Layered Sandwich Structure

Abstract

This homogenized, multilayer sandwich structure has a total bending stiffness. The structure has two external skins each of a material having a modulus, a thickness and a width with contribution to the total moment of inertia. The structure also has a core of a foam material sandwiched between the two external skins, wherein the core has a modulus, a thickness and a width with contribution to the total moment of inertia. The external skins are fixed to the core, the strength of the structure being dependent on the core thickness via cubic power, as well as on the placement of the layers within the structure.

We claim: 
     
         1 . A homogenized, multilayer sandwich structure wherein the structure has a total bending stiffness comprising:
 two external skins each of a material having a modulus, a thickness and a width with contribution to the total moment of inertia;   a core of a foam material sandwiched between the two external skins, wherein the core has a modulus, a thickness and a width with contribution to the total moment of inertia; and   wherein the external skins are fixed to the core, the strength of the structure being mainly dependent on the core thickness via cubic power and the placement of layers within the structure.   
     
     
         2 . A structure according to  claim 1  further comprising:
 the core being a reference layer; and 
 wherein layer homogenization is achieved via changing the width of skins by a multiplier (n,g) calculated as a ratio of the skins modulus to the modulus of the reference layer. 
 
     
     
         3 . A homogenized, multilayer sandwich structure wherein the structure has a total bending stiffness (S T );
 wherein S T  is a complex function of each layer's modulus (Ei) and each layers contribution to a moment of inertia (I i );   wherein I i  is defined by the thickness of a layer, the layers location in the structure and the width of the layer;   wherein layers of different moduli are represented by a reference layer (E 1 ); and   wherein layer homogenization is achieved via changing the width of a layer by a multiplier calculated as a ratio of a layer's modulus to the modulus of the reference layer.   
     
     
         4 . A structure according to  claim 3  wherein: 
       
         
           
             
               
                 
                   
                     
                       S 
                       T 
                     
                     = 
                     
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           n 
                         
                          
                         
                             
                         
                          
                         
                           S 
                           i 
                         
                       
                       = 
                       
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             n 
                           
                            
                           
                               
                           
                            
                           
                             
                               E 
                               i 
                             
                             · 
                             
                               I 
                               i 
                             
                           
                         
                         = 
                         
                           
                             
                               E 
                               1 
                             
                              
                             
                               
                                 ∑ 
                                 
                                   i 
                                   = 
                                   1 
                                 
                                 n 
                               
                                
                               
                                   
                               
                                
                               
                                 
                                   
                                     E 
                                     i 
                                   
                                   
                                     E 
                                     1 
                                   
                                 
                                  
                                 
                                   I 
                                   i 
                                 
                               
                             
                           
                           = 
                           
                             
                               E 
                               1 
                             
                              
                             
                               
                                 ∑ 
                                 
                                   i 
                                   = 
                                   1 
                                 
                                 n 
                               
                                
                               
                                   
                               
                                
                               
                                 
                                   n 
                                   i 
                                 
                                  
                                 
                                   I 
                                   i 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
                 
                   
                     Eq 
                     . 
                     
                         
                     
                      
                     
                       ( 
                       1 
                       ) 
                     
                   
                 
               
             
           
         
         Where: 
       
       
         
           
             
               
                 n 
                 i 
               
               = 
               
                 
                   E 
                   i 
                 
                 
                   E 
                   1 
                 
               
             
           
         
       
       is the ratio of the modulus of the i th  layer to the reference (i=1) layer 
     
     
         5 . A structure according to  claim 4  wherein: 
       
         
           
             
               
                 
                   
                     
                       I 
                       i 
                     
                     = 
                     
                       
                         
                           
                             Wn 
                             i 
                           
                            
                           
                             h 
                             i 
                             3 
                           
                         
                         12 
                       
                       + 
                       
                         
                           Wn 
                           i 
                         
                          
                         
                           
                             
                               h 
                               i 
                             
                              
                             
                               ( 
                               
                                 
                                   r 
                                   i 
                                 
                                 - 
                                 R 
                               
                               ) 
                             
                           
                           2 
                         
                       
                     
                   
                 
                 
                   
                     Eq 
                     . 
                     
                         
                     
                      
                     
                       ( 
                       2 
                       ) 
                     
                   
                 
               
             
           
         
         Where: 
       
       
         
           
             
               R 
               = 
               
                 
                   
                     ∑ 
                     
                       i 
                       = 
                       1 
                     
                     n 
                   
                    
                   
                       
                   
                    
                   
                     
                       n 
                       i 
                     
                      
                     
                       h 
                       i 
                     
                      
                     
                       r 
                       i 
                     
                   
                 
                 
                   
                     ∑ 
                     
                       i 
                       = 
                       1 
                     
                     n 
                   
                    
                   
                       
                   
                    
                   
                     
                       n 
                       i 
                     
                      
                     
                       h 
                       i 
                     
                   
                 
               
             
           
         
       
       is a neutral axis of a composite layer