The aim of this work is to develop a new numerical calculation program to determine the effect of the stagnation temperature on the calculation of the supersonic flow around a pointed airfoils using the equations for oblique shock wave and the Prandtl Meyer expansion, under the model at high temperature, calorically imperfect and thermally perfect gas, lower than the dissociation threshold of the molecules. The specific heat at constant pressure does not remain constant and varies with the temperature. The new model allows making corrections to the perfect gas model designed for low stagnation temperature, low Mach number, low incidence angle and low airfoil thickness. The stagnation temperature is an important parameter in our model. The airfoil should be pointed at the leading edge to allow an attached shock solution to be seen. The airfoil is discretized into several panels on the extrados and the intrados, placed one adjacent to the other. The distribution of the flow on the panel in question gives a compression or an expansion according to the deviation of the flow with respect to the old adjacent panel. The program determines all the aerodynamic characteristics of the flow and in particular the aerodynamic coefficients. The calculation accuracy depends on the number of panels considered on the airfoil. The application is made for high values of stagnation temperature, Mach number and airfoil thickness. A comparison between our high temperature model and the perfect gas model is presented, in order to determine an application limit of the latter. The application is for air.

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The aim of this work is to develop a new numerical calculation program to calculate the shear stress subjected to a shear force for the general case of deflected bending, and to develop in this context a new numerical computational program for the calculation of the shear stress distribution in an arbitrary complex cross-section, in light to determine the position, and the value of the maximum stress, and consequently the determination of the shape factor seen in their practical importance. The calculation is valid for any axis and not necessary for the two principal axis of inertia. The calculation of the geometric characteristics of the section is necessary in this case. The formulae is done by the calculation of the static moment of the cutoff portion of section, where the calculation is made by an evaluation of an integral of complex function. View the obtained of a complex function, the calculation is given numerically by the use of the high order Gauss-Legendre formulae. The validation of the results is made by the convergence of the numerical accurate results to those for a chosen section like the arbitrary triangle which the exact result can be calculated analytically by the use of the new formulae. In this case, the solution is seen when the relative error given by the quadrature approaches to zero. The application will be for unsymmetrical section, views their practical interests in engineering.

The work focuses to develop a new numerical calculation program for determining the gas effect at high temperature instead air on the calculation of the oblique and conical shock waves parameters and make applications for various external and internal aerodynamics problems like, the calculation of the suitable intake adaptation parameters, dihedron and cone wave drag, aerodynamic coefficients of a pointed supersonic airfoil and oblique shock reflection. All this for future aerodynamics (gas dynamics) like the phenomenon of climate change in the near and far future because of the enlargement progressive of the layer ozone hole which will lead to an increase in the temperature of the ambient medium, and by the environment pollution by the shining of the waste which will cause a new decomposition of gases from the ambient environment. Another interesting application for actual aerodynamics (gas dynamics) is the performance of tests in wind tunnels supplied by a combustion chamber making a reaction of gases giving a gas with new thermodynamics parameters which is not necessarily air. To make a calculation, the selected gases are H 2 , O 2 , N 2 , CO, CO 2 , H 2 O, NH 3 , CH 4 and air.

The aim of this work is to develop a new generalized formula and a numerical computation program for evaluating the energy form coefficient of a complex and arbitrary cross section for full and thin-walled cross section with respect to any central axis, for the bending of beams of small lengths in comparison with the transverse dimension of the section. This coefficient plays a very important role in the calculation of the deformation energy of beams subjected to bending under the effect of a shearing force for short beams. It also enters in the formulation of FEM bending model, in order to calculate the stresses and the strains due to the external forces. The application is made for complex sections used in various fields of construction and in particular for airfoils designed for aerospace construction. A method is developed to calculate this coefficient as a function of the rotation of the central axes. The calculation of the area, the moments, and the product of inertias with respect to the central axes is necessary. The formula for calculating this coefficient is presented as a definite integral of a non-analytical function determined point by point along the direction of the application of the shear force. This function is based on the calculation of the partial static moments. The calculation of the latter is based on the development of a technique by subdividing the upper part of the section into adjacent common triangles at one point for the full solid section or by segments on the boundary for the thin-walled section. To speed up the process of numerically calculating this integral with high precision and reduced time, Gauss Legendre quadrature of order 40 is used. The calculation of the distribution of the tangential stress as well as its maximum value is determined. A shear shape coefficient is therefore determined. In the second part of this work, an application is made for the static calculation by the FEM of a hyper static beam with a view to determining the influence of this coefficient on all the parameters of resistance and bending stiffness as a correction of the classical model of bending by the FEM. A study of the error made by the classical bending model on our shear effect model is presented. A coefficient of efficiency of a section is presented.