Rezak Ayad

A new hybrid‐mixed variational approach for Reissner–Mindlin plates. The MiSP model

A valuable variational approach for plate problems based on the Reissner–Mindlin theory is presented. The new MiSP (Mixed Shear Projected) approach is based on the Hellinger–Reissner variational principle, with a particular representation of transversal shear forces and transversal shear strains. The approximations of the shear forces are derived from those of the bending moments using the corresponding equilibrium relations. The shear strains are defined in terms of the edge tangential strains that are projected on the element degrees of freedom. Two finite elements are developed on the MiSP approach basis: 3-node triangular element MiSP3 and 4-node quadrilateral element MiSP4. Both elements can be considered as the most simple among the existent mixed elements. A modified MiSP model with a derived 4-node element is also presented. Numerical experiments are presented which show that the MiSP elements do not exhibit shear locking and give excellent results for thick and thin plates. They also pass the patch test for a general triangle and quadrilateral.

Analysis of the mechanical behaviour of flax and glass fabrics-reinforced thermoplastic and thermoset resins

This paper aims at comparing the mechanical behaviour of different composite materials constituted of twill flax and glass fabrics-reinforced liquid thermoplastic and thermoset resins. The main objective is to study the possibility of thermoplastic to replace thermoset matrix, and flax fibre to replace glass fibre. For this purpose, the studied composites were fabricated using the vacuum infusion technique. Next, they were subjected to several monotonic and load-unload tensile tests in order to determine their mechanical properties and their evolution with damage. Two elastic damage and elastic-plastic damage models were also considered to predict their behaviour. The obtained results show that the used thermoplastic resin could constitute an interesting alternative to the thermoset resin for the vacuum infusion process. Furthermore, the flax fibre composites, in particular those based on the thermoplastic resin, present specific tensile moduli close to those of glass composites.

Un élément quadrilatéral de plaque basé sur une formulation mixte-hybride avec projection en cisaillement

ABSTRACT This work deals with the formulation of a new 4-node quadrilateral element for the linear analysis of plate bending with transverse shear effect. This formulation is based on a variational hybrid-mixed model called MiSP (Mixed Shear Projected). The approximation of the shear forces results from that of bending moments with an explicit satisfaction of two of the three equilibrium equations. The TS deformations are defined in terms of the edge deformations which are projected on the nodal degrees of freedom. The convergence of the element is checked on a series of constant and rigid mode patch-tests, and its precision is evaluated on two series of benchmark examples related to skewed and circular plates.

An enhanced discrete Mindlin finite element model using a zigzag function

The present work deals with the formulation and the evaluation of a discrete finite element model for Reissner/Mindlin composite plates, including the introduction of zigzag form in order to improve plane and shear stress accuracy. The model is characterised by a piecewise linear variation of displacement, which allows to fulfil the stress continuity requirements. For this purpose, a new four-node quadrilateral enhanced finite element based on a quadratic displacement field is proposed. In the second version, it incorporates two additional zigzag terms and does not require shear correction. The element is validated across some known problems in the literature, highlighting the improvement of thickness stress distributions, by comparison with the initial model without zig zag function.

Une méthode de pseudo-concentration pour la simulation 3D volumique du remplissage de moules d'injection

ABSTRACT A full 3D filling algorithm for injection moulding of molten polymers is presented. The non-Newtonian fluid flows governing equations are solved using a mixed velocity- pressure finite element formulation with a mini-element. To track the polymer front, a transport equation of a pseudo-concentration function is solved using a control volume technique. The ability of the proposed algorithm to simulate the filling of three-dimensional moulds is demonstated through complicated flows and geometries examples.

A new 3D 6-node solid finite element based upon the “Space Fibre Rotation” concept

This paper presents the development of a new 6-node solid wedge element with three translational and three rotational degrees of freedom per node. It is based on the model Space Fibre Rotation (SFR). Using the rotation of a material fibre in 3D space, the SFR approach allows to get a more accurate displacement field, which becomes quadratic without changing the number of nodes of the element. It is economical since only two integration points are used. In order to evaluate the usual element stiffness, a small penalty stiffness is introduced so that no zero energy modes appear while preserving the advantage of reduced integration. Several benchmark tests have demonstrated the improved performance of the present element.

A space fibre as added value in finite element modelling for optimal analysis of problems involving contact

The present work deals with the non-linear formulation of an axisymmetric hyperelastic solid model, based on the concept space fibre rotation (SFR). The SFR-Axi model uses the kinematics of a space fibre to obtain a quite accurate displacement field. It improves in a significant way the precision of the linear element Q4-Axi. It can even be compared, on the accuracy and CPU time level, with the high-order elements as Q8-Axi for instance. A hyperelastic law, based on the Mooney–Rivlin model, is implemented to allow to the present model a better simulation of the forming process of hollow plastic bodies. The numerical results relate to primarily some known tests of hyperelastic structures, with and without contact (swellings).

Remeshing procedure for discrete membrane finite element: application to woven composite forming

Pre-impregnated woven fabric is an increasingly important component as the reinforcement phase of composite materials for many mechanical structures (automotive and aerospace). Modelling woven fabrics is difficult due, in particular, to the need to simulate the response both at the scale of the entire fabric and at the meso-level, the scale of the fibre that composes the weave. Here, we present new finite element for the simulation of the 3D, pre-impregnated woven fabric preform. Continuum-level modelling technique that, through the use of an appropriate bi-component unit cell (fiber rotation quadrilateral element connected to truss elements), captures the deformation of the mesostructure of the fabric without explicitly modelling every fibre. Simulations of the experiments demonstrate that the finite elements are capable of efficiently simulating large, complex structures and forming processes.

A Mindlin multilayered hybrid-mixed approach for laminated and sandwich structures without shear correction factors

A new hybrid-mixed variational approach for the linear analysis of laminated and sandwich plates, without transverse shear correction factors, is presented. It’s based on the first order theory of Reissner/Mindlin. A quadratic approximation through the thickness is proposed for transverse shear stresses (continuity C-1), and two equilibrium equations are used for their approximation. This reduces in consequence the number of interpolation parameters of bending stresses, which are eliminated using the static condensation technique. The proposed approach has been adapted to a quadrilateral 4-node finite element, free of locking, to which performances have been analyzed using some known problems of sandwich and laminated structures.

Une formulation mixte-hybride naturelle robuste pour la modélisation des coques courbes isotropes

Ce travail traite d’une formulation mixte-hybride naturelle pour l’analyse linéaire des coques courbes homogènes et isotropes. Le modèle NHMiSP (Natural Hybrid-Mixed with Shear Projection) est formulé sur la base de l’approche géométrique du solide dégénéré. En conséquence, il peut-être utilisé pour modéliser des coques de forme quelconque présentant un gauchissement. Le modèle de membrane est basé sur l’approche hybride naturelle de Pian. La formulation du modèle de flexion est basée sur le principe classique de Hellinger- Reissner. La satisfaction, au niveau variationnel, des équations d’équilibre en flexion, pour définir les contraintes de cisaillement transversal (CT), rend le présent modèle partiellement hybride. Le verrouillage en CT est évité par l’introduction des déformations de substitution (méthode ANS : Assumed Natural Strains). L’élément fini ainsi obtenu (un quadrilatère courbe à 4 noeuds) est validé avec succès à travers des tests standard de coques.