt werden. Da die Komplexität von Bauteilen aus FKV und die Qualitätsanforderungen an die 3D-Preforms zunehmen, sind FEM-Modelle mit höherem Darstellungsgrad erforderlich. Im am weitesten entwickelten mesoskaligen FEM-Modell für MLG verhindert die zu starke Vereinfachung des Strickfadensystems mit Federelementen jedoch die Fähigkeit dieses FEM-Modells, Faserverschiebungen und Gassenbildung bei großer Verformung zu beschreiben, wobei das Gleiten zwischen den Fäden berücksichtigt werden muss. Ziel ist daher die Entwicklung, Validierung und Anwendung eines mesoskaligen FEM-Modells für MLG, um die derzeitigen Einschränkungen zu überwinden. Es werden neue Modellierungsstrategien für biaxiale MLG auf der Mesoskala entwickelt. Die mechanischen Eigenschaften von MLG werden durch eine Reihe von textilphysikalischen Prüfungen charakterisiert und analysiert, die alle notwendigen Daten für den Aufbau sowie die Validierung der FEM-Modelle liefern. Es sollen zwei Ansätze zur Modellierung des Verstärkungsgarns implementiert und verglichen werden: durch Balken- und durch Schalenelemente. Die validierten Modelle können für die Umformsimulation verwendet werden. Es folgt eine Benchmark-Studie über die Kapazität und Zuverlässigkeit der verfügbaren Makromodelle und der entwickelten Mesomodelle durch Umformsimulation. Als Grundlage für die Benchmark-Studie werden Umformversuche durchgeführt. Das zweite Ziel der Arbeit ist die Modellierung von FKV auf verschiedenen Skalen. Die Modellierung von FKV auf der Makroebene wird mit den Daten der Faserorientierung durchgeführt, die aus der Umformsimulation gewonnen werden. Eine Mapping-Methode hilft dabei, die vorhergesagte Faserorientierung aus der Umformsimulation von dem MLG Mesomodell auf das FKV-Makromodell zu übertragen. Um den FKV zu charakterisieren und die Parameter für das FKV Modell vorzubereiten, werden Versuche mit FKV durchgeführt und ausgewertet. Basierend auf dem Mesomodell des MLG wird eine weiteres FKV-Modell vorgeschlagen, wobei Garn und Matrix getrennt modelliert werden. Dieses mesoskalige FKV-Modell enthält auch eine Kontaktformulierung, mit der die Delamination im FKV-Bauteil vorhergesagt werden kann. Prüfungen von Schale-Rippen Strukturen dienen als Grundlage für die Modellvalidierung. Das validierte Modell wird erfolgreich zur Vorhersage des mechanischen Verhaltens weiterer Schale-Rippen Strukturen mit unterschiedlicher Höhe und Anordnung der Rippen verwendet.:Kapitel 1 stellt die Einleitung und Problemstellung von dem Thema FKV vor. Kapitel 2 gibt eine Übersicht über Stand-der-Technik von den Hochleistungsfasern, Herstellung von textilen Verstärkungen und Halbzeugen, Fertigung von FKV sowie von Prüftechnik für Textilien und FKV. Zunächst wurden in Kapitel 3 eine Einführung in die Modellierung mit FEM allgemein und Stand-der-Technik der Modellierung von technische Textilien gegeben. In Kapitel 4 wurden die Zielsetzung und das Forschungsprogramm festgelegt. Die experimentellen Arbeiten werden in Kapitel 5 vorgestellt. Der erste Schritt ist die Auswahl des Materials und der Konfiguration für die MLG. Sowohl das Ausgangsmaterial als auch die produzierten MLG sollten systematisch getestet werden. Als Referenz wird auch ein Leinwandgewebe in die Prüfprogramme aufgenommen. Neben der Charakterisierung von textilen Flächengebilden sollen auch deren gleichwertige FKV geprüft werden. Das erste Ziel des Forschungsprogramms wird in Kapitel 6 erreicht, wobei verschiedene Ansätze zur Modellierung von MLG vorgestellt und validiert werden. Die entwickelten und validierten FEM-Modelle werden für die Benchmark-Studie der Umformsimulation in Kapitel 7 verwendet. Kapitel 8 befasst sich mit der Modellierung von FKV in verschiedenen Skalen. Zunächst wird das Mapping-Verfahren vorgestellt. Es wird ein Mapping für ein schalenförmiges T-Napf-Bauteil durchgeführt. Die trukturanalyse für das T-Napf-Bauteil erfolgt für übliche Lastfälle. Zweitens wird ein mesoskaliges FEM Modell für MLG-verstärkte FKV vorgeschlagen. Dieses Modell wird auf der Grundlage der Prüfdaten aus Kapitel 5 validiert. Das validierte Modell wird dann zur Vorhersage des mechanischen Verhaltens eines Schale-Rippen-FKV-Bauteils unter Biegebelastung verwendet. Kapitel 9 gibt eine Zusammenfassung von den Forschungsergebnissen und Vorschlägen für mögliche weitere Forschungen rund um dem Thema MLG als Verstärkung für FKV. Die Kombination von vorhandenen Makro-und Mesomodellen in einer einzigen Simulation kann die Berechnungskosten senken, ohne die Vorhersagenfähigkeiten des Modelles kompromittiert zu werden