Generative design shape optimization with size limited fatigue damage for computer aided design and manufacturing

Abstract

Methods, systems, and apparatus, including medium-encoded computer program products, for computer aided design of physical structures using generative design processes, A method includes obtaining, by a computer aided design program, a design space for a modeled object, one or more design criteria for the modeled object, one or more in-use load cases, and a critical fatigue crack length for a material from which A physical structure will be manufactured; iteratively modifying a generatively designed three dimensional shape of the modeled object in the design space in accordance with the critical fatigue crack length for the material, wherein the iteratively modifying comprises enforcing a design criterion that limits a minimum thickness of the generatively designed three dimensional shape, the minimum thickness being based on the critical fatigue crack length for the material.

What is claimed is: 
     
         1 . A method comprising:
 obtaining, by a computer aided design program, a design space for a modeled object, for which a corresponding physical structure will be manufactured, one or more design criteria for the modeled object, one or more in-use load cases for the physical structure, and a critical fatigue crack length for a material from which the physical structure will be manufactured;   iteratively modifying, by the computer aided design program, a generatively designed three dimensional shape of the modeled object in the design space in accordance with the one or more design criteria, the one or more in-use load cases for the physical structure, and the critical fatigue crack length for the material, wherein the iteratively modifying comprises enforcing a design criterion that limits a minimum thickness of the generatively designed three dimensional shape of the modeled object, the minimum thickness being based on the critical fatigue crack length for the material; and   providing, by the computer aided design program, the generatively designed three dimensional shape of the modeled object for use in manufacturing the physical structure corresponding to the modeled object using one or more computer-controlled manufacturing systems.   
     
     
         2 . The method of  claim 1 ,
 wherein the one or more design criteria comprise a required number of loading cycles for the modeled object for each of the one or more in-use load cases for the physical structure;   wherein the obtaining further comprises obtaining one or more specifications of material from which the physical structure will be manufactured, the one or more specifications comprising data relating fatigue strength to loading cycles; and   wherein the iteratively modifying further comprises:
 performing numerical simulation of the modeled object in accordance with a current version of the three dimensional shape and the one or more in-use load cases to produce a current numerical assessment of a physical response of the modeled object, 
 finding a maximized stress or strain element, for at least one of the one or more in-use load cases for the physical structure, from the current numerical assessment of the physical response of the modeled object, 
 determining an expected number of loading cycles for each of the at least one of the one or more in-use load cases for the physical structure using the maximized stress or strain element and the data relating fatigue strength to loading cycles, 
 redefining a fatigue safety factor inequality constraint for the modeled object based on a damage fraction calculated from the required number of loading cycles for the modeled object and the expected number of loading cycles for each of the at least one of the one or more in-use load cases for the physical structure, and 
 computing shape change velocities for an implicit surface in a level-set representation of the three dimensional shape in accordance with at least the fatigue safety factor inequality constraint. 
   
     
     
         3 . The method of  claim 2 ,
 wherein the one or more specifications comprise two or more specifications of respective different materials from which the physical structure will be manufactured, the data comprises data relating fatigue strength to loading cycles for each of the different materials, determining the expected number of loading cycles comprises determining a separate number of expected loading cycles for each of the different materials, and redefining the fatigue safety factor inequality constraint comprises:   calculating a separate fatigue safety factor for each of the different materials based on respective damage fractions calculated from respective ones of the numbers of expected loading cycles for the different materials; and   using a minimum value of the fatigue safety factors for the different materials to redefine the fatigue safety factor inequality constraint for the modeled object; and   wherein computing the shape change velocities comprises computing at least one shape change velocity using a gradient determined from a shape derivative of the fatigue safety factor.   
     
     
         4 . The method of  claim 3 , wherein the finding comprises calculating a maximum stress value for an in-use load case based on at least a standard deviation of a stress distribution in the current numerical assessment of the physical response of the modeled object. 
     
     
         5 . The method of  claim 1 , wherein the enforcing uses a measure of thickness for the generatively designed three dimensional shape of the modeled object that is a combination of at least two distinct thickness measures. 
     
     
         6 . The method of  claim 5 , wherein the at least two distinct thickness measures comprise (i) a first distance measure being a length within the modeled object of a ray cast in a negative normal direction from a surface point of the modeled object, and (ii) a second distance measure being a diameter of a largest sphere that touches the surface point of the modeled object and fits inside the modeled object as determined by checking discrete sampling locations defined on the sphere's surface. 
     
     
         7 . The method of  claim 6 , wherein the enforcing comprises using a volume fraction or a minimum thickness based inequality constraint as a proxy for the design criterion that limits the minimum thickness, wherein the volume fraction or the minimum thickness based inequality constraint is modified using an importance factor, which is set to zero during an initial stage of the iteratively modifying and is adjusted during a subsequent stage of the iteratively modifying based on whether or not one or more other constraints were violated in a prior iteration of the iteratively modifying. 
     
     
         8 . The method of  claim 7 , comprising:
 adjusting a target value of the volume fraction or the minimum thickness based inequality constraint between an initial target value and a final target value across multiple iterations of the iteratively modifying; and   using a proportional-integral-derivative controller to adjust and stabilize changes made in an amount of modification for the modeled object, determined from evaluation of the volume fraction or the minimum thickness based inequality constraint, as the target value is adjusted across the multiple iterations.   
     
     
         9 . The method of  claim 1 , wherein obtaining the critical fatigue crack length for the material comprises:
 obtaining one or more specifications of the material from which the physical structure will be manufactured; and   calculating the critical fatigue crack length for the material from information in the one or more specifications, the information comprising a modulus of the material's fatigue crack growth curve.   
     
     
         10 . The method of  claim 1 , wherein the generatively designed three dimensional shape of the modeled object comprises a level-set representation of an implicit surface, the one or more design criteria comprise a required number of loading cycles for the modeled object for each of the one or more in-use load cases for the physical structure, and the iteratively modifying comprises:
 performing numerical simulation of the modeled object in accordance with a current version of the three dimensional shape and the one or more in-use load cases to produce a current numerical assessment of a physical response of the modeled object;   determining an expected number of loading cycles for each of the one or more in-use load cases for the physical structure using the current numerical assessment and the measure of thickness to enforce the design criterion that limits the minimum thickness;   redefining a fatigue safety factor inequality constraint for the modeled object based on a damage fraction calculated from the required number of loading cycles for the modeled object and the expected number of loading cycles for each of the one or more in-use load cases for the physical structure;   computing shape change velocities for the implicit surface in accordance with at least the fatigue safety factor inequality constraint;   updating the level-set representation using the shape change velocities to produce an updated version of the three dimensional shape of the modeled object; and   repeating at least the performing, the determining, the redefining, the computing and the updating until a predefined number of shape modification iterations have been performed or until the generatively designed three dimensional shape of the modeled object in the design space converges to a stable solution for the one or more design criteria and the one or more in-use load cases.   
     
     
         11 . The method of  claim 10 , wherein the one or more in-use load cases for the physical structure comprise two or more in-use load cases for the physical structure, the one or more design criteria comprise a required number of loading cycles for the modeled object for each of the two or more in-use load cases for the physical structure, determining the expected number of loading cycles comprises determining a separate number of expected loading cycles for each of multiple points on the implicit surface for each of the two or more in-use load cases, and redefining the fatigue safety factor inequality constraint comprises:
 summing, for each of the multiple points, load-specific damage fractions corresponding to the two or more in-use load cases, wherein each load-specific damage fraction comprises an expected number of loading cycles, for one of the multiple points and one of the in-use load cases, divided by the required number of loading cycles for the one of the in-use load cases, to produce a sum of the load-specific damage fractions for each of the multiple points;   inverting each of the sums of the load-specific damage fractions; and   using a minimum value of the inverted sums of the load-specific damage fractions to redefine the fatigue safety factor inequality constraint for the modeled object.   
     
     
         12 . The method of  claim 11 , wherein computing the shape change velocities comprises computing at least one shape change velocity using an amount determined from a shape derivative formula that approximates a shape derivative of the fatigue safety factor. 
     
     
         13 . The method of  claim 12 , wherein the shape derivative formula that approximates the shape derivative of the fatigue safety factor comprises a volume fraction or a minimum thickness based inequality constraint that is modified using an importance factor, which is adjusted based on whether or not one or more other constraints were violated in a prior iteration of the iteratively modifying. 
     
     
         14 . The method of  claim 13 , comprising:
 adjusting a target value of the volume fraction or the minimum thickness based inequality constraint between an initial target value and a final target value across multiple iterations of the iteratively modifying; and   using a proportional-integral-derivative controller to stabilize changes made in the amount determined from the shape derivative formula, and to adjust a total contribution of the amount determined from the shape derivative formula to the shape change velocities used in the updating, as the target value is adjusted across the multiple iterations.   
     
     
         15 . The method of  claim 1 , wherein the one or more computer-controlled manufacturing systems comprise an additive manufacturing machine, and the operations comprise:
 generating toolpath specifications for the additive manufacturing machine from the three dimensional model; and   manufacturing the physical structure corresponding to the object with the additive manufacturing machine using the toolpath specifications.   
     
     
         16 . A system comprising:
 a non-transitory storage medium having instructions of a computer aided design program stored thereon; and   one or more data processing apparatus configured to run the instructions of the computer aided design program to:   obtain a design space for a modeled object, for which a corresponding physical structure will be manufactured, one or more design criteria for the modeled object, one or more in-use load cases for the physical structure, and a critical fatigue crack length for a material from which the physical structure will be manufactured;   iteratively modify a generatively designed three dimensional shape of the modeled object in the design space in accordance with the one or more design criteria, the one or more in-use load cases for the physical structure, and the critical fatigue crack length for the material, wherein the one or more data processing apparatus are configured to run the instructions of the computer aided design program to iteratively modify the generatively designed three dimensional shape of the modeled object by being configured to run the instructions of the computer aided design program to enforce a design criterion that limits a minimum thickness of the generatively designed three dimensional shape of the modeled object, the minimum thickness being based on the critical fatigue crack length for the material; and   provide the generatively designed three dimensional shape of the modeled object for use in manufacturing the physical structure corresponding to the modeled object using one or more computer-controlled manufacturing systems.   
     
     
         17 . The system of  claim 16 , comprising an additive manufacturing machine, wherein the one or more data processing apparatus are configured to run the instructions of the computer aided design program to generate toolpath specifications for the additive manufacturing machine from the three dimensional model, and manufacture the physical structure corresponding to the object with the additive manufacturing machine using the toolpath specifications. 
     
     
         18 . A non-transitory computer-readable medium encoding a computer aided design program operable to cause one or more data processing apparatus to perform operations comprising:
 obtaining, by a computer aided design program, a design space for a modeled object, for which a corresponding physical structure will be manufactured, one or more design criteria for the modeled object, one or more in-use load cases for the physical structure, and a critical fatigue crack length for a material from which the physical structure will be manufactured;   iteratively modifying, by the computer aided design program, a generatively designed three dimensional shape of the modeled object in the design space in accordance with the one or more design criteria, the one or more in-use load cases for the physical structure, and the critical fatigue crack length for the material, wherein the iteratively modifying comprises enforcing a design criterion that limits a minimum thickness of the generatively designed three dimensional shape of the modeled object, the minimum thickness being based on the critical fatigue crack length for the material; and   providing, by the computer aided design program, the generatively designed three dimensional shape of the modeled object for use in manufacturing the physical structure corresponding to the modeled object using one or more computer-controlled manufacturing systems.   
     
     
         19 . The non-transitory computer-readable medium of  claim 18 , wherein the one or more computer-controlled manufacturing systems comprise an additive manufacturing machine, and the operations comprise:
 generating toolpath specifications for the additive manufacturing machine from the three dimensional model; and   manufacturing the physical structure corresponding to the object with the additive manufacturing machine using the toolpath specifications.