Generative design shape optimization with damage prevention over loading cycles for computer aided design and manufacturing

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 one or more specifications of material from which the physical structure will be manufactured, 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, and

the one or more specifications comprise data relating fatigue strength to loading cycles;

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 one or more specifications, wherein 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,

finding a maximized stress or strain element, for each 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 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 one or more in-use load cases for the physical structure,

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,

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 finding, 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; 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 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.

3. The method of claim 2 , 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, and calculating the separate safety factor for each respective one of the different materials comprises:

summing load-specific damage fractions corresponding to the two or more in-use load cases, wherein each load-specific damage fraction comprises a number of expected loading cycles, for one of the different materials 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; and

inverting the sum of the load-specific damage fractions to obtain the separate safety factor.

4. The method of claim 2 , 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.

5. The method of claim 2 , wherein obtaining the two or more specifications comprises receiving a set of data points for each of the different materials, each of the data points comprising a load cycles number and a fatigue strength value data pair, and determining the separate number of expected loading cycles for each of the different materials comprises:

returning a number of loading cycles from one or more curves fit to the set of data points in a plastic region and an elastic region of the data relating fatigue strength to loading cycles; and

returning a highest load cycles number from the set of data points in an endurance region of the data relating fatigue strength to loading cycles.

6. The method of claim 2 , 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.

7. The method of claim 6 , wherein the shape derivative formula that approximates the shape derivative of the fatigue safety factor comprises a volume fraction or a stress 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.

8. The method of claim 7 , comprising:

adjusting a target value of the volume fraction or a 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 as the target value is adjusted across the multiple iterations.

9. The method of claim 7 , comprising using a proportional-integral-derivative controller to adjust a total contribution of the amount determined from the shape derivative formula to the shape change velocities used in the updating.

10. The method of claim 1 , 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.

11. 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 one or more specifications of material from which the physical structure will be manufactured, 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, and

the one or more specifications comprise data relating fatigue strength to loading cycles;

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 one or more specifications, 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

perform 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,

find a maximized stress or strain element, for each 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,

determine an expected number of loading cycles for each 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,

redefine 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,

compute 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,

update the level-set representation using the shape change velocities to produce an updated version of the three dimensional shape of the modeled object, and

repeat at least the performing, the finding, 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; and

providing 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.

12. The system of claim 11 , 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.

13. 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 one or more specifications of material from which the physical structure will be manufactured, 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, and

the one or more specifications comprise data relating fatigue strength to loading cycles;

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 one or more specifications, wherein 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,

finding a maximized stress or strain element, for each 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 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 one or more in-use load cases for the physical structure,

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,

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 finding, 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; 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.

14. The non-transitory computer-readable medium of claim 13 , 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.

15. The computer-readable medium of claim 13 , 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.

16. The computer-readable medium of claim 15 , 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, and calculating the separate safety factor for each respective one of the different materials comprises:

summing load-specific damage fractions corresponding to the two or more in-use load cases, wherein each load-specific damage fraction comprises a number of expected loading cycles, for one of the different materials 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; and

inverting the sum of the load-specific damage fractions to obtain the separate safety factor.

17. The computer-readable medium of claim 15 , 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.

18. The computer-readable medium of claim 15 , wherein obtaining the two or more specifications comprises receiving a set of data points for each of the different materials, each of the data points comprising a load cycles number and a fatigue strength value data pair, and determining the separate number of expected loading cycles for each of the different materials comprises:

returning a number of loading cycles from one or more curves fit to the set of data points in a plastic region and an elastic region of the data relating fatigue strength to loading cycles; and

returning a highest load cycles number from the set of data points in an endurance region of the data relating fatigue strength to loading cycles.

19. The computer-readable medium of claim 15 , 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.

20. The computer-readable medium of claim 19 , wherein the shape derivative formula that approximates the shape derivative of the fatigue safety factor comprises a volume fraction or a stress 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.

21. The computer-readable medium of claim 20 , wherein the operations comprise:

adjusting a target value of the volume fraction or a 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 as the target value is adjusted across the multiple iterations.

22. The computer-readable medium of claim 20 , wherein the operations comprise using a proportional-integral-derivative controller to adjust a total contribution of the amount determined from the shape derivative formula to the shape change velocities used in the updating.

23. The computer-readable medium of claim 13 , 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.