Method for the structural analysis of panels consisting of an isotropic material and stiffened by triangular pockets

Abstract

A method for dimensioning of panels stiffened by triangular pockets that make it possible to take into account aeronautical specifics and more particularly the stresses that are admissible for the different types of buckling and the calculations of adapted reserve factors is presented. The method relates to dimensioning of a substantially plane panel of homogeneous and isotropic material by an analytical procedure, wherein the panel is composed of a skin reinforced by an assembly of three parallel bundles of stiffeners integrated with the panel, and triangular pockets defined on the skin, the stiffeners are strip-shaped and the panel must satisfy a specification of mechanical resistance to predetermined external loads, including steps organized in such a way that they can be repeated iteratively for different values of input data until reserve factors are obtained to determine the dimensions and arrangement of the panel elements necessary to obtain the imposed mechanical resistance.

1 . (canceled) 
     
     
         2 : A method for dimensioning of a substantially plane panel of homogeneous and isotropic material by an analytical procedure, the panel having a skin reinforced by an assembly of three parallel bundles of stiffeners integrated with the panel, and triangular pockets defined on the skin by the stiffeners, wherein the stiffeners are strip-shaped and the panel must satisfy a specification of mechanical resistance to predetermined external loads, the method includes:
 acquiring values of input data commensurate with a geometry of the panel, a material of the panel, and loading applied to the panel;   calculating stresses applied on the skin of the panel and the stiffeners, based on the geometry of the panel stiffened by the triangular pockets, and on applied external loads;   calculating internal loads induced on the panel;   performing a strength analysis including calculating reserve factors of the material at a limit load and at an ultimate load;   calculating local stresses admissible by the panel, including calculating the reserve factors at maximum stresses; and   calculating general instability of the panel, including calculating a reserve factor for a stiffened flat panel under pure or combined loading conditions.   
     
     
         3 : The method of  claim 2 , wherein the input data includes the mechanical parameters related to the material, dimensions of the panel, cross sections of the stiffeners, dimensions of the core, a constant thickness of the panel and limit loads of the panel. 
     
     
         4 : The method of  claim 2 , wherein calculating the internal loads induced on the panel further include performing a correction of the applied loads that takes plasticity into account using an iterative method of calculation of plastic stresses, carried out until five parameters of the material (E 0°   st , E +□   st , E −□   st , E skin , □ ep ) acquired during the first step are substantially equal to the same parameters obtained after calculation of plastic stress. 
     
     
         5 : The method of  claim 2 , wherein calculating the local stresses further includes calculating admissible buckling flows and reserve factors for isosceles triangular pockets, wherein the applied stresses taken into account for calculating the reserve factor are stresses acting exclusively in the skin and external flows used are skin flows that do not correspond to a complete loading of the panel. 
     
     
         6 : The method of  claim 5 , wherein calculating admissible buckling flows further includes calculating admissible values for plates subjected to cases of pure loading (compression in two directions in the plane, shear) by using a finite elements procedure, and calculating curves of interaction between these cases of pure loading. 
     
     
         7 : The method of  claim 6 , wherein calculating admissible values includes creating a parametric finite elements model of a triangular plate, executing numerous different combinations to obtain buckling results, obtaining parameters compatible with a polynomial analytical formulation. 
     
     
         8 : The method of  claim 7 , wherein, in the case of pure loading, the interaction curves are defined by creating finite elements models of a plurality of triangular plates having different isosceles angles, wherein the isosceles angle θ is defined as a base angle of the isosceles triangles, and for each isosceles angle the following steps are performed:
 determining the admissible folding flow (without plastic correction) for diverse plate thicknesses via finite elements model, 
 plotting a curve of admissible buckling flow as a function of the ratio 
 
       
         
           
             
               
                 D 
                 
                   h 
                   2 
                 
               
                
               
                 ( 
                 D 
               
             
           
         
       
       plate stiffness, h height of the triangle), wherein this curve is determined for small values of the ratio 
       
         
           
             
               D 
               
                 h 
                 2 
               
             
           
         
       
       by a second degree equation that is a function of this ratio, in which the coefficients K 1  and K 2  depend on the angle and on the load case under consideration, and
 plotting the evolution of the coefficients K 1  and K 2  of the polynomial equation as a function of the base angle of the isosceles triangle, wherein these coefficients are plotted as a function of the angle of the triangular plates under consideration, then interpolating to determine a polynomial equation with which these constants can be calculated regardless of the isosceles angle. 
 
     
     
         9 : The method of  claim 7 , wherein in the case of combined loading, the following hypothesis is used: if certain components of the combined load are in tension, then these components are not taken into account for the calculation, and in that the interaction curves are defined by
 creating finite elements models of a plurality of triangular plates having different isosceles angles, wherein the isosceles angle is defined as the base angle of the isosceles triangle, the following step are performed   determining the inherent buckling value corresponding to different distributions of external loads,   plotting interaction curves for each angle and each combination of loads, then approximating these curves with a single equation covering all combinations:   
       
         
           
             
               
                 
                   
                     E 
                     eX 
                     A 
                   
                   + 
                   
                     R 
                     cY 
                     B 
                   
                   + 
                   
                     R 
                     s 
                     C 
                   
                 
                 = 
                 
                   1 
                    
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         
                           where 
                            
                           
                               
                           
                            
                           
                             R 
                             i 
                           
                         
                         = 
                         
                           
                             N 
                             i 
                             app 
                           
                           
                             N 
                             i 
                             crit 
                           
                         
                       
                       , 
                       
                         i 
                         = 
                         cX 
                       
                       , 
                       
                         cY 
                          
                         
                             
                         
                          
                         or 
                          
                         
                             
                         
                          
                         s 
                       
                     
                     ) 
                   
                 
               
               , 
             
           
         
       
       wherein A, B, C are empirical coefficients. 
     
     
         10 : The method of one of  claim 7 , wherein in the case of isosceles triangular plates in simple or nested bracing relationship, in case of combined loading, one interaction curve: R cX +R cY +R s   3/2 =1, is used for all loading cases. 
     
     
         11 : The method of  claim 10 , wherein calculating the reserve factor is calculated on the basis of external flows of the stiffened panel and of limit conditions in simple or nested bracing relationship. 
     
     
         12 : A non-transitory computer readable medium storing computer-readable instructions therein which when executed by a computer cause the computer to perform a method for dimensioning of a substantially plane panel, the method comprising:
 acquiring values of input data commensurate with a geometry of the panel, a material of the panel, and loading applied to the panel;   calculating stresses applied on the skin of the panel and the stiffeners, based on the geometry of the panel stiffened by the triangular pockets, and on applied external loads;   calculating internal loads induced on the panel;   performing a strength analysis including calculating reserve factors of the material at a limit load and at an ultimate load;   calculating local stresses admissible by the panel, including calculating the reserve factors at maximum stresses; and
 calculating general instability of the panel, including calculating a reserve factor for a stiffened flat panel under pure or combined loading conditions.