Generative design shape optimization based on a target part reliability for computer aided design and manufacturing

1. A method comprising:

obtaining a design space for a modeled object, for which a corresponding physical structure is to be manufactured using one or more materials, and design criteria for the modeled object including one or more loading cases for numerical simulation of the physical structure and at least one design constraint on an acceptable likelihood of failure for the physical structure, wherein a statistical model that relates a structural performance metric to specific likelihoods of failure for the one or more materials is used to translate between the acceptable likelihood of failure and a value for the structural performance metric;

iteratively modifying a generatively designed three dimensional shape of the modeled object in the design space in accordance with the design criteria including the one or more loading cases for the numerical simulation of the physical structure and the at least one design constraint to stay under the acceptable likelihood of failure for the physical structure, wherein the numerical simulation includes computing the structural performance metric, which is evaluated against the at least one design constraint; and

providing the generatively designed three dimensional shape of the modeled object for use in manufacturing the physical structure;

wherein the at least one design constraint specifies a maximum likelihood of failure, obtaining the at least one design constraint comprises setting the maximum likelihood of failure based on the acceptable likelihood of failure for the physical structure, and the iteratively modifying comprises evaluating the maximum likelihood of failure at each of multiple different locations on or in the modeled object by calculating a likelihood of failure at the location using the statistical model and a value for the structural performance metric indicated for the location by the numerical simulation in accordance with one or more specific geometric parameters of the modeled object at the location.

2. The method of claim 1 , wherein the statistical model is a Weibull statistical model of a probability of failure distribution function.

3. The method of claim 1 , wherein the statistical model comprises a survivor function that relates values of the performance metric to specific likelihoods of failure for the one or more materials across different thicknesses of the one or more materials.

4. The method of claim 3 , wherein the one or more materials comprise different versions of a same base material, the different versions corresponding to different build orientations for the same base material.

5. The method of claim 3 , wherein the one or more materials comprise different base materials, different versions of a same base material, or both.

6. The method of claim 1 , wherein the one or more specific geometric parameters of the modeled object at the location comprise thickness and build orientation.

7. The method of claim 1 , wherein the iteratively modifying comprises:

computing shape change velocities for an implicit surface in a level-set representation of the generatively designed three dimensional shape in accordance with the at least one design constraint; and

updating the level-set representation using the shape change velocities to produce an updated version of the generatively designed three dimensional shape of the modeled object.

8. The method of claim 7 , wherein computing the shape change velocities comprises computing at least one shape change velocity using a gradient determined from a shape derivative evaluated for the at least one design constraint at each of the different locations.

9. The method of claim 7 , 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 evaluated for the at least one design constraint, at each of the different locations, using adaptive control.

10. The method of claim 9 , wherein the shape derivative formula comprises a volume fraction based inequality constraint that is modified using a Proportional-Integral-Derivative controlled stabilization factor and 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.

11. The method of claim 1 , wherein the iteratively modifying comprises iteratively modifying both a geometry and a topology of the generatively designed three dimensional shape.

12. The method of claim 1 , wherein the one or more loading cases comprise at least a first loading case that specifies a load to be supported by the physical structure during manufacturing of the physical structure, and at least a second loading case that specifies a load to be supported by the physical structure during use of the physical structure.

13. The method of claim 1 , wherein the providing comprises:

generating, from the generatively designed three dimensional shape of the modeled object, toolpath specifications for one or more computer-controlled manufacturing systems; and

manufacturing the physical structure corresponding to the modeled object with the one or more computer-controlled manufacturing systems using the toolpath specifications.

14. 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 is to be manufactured using one or more materials, and design criteria for the modeled object including one or more loading cases for numerical simulation of the physical structure and at least one design constraint on an acceptable likelihood of failure for the physical structure, wherein a statistical model that relates a structural performance metric to specific likelihoods of failure for the one or more materials is used to translate between the acceptable likelihood of failure and a value for the structural performance metric,

iteratively modify a generatively designed three dimensional shape of the modeled object in the design space in accordance with the design criteria including the one or more loading cases for the numerical simulation of the physical structure and the at least one design constraint to stay under the acceptable likelihood of failure for the physical structure, wherein the numerical simulation includes computing the structural performance metric, which is evaluated against the at least one design constraint, and

provide the generatively designed three dimensional shape of the modeled object for use in manufacturing the physical structure;

wherein the at least one design constraint specifies a maximum likelihood of failure, the one or more data processing apparatus are configured to run the instructions of the computer aided design program to obtain the at least one design constraint by setting the maximum likelihood of failure based on the acceptable likelihood of failure for the physical structure, and the one or more data processing apparatus are configured to run the instructions of the computer aided design program to evaluate the maximum likelihood of failure at each of multiple different locations on or in the modeled object by calculating a likelihood of failure at the location using the statistical model and a value for the structural performance metric indicated for the location by the numerical simulation in accordance with one or more specific geometric parameters of the modeled object at the location.

15. The system of claim 14 , comprising one or more computer-controlled manufacturing systems, 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 one or more computer-controlled manufacturing systems from the generatively designed three dimensional shape of the modeled object, and manufacture the physical structure corresponding to the modeled object with the one or more computer-controlled manufacturing systems using the toolpath specifications.

16. The system of claim 14 , wherein the statistical model is a Weibull statistical model of a probability of failure distribution function.

17. The system of claim 14 , wherein the statistical model comprises a survivor function that relates values of the performance metric to specific likelihoods of failure for the one or more materials across different thicknesses of the one or more materials.

18. The system of claim 17 , wherein the one or more materials comprise different versions of a same base material, the different versions corresponding to different build orientations for the same base material.

19. The system of claim 17 , wherein the one or more materials comprise different base materials, different versions of a same base material, or both.

20. The system of claim 14 , wherein the one or more specific geometric parameters of the modeled object at the location comprise thickness and build orientation.

21. The system of claim 14 , wherein the one or more data processing apparatus are configured to run the instructions of the computer aided design program to:

compute shape change velocities for an implicit surface in a level-set representation of the generatively designed three dimensional shape in accordance with the at least one design constraint; and

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

22. The system of claim 21 , wherein the one or more data processing apparatus are configured to run the instructions of the computer aided design program to compute at least one shape change velocity using a gradient determined from a shape derivative evaluated for the at least one design constraint at each of the different locations.

23. The system of claim 21 , wherein the one or more data processing apparatus are configured to run the instructions of the computer aided design program to compute at least one shape change velocity using an amount determined from a shape derivative formula that approximates a shape derivative evaluated for the at least one design constraint, at each of the different locations, using adaptive control.

24. The system of claim 23 , wherein the shape derivative formula comprises a volume fraction based inequality constraint that is modified using a Proportional-Integral-Derivative controlled stabilization factor and 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.

25. The system of claim 14 , wherein the one or more data processing apparatus are configured to run the instructions of the computer aided design program to iteratively modify both a geometry and a topology of the generatively designed three dimensional shape.

26. The system of claim 14 , wherein the one or more loading cases comprise at least a first loading case that specifies a load to be supported by the physical structure during manufacturing of the physical structure, and at least a second loading case that specifies a load to be supported by the physical structure during use of the physical structure.

27. 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 a design space for a modeled object, for which a corresponding physical structure is to be manufactured using one or more materials, and design criteria for the modeled object including one or more loading cases for numerical simulation of the physical structure and at least one design constraint on an acceptable likelihood of failure for the physical structure, wherein a statistical model that relates a structural performance metric to specific likelihoods of failure for the one or more materials is used to translate between the acceptable likelihood of failure and a value for the structural performance metric;

iteratively modifying a generatively designed three dimensional shape of the modeled object in the design space in accordance with the design criteria including the one or more loading cases for the numerical simulation of the physical structure and the at least one design constraint to stay under the acceptable likelihood of failure for the physical structure, wherein the numerical simulation includes computing the structural performance metric, which is evaluated against the at least one design constraint; and

providing the generatively designed three dimensional shape of the modeled object for use in manufacturing the physical structure;

wherein the at least one design constraint specifies a maximum likelihood of failure, obtaining the at least one design constraint comprises setting the maximum likelihood of failure based on the acceptable likelihood of failure for the physical structure, and the iteratively modifying comprises evaluating the maximum likelihood of failure at each of multiple different locations on or in the modeled object by calculating a likelihood of failure at the location using the statistical model and a value for the structural performance metric indicated for the location by the numerical simulation in accordance with one or more specific geometric parameters of the modeled object at the location.

28. The non-transitory computer-readable medium of claim 27 , wherein the statistical model comprises a survivor function that relates values of the performance metric to specific likelihoods of failure for the one or more materials across different thicknesses of the one or more materials.

29. The non-transitory computer-readable medium of claim 28 , wherein the one or more materials comprise different versions of a same base material, the different versions corresponding to different build orientations for the same base material.

30. The non-transitory computer-readable medium of claim 28 , wherein the one or more materials comprise different base materials, different versions of a same base material, or both.

31. The non-transitory computer-readable medium of claim 27 , wherein the statistical model is a Weibull statistical model of a probability of failure distribution function.

32. The non-transitory computer-readable medium of claim 27 , wherein the one or more specific geometric parameters of the modeled object at the location comprise thickness and build orientation.

33. The non-transitory computer-readable medium of claim 27 , wherein the iteratively modifying comprises:

computing shape change velocities for an implicit surface in a level-set representation of the generatively designed three dimensional shape in accordance with the at least one design constraint; and

updating the level-set representation using the shape change velocities to produce an updated version of the generatively designed three dimensional shape of the modeled object.

34. The non-transitory computer-readable medium of claim 33 , wherein computing the shape change velocities comprises computing at least one shape change velocity using a gradient determined from a shape derivative evaluated for the at least one design constraint at each of the different locations.

35. The non-transitory computer-readable medium of claim 33 , 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 evaluated for the at least one design constraint, at each of the different locations, using adaptive control.

36. The non-transitory computer-readable medium of claim 35 , wherein the shape derivative formula comprises a volume fraction based inequality constraint that is modified using a Proportional-Integral-Derivative controlled stabilization factor and 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.

37. The non-transitory computer-readable medium of claim 27 , wherein the iteratively modifying comprises iteratively modifying both a geometry and a topology of the generatively designed three dimensional shape.

38. The non-transitory computer-readable medium of claim 27 , wherein the one or more loading cases comprise at least a first loading case that specifies a load to be supported by the physical structure during manufacturing of the physical structure, and at least a second loading case that specifies a load to be supported by the physical structure during use of the physical structure.

39. The non-transitory computer-readable medium of claim 27 , wherein the providing comprises:

generating, from the generatively designed three dimensional shape of the modeled object, toolpath specifications for one or more computer-controlled manufacturing systems; and

manufacturing the physical structure corresponding to the modeled object with the one or more computer-controlled manufacturing systems using the toolpath specifications.