System and method for finite element based on topology optimization

Abstract

A method is disclosed for providing an optimal topology for a structure based on a set of design criteria including at least one support point and at least one force to be applied to the structure. The method includes the steps of identifying a plurality of nodes within a structure design domain, and assigning an initial density value to the plurality of nodes. The method also includes the steps of conducting a finite element analysis on the nodes, determining a stress intensity value for each node, ranking the nodes by relative stress intensity values, and adjusting the density value for each node. The method also includes the step of repeating the steps of conducting a finite element analysis on the nodes, determining the stress intensity value for each node, ranking the nodes by relative stress intensity values, and adjusting the density value for each node until a termination criteria is realized, thereby providing an optimal topology.

1 . A method of providing an optimal topology for a structure based on a set of: design criteria including at least one support point and at least one force to be applied to the structure, said method comprising the steps of:
 identifying a plurality of nodes within a structure design domain, and assigning an initial density value to said plurality of nodes;   conducting a finite element analysis on said nodes;   determining a stress intensity value for each node;   ranking the nodes by relative stress intensity values;   adjusting the density value for each node; and   repeating the steps of conducting a finite element analysis on said nodes, determining the stress intensity value for each node, ranking the nodes by relative stress intensity values, and adjusting the density value for each node until a termination criteria is realized, thereby providing an optimal topology.   
   
   
       2 . The method as claimed in  claim 1 , wherein a final density value for each node is either a substantially maximum density value or a substantially minimum density value. 
   
   
       3 . The method as claimed in  claim 1 , wherein said stress intensity value is a stress value, and the method further includes the step of defining a penalization for certain nodes and identifying the number of nodes for penalization. 
   
   
       4 . The method as claimed in  claim 1 , wherein the stress intensity value is one of a stress value, a strain value or a strain energy value. 
   
   
       5 . The method as claimed in  claim 1 , wherein said method further includes the step of assigning the initial density value to said plurality of nodes involves distributing a mass uniformly through the structure design domain. 
   
   
       6 . The method as claimed in  claim 1 , wherein said method further includes the step of reducing the density of certain nodes based on the ranking of nodes by stress intensity values. 
   
   
       7 . The method as claimed in  claim 1 , wherein said method further includes the step of comparing the densities of certain nodes to a set of known density distributions at each iteration to provide a smooth transition from uniform partially dense to distinct regions of fully dense material and regions of voids. 
   
   
       8 . The method as claimed in  claim 7 , wherein said set of known density distributions are employed to map a proportional position ranking of nodes based on stress, strain or strain energy at an end of each iteration to their nodal densities for a next iteration. 
   
   
       9 . The method as claimed in  claim 1 , wherein said method employs artificial elastic moduli to generate optimal topologies for structures composed of a plurality of materials having different properties in one of tension and compression. 
   
   
       10 . The method as claimed in  claim 1 , wherein said method employs artificial elastic moduli to generate optimal topologies for structures composed of a plurality of materials having different properties in one of strength of stiffness. 
   
   
       11 . The method as claimed in  claim 10 , wherein one of said materials includes a fiber reinforced material. 
   
   
       12 . The method as claimed in  claim 1 , wherein said set of design criteria includes a plurality of force to be applied to the structure. 
   
   
       13 . The method as claimed in  claim 1 , wherein said method is employed to provide a three-dimensionally optimized topography. 
   
   
       14 . The method as claimed in  claim 1 , wherein a nodal density distribution is employed to generate precise geometry in a standard computer aided design file format for direct use in the design and manufacture of minimum weight structures. 
   
   
       15 . A method of providing an optimal topology for a structure based on a set of design criteria including at least one support point and at least one force to be applied to the structure, said method comprising the steps of:
 identifying a plurality of nodes within a structure design domain, and assigning an initial density value to said plurality of nodes;   conducting a finite element analysis on said nodes;   determining a stress intensity value for each node;   ranking the nodes by relative stress intensity values;   reducing the density value for certain nodes based on the ranking; and   repeating the previous four steps until each node has either a substantially maximum density value or a substantially minimum density value.   
   
   
       16 . The method as claimed in  claim 15 , wherein said stress intensity value is one of a stress value, a strain value or a strain energy value. 
   
   
       17 . A method of providing an optimal topology for a structure based on a set of design criteria including at least one support point and at least one force to be applied to the structure, said method comprising the steps of:
 identifying a plurality of nodes within a structure design domain, and assigning an initial density value to said plurality of nodes;   conducting a finite element analysis on said nodes;   determining a stress intensity value for each node;   ranking the nodes by relative stress intensity values;   applying a set of known density distributions to to adjust the density value for certain nodes based on the ranking; and   repeating the previous four steps until each node has either a substantially maximum density value or a substantially minimum density value.   
   
   
       18 . The method as claimed in  claim 17 , wherein said stress intensity value is one of a stress value, a strain value or a strain energy value. 
   
   
       19 . The method as claimed in  claim 17 , wherein said step of assigning the initial density value to said plurality of nodes involves distributing a mass uniformly through the structure design domain. 
   
   
       20 . The method as claimed in  claim 17 , wherein said initial density value is neither the substantially maximum density value or the substantially minimum density value.