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This research is devoted to the adaptive solution and control point net improvement of axisymmetric problems in isogeometric analysis using the error estimation based methods for stress recovery. For this purpose, after the calculation of the energy norm, the estimated value of error in the vicinity of each control point is assigned to the neighboring members of a hypothetical truss-like structure as an artificial thermal gradient. By analysis of this network of rods under the temperature variations a new arrangement of control points is obtained. Repeating this process of thermal isogeometric analysis will eventually lead to a better distribution of errors in the domain of the problem and results in an optimal net of control points for the calculation of the integrals. To demonstrate the performance and efficiency of the proposed method, two axisymmetric elasticity problems with available analytical solutions are considered. The obtained results indicate that this innovative approach is effective in reducing errors of axisymmetric problems and can be employed for improving the accuracy in the context of the isogeometric analysis method. Innovated method of this research focuses on adaptive analysis and Network improving of axisymmetric problems in isogeometric analysis using error estimation methods based on stress recovery. For this purpose after calculation the energy norm, estimated value of error in the vicinity of control points is assigned to each rod as the thermal gradient. Thus after analyzing the hypothetical rods network under the temperature changes a new arrangement of control points and knot vectors can be obtained. The use of multi-cycle of this process in isogeometric analysis will lead to a better distribution of errors in the domain and thus achieve optimal network to calculate the integrals. To measure the efficiency of this method and demonstrate the increased carefully in axisymmetric problems, which has the analytical solution, two elasticity problem is evaluated. The results show that innovative network improving method has good efficiency to reduce the error rate and can be used to increase the accuracy of isogeometric analysis results. Innovated method of this research focuses on adaptive analysis and Network improving of axisymmetric problems in isogeometric analysis using error estimation methods based on stress recovery. For this purpose after calculation the energy norm, estimated value of error in the vicinity of control points is assigned to each rod as the thermal gradient. Thus after analyzing the hypothetical rods network under the temperature changes a new arrangement of control points and knot vectors can be obtained. The use of multi-cycle of this process in isogeometric analysis will lead to a better distribution of errors in the domain and thus achieve optimal network to calculate the integrals. To measure the efficiency of this method and demonstrate the increased carefully in axisymmetric problems, which has the analytical solution, two elasticity problem is evaluated. The results show that innovative network improving method has good efficiency to reduce the error rate and can be used to increase the accuracy of isogeometric analysis results.

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In this paper, an analytical solution for stress and displacement in an inhomogeneous half space under the action of concentrated normal surface loading is investigated. The Young modulus is considered to vary with the spherical radius R in a power law form of order n, while the Poisson’s ratio is taken to be constant. The problem is solved analytically using an elasticity approach and considering a semi-inverse method in which, based on equilibrium equations on the surface of an arbitrary hemisphere in the half-space and centered at the point of application of load, some stress components are assumed to be proportional to 1/R2. It is then shown that this assumption is valid and all stress components in this axisymmetric problem are proportional to 1/R2, while displacements are proportional to 1/R(n+1). and their variation with azimuthal coordinate φ is in the form of a special function called hyper-geometric function. Illustrative examples are presented, which show variations of stresses and displacements both in R and φ directions. It is seen that the inhomogeneity parameter has a significant effect on both of these field variables.

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Inlet performance is an important field in aerodynamic design of aerial vehicle engines. This study has been focused on numerical investigation of Mach number effects on a supersonic axisymmetric mixed compression inlet performance. For this purpose, a density based finite volume CFD code has been developed. A structured multi-block grid and an explicit time discretization of Reynolds averaged Navier-Stokes (RANS) equations have been used. Furthermore, Roe’s approximated Riemann solver has been utilized for computing inviscid flux vectors. Also, the monotone upstream centered schemes for conservation laws (MUSCL) extrapolation with Van Albada limiter has been used to obtain second order accuracy. In addition, Spalart-Allmaras one-equation turbulence model has been used to close the governing equations. The code is validated in three test cases by comparing numerical results against experimental data. Finally, the code has been utilized for numerically simulation of a specific supersonic mixed compression inlet. The effects of free stream Mach number on performance parameters, including mass flow ratio (MFR), drag coefficient, total pressure recovery (TPR), and flow distortion (FD) have been discussed and investigated. Results show that Mach number increase, leads to TPR and drag coefficient decrease; however, MFR and FD increase. Also, FD variations with respect to other performance parameters are significant, such that Mach number increase from 1.8 to 2.2 leads to more than 100% FD increment while MFR has been increase less than 10%. By using this code, it will be possible to design, parametric study, and geometrical optimization of axisymmetric supersonic inlet.