A nonlinear elasto-plastic analysis of Reissner-Mindlin plates by finite element method

In this paper, a finite element simulation of nonlinear elasto-plastic deformations of Reissner-Mindlin bending plates is described. The previously proposed four-node Q4g element with transverse energy of shearing for thick bending plates is extended to account for isotropic material nonlinearities. An incremental finite element procedure has been used for the elasto-plastic analysis of the thick bending plate. Modified Newton-Raphson method has been used to solve the nonlinear equations. Von-Mises yield criteria have been applied for yielding of the materials along with the associated flow rule. To verify the present element, simple tests are demonstrated and various elasto-plastic problems in which the development of the plastic zone are solved

On the use of the stepped isostress method in the prediction of creep behavior of polyamide 6

The stepped isostress method (SSM) is an advanced technique which allows the prediction of the long-term behavior and enables the construction of creep master curves of materials with short-term experimental tests. However, the performance of this method is highly dependent on the numerical model and the time spent in data processing. In this paper, the effect of the extrapolation techniques on the creep curves trend is investigated using the SSM data of Polyamide test. Three extrapolation functions are used to offset the delay of the stress history: polynomial, power and exponential functions. Furthermore, a numerical routine is developed during the last step of the SSM, where the shift factors are computed taking into account the rescaling and the dwell times of each level of stresses. The processing of the SSM raw data has revealed that the rescaling parameters are the most determining factors to reach an accurate long-term creep curves. The rescaling process has shown an appropriate time, whether achieved by the exponential or power functions. Larger shift factors for exponential functions are assessed and therefore a long period of creep master curve was obtained

Detection and diagnosis of fault bearing using wavelet packet transform and neural network

Bearings, considered crucial components in rotating machinery, are widely used in the industry. Bearing status monitoring has become an essential step in the deployment of preventive maintenance policy. This work is part of the diagnosis and classification of bearing defects by vibration analysis of signals from defective bearings using time domain and frequency analysis and wavelet packet transformations (Wavelet Packet Transform WPT) with Artificial Neural Networks (ANN). WPT is used for extracting defect indicators to train the neural classifier. The main goal is the determination of the wavelet generating the most representative indicators of the state of the bearings for better detection and classification of defects. Using the WPT-based neural classifier, the obtained simulation results showed that the db6 wavelet with level 3 decomposition is best suited for diagnosing and classifying bearing defect

Contribution à la Modélisation de Composites 2D/3D à l’Aide d’Éléments Finis Spéciaux

This doctoral thesis deals with the finite element formulation and evaluation of a modified Mindlin's discrete variational model for static, dynamic, linear and non-linear composite plates and shells analysis. Including additional terms of zigzag type, in order to improve the accuracy of stress, the model has been reformulated to take into account the linear picewise of displacement variation. Consequently, two finite plate and shell elements with four nodes, called DMQP and DMQS (Discrete Quadrilateral Mindlin Plates and Shells respectively), enhanced by quadratic field rotations, have been developed and validated under REFLEX and ABAQUS codes. Both elements including the zigzag effect have been also developed in a second version, and validated through several static and dynamic test problems known from the literature, highlighting the independence towards the transverse shear correction and in particular the stress accuracy with respect to the initial model without the zigzag effect. The satisfactory results of this model found through cases of linear isotropic shell tests, motivated us to extend this approach to the non-linear geometric applications. An isoparametric curve element of shell has been developed for this purpose, where small elastic deformation assumptions of and large displacements and moderate rotations are adopted. It is geometrically simple and has only four nodes at corners and 6 DOF/node. The elementary calculation of the tangent stiffness matrix consists in combining the linear part of the curved shell element (DMQS) with that of the membrane Q4 non-linear part. An Updated Lagrangian Formulation at each Iteration (ULFI) is used with Newton-Raphson resolution Method. Some standard tests of nonlinear geometrical shell structures are presented; they show a very good convergence and global behavior better than such elements

Contribution to the 2D/3D Modeling Composites using Special Finite Elements.

La présente thèse doctorale traite de la formulation et l'évaluation élément fini d'un model variationel de Mindlin discret et modifié pour l'analyse du comportement statique et dynamique, linéaire et non linéaire des plaques et coques composites. Incluant des termes additionnels de type zigzag, en vue d'améliorer la précision de contraintes, le modèle a été reformulé afin de prendre en considération la variation linéaire par couche du déplacement. En conséquence, deux éléments finis de plaques et coques à quatre nœuds, baptisés respectivement DMQP et DMQS (Discret Mindlin Quadrilateral Plates/ Shells), améliorés par un champ de rotations quadratique ont été développés et validés sur les codes de calcul REFLEX et ABAQUS. Dans une seconde version, les deux éléments avec un effet de zigzag ont été développés et validés à travers quelques tests statiques et dynamiques connus de la littérature. Les résultats montrent une indépendance vis-à-vis de la correction du cisaillement transverse et une précision des contraintes meilleure à celle obtenue par rapport le modèle initial (sans l'effet de zigzag).Les résultats satisfaisants de ce modèle constatés à travers les cas-tests linéaires de coque isotropes, nous ont motivés à étendre la présente approche aux applications non-linéaires géométriques. Un élément isoparamétrique courbe de coque a été développé à cet effet, avec l'hypothèse des petites déformations élastiques et grands déplacements et rotations modérées. Il est géométriquement simple et ne possède que quatre nœuds aux sommets et 6 ddl/nœud. Le calcul élémentaire de la matrice de rigidité tangente consiste à associer la partie linéaire du modèle de coque courbe (DMQS) avec celle non linéaire de l'élément standard Q4 de membrane. Une formulation lagrangienne actualisée à chaque itération (FLAI) a été utilisée avec la méthode de résolution de Newton-Raphson. Quelques tests standards non-linéaires des structures coques sont présentés, ils montrent un très bon comportement global et une convergence meilleure que celle d'éléments pareils.This doctoral thesis deals with the finite element formulation and evaluation of a modified Mindlin's discrete variational model for static, dynamic, linear and non-linear composite plates and shells analysis. Including additional terms of zigzag type, in order to improve the accuracy of stress, the model has been reformulated to take into account the linear picewise of displacement variation. Consequently, two finite plate and shell elements with four nodes, called DMQP and DMQS (Discrete Quadrilateral Mindlin Plates and Shells respectively), enhanced by quadratic field rotations, have been developed and validated under REFLEX and ABAQUS codes.Both elements including the zigzag effect have been also developed in a second version, and validated through several static and dynamic test problems known from the literature, highlighting the independence towards the transverse shear correction and in particular the stress accuracy with respect to the initial model without the zigzag effect.The satisfactory results of this model found through cases of linear isotropic shell tests, motivated us to extend this approach to the non-linear geometric applications. An isoparametric curve element of shell has been developed for this purpose, where small elastic deformation assumptions of and large displacements and moderate rotations are adopted. It is geometrically simple and has only four nodes at corners and 6 DOF/node. The elementary calculation of the tangent stiffness matrix consists in combining the linear part of the curved shell element (DMQS) with that of the membrane Q4 non-linear part. An Updated Lagrangian Formulation at each Iteration (ULFI) is used with Newton-Raphson resolution Method. Some standard tests of nonlinear geometrical shell structures are presented; they show a very good convergence and global behavior better than such elements

Elastoplastic analysis of plane structures using improved membrane finite element with rotational DOFs: Elastoplastic analysis of plane structures

In this work, the small-strain elastoplastic behavior of structures is analyzed using an improved nonlinear finite element formulation. In this framework, an eight-node quadrilateral finite element denoted PFR8 (Plane Fiber Rotation) that belongs to the set of elements with rotational degrees of freedom is developed. Its formulation stems from the plane adaptation of the Space Fiber Rotation (SFR) concept that considers virtual rotations of nodal fiber within the element. This approach results in an enhancement of the displacement vector approximation. Von-Mises yield criteria have been applied for yielding of the materials along with the associated flow rule. Newton-Raphson method has been used to solve the nonlinear equations. To assess the performance of the proposed element, benchmark problems are addressed and the results are compared with some analytical and numerical solutions from the literature