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Abstract. This paper demonstrates the applicability of a novel meshless method in solving problems related to aeronautical engineering, the constraint-natural element method is used to optimize a wing rib where it present several shape of cut-outs deals with the results findings we select the optimum design, we focus on the description and analysis of the constraint-natural element method and its application for simulating mechanical problems, the constraint natural element method is the alternative method for the finite element method where the shape functions is constructed on an extension of Voronoi diagram dual of Delaunay tessellation for non-convex domains. IntroductionThe wing ribs are structural elements of the airplane; with the longeron they form the skeleton for the wing skin where their functions are to maintain its shape. The ribs do not participate in the strength of the aircraft as a whole, but transmit the forces encountered by the skin to the longeron. They are subjected to loading systems. External loads applied in the plane of the rib produce a change in shear force in the wing across the rib [1]. The geometry may also include holes to reduce the weight of the wing without altering its strength. The ribs are cut to allow to fuels or equipment to pass through it [2], [3]. In this paper the wing rib of a light aircraft are analyzed with different cut-outs design.The design of a new wing rib requires stress analysis. In engineering, stress analysis is a tool rather than a goal; the aim is to determine the stress and to predict the failure in materials subjected to forces or increase the strength of the structure without increasing the weight. Stress analysis can be performed using conventional and analytical mathematical techniques, an experimental testing or computational simulation.Widely used in computational mechanics the finite element method is considered as the robust method to analysis mechanical phenomena [4] but this method failed to analyze some case such as large transformations problems, a localization of initiation and propagation of a crack, displacement of interfaces between solid and fluid. In the last few years there has been an increasing interest in a novel numerical method alternative to the finite element method, meshless methods have been developed with the aim to solve problems associated mesh steps linking to the finite element method. meshless method construct the interpolating around a set of point that means no connection between nodes and no contract of shape of the element, the refining of mesh or in this case a set of point is automatically by admitting new points; however those methods suffer from a major problem where the imposition of boundary conditions is very complex and the support of the shape function must be contained a sufficient number of neighboring nodes.

Abstract. The present work is a proposed optimization model of grid sub-stiffened panels for aerospace applications, having a better knowledge about the stability analysis of conventional grid sub-stiffened panels against loading and different mode of failure occurring lead us thinking about the topology optimization. In a first stage, we will analyse the stability performance of such structures against specific mechanical loading and conclude some techniques to introduce a topology optimization through PSO algorithm of some design variables. The aim is the better exploitation of the sub-stiffened panel along the plan so that the area less stressed due the charging will be extruded in mass for the enhancement of the concept of looking for better performance with a structure already saved in weight.

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