Contribution de l’approche en déformation pour l’analyse linéaire et non-linéaire des structures

Abstract

In this thesis a new membrane finite element for linear and materially nonlinear analysis is developed. The displacement field of this element has been developed by the use of the strain based approach, and it is based on the assumed functions for the various components of strain which satisfy the compatibility equation. This rectangular finite element named SBREDR (Strain Based Rectangular Element with Drilling Rotation) has the three degrees of freedom at each of the four corner nodes (the two translations and the in-plane rotation) and the displacement functions of the developed element satisfy the exact representation of the rigid body modes. For elastoplastic analysis, Von Mises, Tresca and Mohr-Coulomb yield criteria are adopted, and both initial stress and initial strain methods are employed. In order to reflect exactly both elastic and elastoplastic behaviors of the developed element in the structural analysis, plane stress, plane strain, and axisymmetrical problems are considered. Numerical experiments in both linear and nonlinear analysis have been conducted to assess accuracy and reliability of the developed element compared to the theoretical results and other membrane finite elements. The performance of this element is evaluated through a series of tests in both analyzes. Numerical results obtained using this element agree well with those from theoretical solutions and show that this element has quite rapid rate of convergence to the reference solutions for all tests. In the second part we numerically study the elastoplastic and dynamic behaviors of membrane structures using the strain based approach through a finite element named SBRIE. Both behaviors of this element were investigated for the first time, and in order to have a good study of behaviors, it proved necessary that a new isoparametric formulation will be introduced on this element. For validation purposes some selected numerical examples are solved using the SBRIE element in both analysis and compared to the reference and to the analytical solutions reported in the literature.