Modular origami approach for rigid foldable steel load-bearing plate lattices in arbitrary sizes

Abstract

An approach for fabricating rigid foldable steel load-bearing structures is disclosed. The invention employs unit cells with an expanded-truncated rectangular pyramid geometry, formed from metallic sheet stock through a progressive folding process. The modular design reduces strain concentrations, eliminates edge-edge connections, and enables robust mechanical joining methods such as riveting. The manufacturing process uses press-forming molds to ensure precision and accommodate springback in metallic materials. The resulting structures exhibit customizable relative densities, enhanced mechanical performance, and improved energy absorption, making them suitable for static and dynamic loading scenarios.

What is claimed is: 
     
         1 . A regular repeated structure, comprising:
 a plurality of unit cells, each unit cell having an expanded-truncated rectangular pyramid geometry, wherein:   the unit cell includes a height (h), width (w), expanded flaps (b), truncation (e), and angles (θ 2  and ρ 1 );   the expanded flaps (b) provide facet-facet contact points for assembly; and   the unit cells are discretely assembled into a structure using mechanical connectors.   
     
     
         2 . The structure of  claim 1 , wherein the unit cells are formed of sheet stock. 
     
     
         3 . The structure of  claim 2 , wherein the sheet stock is made of metal. 
     
     
         4 . The structure of  claim 1 , wherein the mechanical connectors are rivets. 
     
     
         5 . The structure of  claim 1 , wherein the unit cells are assembled into a lattice structure configured in an arbitrary array of n×m×i unit cells. 
     
     
         6 . The structure of  claim 2 , wherein the unit cells are folded using a progressive folding process comprising:
 cutting the sheet stock into a flat preform configuration;   imprinting a crease map onto the flat preform using a press-forming mold;   applying intermediate strain to the flat preform using a second press-forming mold; and   overfolding the unit cell using a third press-forming mold to account for springback.   
     
     
         7 . The structure of  claim 1 , wherein the sheet stock is stainless steel. 
     
     
         8 . The structure of  claim 1 , wherein the unit cells are formed via a process selected from the group of processes including essentially folding, stamping, molding, casting, die casting, thermoforming, roll forming, hydroforming, explosive forming, electromagnetic forming, additive manufacturing, incremental sheet forming, machining, and combinations thereof. 
     
     
         9 . A method of manufacturing a regular repeated structure, comprising:
 cutting sheet stock into a flat preform configuration;   progressively folding the flat preform into a unit cell having an expanded-truncated rectangular pyramid geometry, wherein the folding process includes imprinting a crease map, applying intermediate strain, and overfolding to account for springback;   assembling a plurality of unit cells into a structure using mechanical connectors; and   configuring the structure into an arbitrary array of n×m×i unit cells.   
     
     
         10 . The method of  claim 9 , wherein the sheet stock is steel. 
     
     
         11 . The method of  claim 9 , wherein the mechanical connectors are rivets. 
     
     
         12 . The method of  claim 9 , further comprising introducing small holes at vertices of the flat preform where multiple creasing lines converge to mitigate local malformations. 
     
     
         13 . The method of  claim 9 , further comprising modifying the geometry of the unit cells to include triangular truncated pyramids or other configurations to customize properties. 
     
     
         14 . The method of  claim 9 , wherein the progressively folding step further comprises placing the flat preform into a mold and pressing the flat preform to form a fold to further shape the preform. 
     
     
         15 . A method of manufacturing a regular repeated structure, comprising:
 forming the flat preform into a unit cell having an expanded-truncated rectangular pyramid geometry, wherein the forming process includes imprinting a crease map, applying intermediate strain, and accounting for springback;   assembling a plurality of unit cells into a structure using mechanical connectors; and   configuring the structure into an arbitrary array of n×m×i unit cells.   
     
     
         16 . The method of  claim 15 , wherein the unit cells are formed via a process selected from the group of processes including essentially folding, stamping, molding, casting, die casting, thermoforming, roll forming, hydroforming, explosive forming, electromagnetic forming, additive manufacturing, incremental sheet forming, machining, and combinations thereof. 
     
     
         17 . A method for simulating the mechanical response of a regular repeated structure using periodic boundary conditions, comprising:
 selecting a representative volume element (RVE) corresponding to a unit cell of the plate lattice, the RVE defined by a bounding box delineated by three lattice vectors LVx, LVy, and LVz;   meshing the unit cell with symmetric seeding across the XY, XZ, and YZ planes;   identifying pairs of boundary nodes (na,nb) such that the difference in their coordinates satisfies:   
       
         
           
             
               
                 
                   nb 
                   - 
                   
                     n 
                     ⁢ 
                     a 
                   
                 
                 = 
                 
                   
                     n 
                     ⁢ 
                     1 
                     ⁢ 
                     L 
                     ⁢ 
                     V 
                     ⁢ 
                     x 
                   
                   + 
                   
                     n 
                     ⁢ 
                     2 
                     ⁢ 
                     LVy 
                   
                   + 
                   
                     n 
                     ⁢ 
                     3 
                     ⁢ 
                     LVz 
                   
                 
               
               , 
             
           
         
         where n1, n2, n3 are components of any possible linear combination of the three lattice vectors; 
         pairing the displacements of the identified node pairs according to 
       
       
         
           
             
               
                 
                   ub 
                   - 
                   ua 
                 
                 = 
                 
                   H 
                   ⁡ 
                   ( 
                   
                     Xb 
                     - 
                     Xa 
                   
                   ) 
                 
               
               , 
             
           
         
         where H is a displacement gradient matrix and Xa, Xb are the coordinates of the selected nodes in the undeformed mesh state; 
         designing the displacement gradient matrix H with virtual nodes to impose a macroscopic deformation, including a constant strain value corresponding to uniaxial compression in the Z-axis; 
         and running a batch of finite element simulations to obtain the unit cell stress response to the applied strain. 
       
     
     
         18 . The method of  claim 17 , wherein the finite element simulations account for the elastoplastic behavior of the metallic material forming the plate lattice structure. 
     
     
         19 . The method of  claim 17 , wherein the unit cell parameters, including height, folding angles, and relative density, are varied across simulations to optimize mechanical performance characteristics.