International Journal of Engineering Inventions ISSN: 2278-7461, www.ijeijournal.com Volume 1, Issue 4 (September2012) PP: 47-57 47 Multicellular Multilayer Plate Model: Numerical Approach and Phenomenon Related To Blockade by Shear Mohamed Ibrahim 1 , Abderrahmane El Harif 2 1,2 Laboratory of Mechanics (LM), Department of Physics, Faculty of Sciences-Rabat, P.O. Box 1014, Morocco Abstract--A numerical model on the flexibility method in the case of a multilayer beam finite element has been developed and the contributions to its recent developments being made at Mechanical laboratory, Department of physics, Faculty of Sciences Rabat (Morocco). The results of the experiments and those of numerical calculations were concordant in the case of quasi-static loading. These results were based on the approach "finite element" coupled with a non-linear model [23]. Firstly, we present here the results based approach "finite element" related to the analysis of a bending square plate under concentrated and uniform load, clamped or simply supported on the contour. On the other hand, we present some results which we evidence to the problem related to the shear locking. The numerical model is based on a three- dimensional model of the structure seen here as a set of finite elements for multilayered plates multi cellular matrix (concrete) and a set of finite element fibers for reinforcement. The results obtained confirm the ability of these tools to correctly represent the behavior of quasi-statics of such a complex system and presage the deepening of a digital tool developed. Keywords––multicellular multilayer plate, numerical approach, Finite element flexible I. INTRODUCTION The phenomenon related to blockade by shear (or appearance of a parasitic stiffness) is a numerical problem that drew attention of many researchers in the past twenty years and an abundance of solutions which has been discussed in [3, 9, 10, 11, 12, 19, 20, 22].One way to avoid the appearance of shear locking and thus make the solution independent of the slenderness ratio (the ratio of length L / thickness h) is to calculate the terms of the stiffness matrix by integrating accurately the relative terms bending and sub-integrating the terms relating to shear [4,5,6,8,13,14,15,16,17,21 ,22].To improve this phenomenon related to the numerical computation and propose a more efficient solution, we developed a model based on the flexibility method [23]. The model is formulated on the basis of the forces method by an exact interpolation stresses [18]. This makes it possible to calculate the flexibility matrix, which is the inverse of the stiffness matrix. The purpose of this study is the modeling of the structural response of the sails carriers subjected to seismic effects using a comprehensive three- dimensional numerical model using a nonlinear finite element approach coupled with a damage model developed for the behavior of concrete material. In this second paper, drawing on the results of the first article and those of [1,2 ,7], we present only some results related to the analysis of a homogeneous square plate in bending subjected to a concentrated and uniform load. II. MODELING Complementary to the trials and their interpretation, numerical modeling of this situation type has several advantages. In this case, it already developed an ambitious and effective model capable of taking into account the different aspects of this complicated problem, including the quasi-static and dynamic loading. Then after this satisfactory model, it has to constitute a way to complement the experimental measurements by providing new data. As such, it should contribute to a better understanding of the phenomena involved and to further provide a basis for dimensionality development methods. 1. METHODOLOGY An immediate challenge before addressing the simulation of such problems is to choose the right methodology. The philosophy retained here is to realize the contribution of research in civil engineering to respond in a context of operational engineering. The choice was made on the use of finite element plate‟s multilayer multistage three nodes and two degrees of freedom per node. A realistic numerical prediction of the structural response of such a structure requires a rigorous three-dimensional geometric model of the system components. This model and its numerical analysis are implemented in the finite element code RE-FLEX. Then, the plate is meshed by including its geometry in a full mesh adapted to the different areas of the problem (it is discredited into layers and its thickness h in cells along x and y the surface) [Fig.1].