MEMOIRE MAGISTER EN GENIE MECANIQUE Option : Construction Mécanique

Abstract

The objective of this work is to determine the influence of type of element on the non linear analysis (elasto-plasticity) of plates in bending using the finites elements method based on the displacement model, using the thick plates theory of Reissner-Mindlin which takes account of the transverse shearing effect (the Kirchhoff's theory without transverse shearing is interpreted like a limit case in the theory of Reissner-Mindlin). The work is divide in to three big parts: finites elements formulation of plates elements, the theory of elasto-plasticity and the numeric experimentation. The first part concerns finites elements formulation of plates: hypotheses of Kichhoff's theories and Reissner-Mindlin, and stress-strain relations, as well as forms functions of finites elements plates incorporated in the program: the four nodes elements; the bilinear element Q4, the element with constant transverse shear by side Q4, the quadratics elements with eight nodes (Serendip Q8), with nine nodes (Lagrange Q9), also, the nine nodes Hétérosis element (HT9) The second part is consecrated for the behavior elasto-plastic theory of materials : behavior's law, hardening's law, plasticity criterion, at last, a preview on the non linear analysis of structures and the different techniques of non linear system resolution as well as the different convergence criterion were illustrated. The third part concerns the development of a finite elements program for the non-linear analysis (elasto-plasticity) of plates bending, the program contains a library of elements and blocks or subroutines which execute the different operations of the analysis. Besides, the program permits to choose the criteria of plasticity and the method of non-linear resolution system. Finally, some numeric experimentation have been elaborated, simulating the ultimate loads and the propagation of plastic zones for different cases (boundary conditions, thickness, criterion of plasticity and resolution methods).