Optimisation de la rupture et de l’endommagement de differents materiaux sandwichs

Abstract

Knowledge of the failure behavior of sandwich materials, including the study of the processes leading to it is very important due to the increasing use of these materials under more and more arduous conditions. The objective of our work is to perform an optimization study of fracture and damage of sandwich beams with composite laminated coating oriented at [+θ°/-θ°]3s , [+45°/-45°]3s and [0°/90°]3s loaded in three points bending. This task was carried out by means of stochastic methods such as genetic algorithms for locating the optimum of a function in the space of parameters valorised. The overall law behavior of sandwich structure into two failure modes of face yielding and face wrinkling is determined by the use of mathematical approaches based on the formulation of the equilibrium equations and laminated structures theory taking into account transverse shear stresses and sandwish beams theory. Stresses in each component layer coatings, upper and lower, are calculated in accordance with maximum stress criterion. The changing of the material coating nature and research of the orientation effect of the fiber reinforcement and transverse shear stresses are used to determine the performance of the sandwich structure into two failure modes of face yielding and face wrinkling. In order to increase the performance of sandwich beams, in three points ending, an optimization program based on the principles of genetic algorithms has been developed to maximize the tensile strength in the two ailure modes of face yielding and face wrinkling, depending on the orientation of plies : 0°, + 45°, - 45 ° and 90°. The equations used to evaluate the individuals in population results from the classical laminate theory with discrete variables. Operators of genetic algorithms (selection, crossover and mutation) are applied to the children of a hundred generations. To achieve optimal solutions, the result appeared effective despite all the non deterministic nature of genetic algorithms. But, to achieve maximum effectiveness, it is important to choose smartly the parameters of genetic algorithms depending on the nature of the problem studied and the mechanical characteristics of the function to be optimized.