Computer aided generative design with overall thickness control to facilitate manufacturing and structural performance

1. A method comprising:

obtaining, by a computer aided design program, a design space for a modeled object, for which a corresponding physical structure is to be manufactured, one or more design criteria for the modeled object, and one or more in-use load cases for the physical structure, wherein the one or more design criteria include a thickness constraint;

iteratively modifying, by the computer aided design program, a generatively designed three dimensional shape of the modeled object, including modifying both a geometry of the three dimensional shape and a topology of the three dimensional shape, in the design space in accordance with the one or more design criteria and the one or more in-use load cases, wherein the iteratively modifying comprises employing the thickness constraint by measuring a current thickness for the three dimensional shape using an overall relationship of a volume of the three dimensional shape with respect to a surface area of the three dimensional shape, wherein the overall relationship comprises a unitless ratio of the volume of the three dimensional shape squared and the surface area of the three dimensional shape cubed; 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 using one or more computer-controlled manufacturing systems.

2. The method of claim 1 , wherein the obtaining comprises:

obtaining an initial three dimensional model as the design space;

obtaining a minimum thickness value for the thickness constraint;

finding an initial surface area of the initial three dimensional model;

calculating an initial volume of material in a hollow three dimensional object having a shape of the initial three dimensional model and a thickness defined by the minimum thickness value; and

setting a target minimum value for the thickness constraint using the unitless ratio of the initial volume and the initial surface area.

3. The method of claim 2 , wherein calculating the initial volume comprises multiplying the initial surface area of the initial three dimensional model by the minimum thickness value.

4. The method of claim 2 , wherein the overall relationship comprises the unitless ratio normalized with respect to a sphere.

5. The method of claim 4 , wherein the overall relationship comprises a sixth root of the normalized unitless ratio.

6. The method of claim 2 , 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;

measuring the current thickness of the current version of the three dimensional shape using the overall relationship of volume with respect to surface area for the three dimensional shape as a whole;

updating the current version of the three dimensional shape based on the current numerical assessment of the physical response, and based on a difference between the current thickness and a current target minimum value for the thickness constraint, to produce an updated version of the three dimensional shape of the modeled object; and

repeating at least the performing, the measuring 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.

7. The method of claim 6 , wherein the updating comprises:

computing shape change velocities for an implicit surface in a level-set representation of the three dimensional shape in accordance with the current numerical assessment and the difference between the current thickness and the current target minimum value for the thickness constraint; and

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

wherein the repeating comprises at least a second portion following a first portion, the second portion of the repeating comprising applying a local thickness constraint using the minimum thickness value, the local thickness constraint having not been applied during the first portion of the repeating.

8. 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, one or more design criteria for the modeled object, and one or more in-use load cases for the physical structure, wherein the one or more design criteria include a thickness constraint,

iteratively modify a generatively designed three dimensional shape of the modeled object, including modifying both a geometry of the three dimensional shape and a topology of the three dimensional shape, in the design space in accordance with the one or more design criteria and the one or more in-use load cases, wherein the iteratively modification employs the thickness constraint by measuring a current thickness for the three dimensional shape using an overall relationship of a volume of the three dimensional shape with respect to a surface area of the three dimensional shape, wherein the overall relationship comprises a unitless ratio of the volume of the three dimensional shape squared and the surface area of the three dimensional shape cubed, and

provide the generatively designed three dimensional shape of the modeled object for use in manufacturing the physical structure using one or more computer-controlled manufacturing systems.

9. The system of claim 8 , wherein the one or more data processing apparatus are configured to run the instructions of the computer aided design program to obtain the design space by being configured to run the instructions of the computer aided design program to:

obtain an initial three dimensional model as the design space;

obtain a minimum thickness value for the thickness constraint;

find an initial surface area of the initial three dimensional model;

calculate an initial volume of material in a hollow three dimensional object having a shape of the initial three dimensional model and a thickness defined by the minimum thickness value; and

set a target minimum value for the thickness constraint using the unitless ratio of the initial volume and the initial surface area.

10. The system of claim 9 , wherein the one or more data processing apparatus are configured to run the instructions of the computer aided design program to calculate the initial volume by being configured to run the instructions of the computer aided design program to multiply the initial surface area of the initial three dimensional model by the minimum thickness value.

11. The system of claim 9 , wherein the overall relationship comprises the unitless ratio normalized with respect to a sphere.

12. The system of claim 9 , 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;

measure the current thickness of the current version of the three dimensional shape using the overall relationship of volume with respect to surface area for the three dimensional shape as a whole;

update the current version of the three dimensional shape based on the current numerical assessment of the physical response, and based on a difference between the current thickness and a current target minimum value for the thickness constraint, to produce an updated version of the three dimensional shape of the modeled object; and

repeat the iterative modification 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.

13. The system of claim 12 , wherein the one or more data processing apparatus are configured to run the instructions of the computer aided design program to update the current version of the three dimensional shape by being 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 three dimensional shape in accordance with the current numerical assessment and the difference between the current thickness and the current target minimum value for the thickness constraint; and

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

wherein the iterative modification comprises a first portion followed by a second portion, and the one or more data processing apparatus are configured to run the instructions of the computer aided design program to apply a local thickness constraint using the minimum thickness value during the second portion of the iterative modification, the local thickness constraint having not been applied during the first portion of the iterative modification.

14. The system of claim 8 , comprising the one or more computer-controlled manufacturing systems, which comprise an additive manufacturing machine or a subtractive 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 or the subtractive manufacturing machine from the generatively designed three dimensional shape of the modeled object, and manufacture the physical structure corresponding to the modeled object with the additive manufacturing machine using the toolpath specifications.

15. 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, one or more design criteria for the modeled object, and one or more in-use load cases for the physical structure, wherein the one or more design criteria include a thickness constraint;

iteratively modifying a generatively designed three dimensional shape of the modeled object, including modifying both a geometry of the three dimensional shape and a topology of the three dimensional shape, in the design space in accordance with the one or more design criteria and the one or more in-use load cases, wherein the iteratively modifying comprises employing the thickness constraint by measuring a current thickness for the three dimensional shape using an overall relationship of a volume of the three dimensional shape with respect to a surface area of the three dimensional shape, wherein the overall relationship comprises a unitless ratio of the volume of the three dimensional shape squared and the surface area of the three dimensional shape cubed; and

providing the generatively designed three dimensional shape of the modeled object for use in manufacturing the physical structure using one or more computer-controlled manufacturing systems.

16. The non-transitory computer-readable medium of claim 15 , wherein the obtaining comprises

obtaining an initial three dimensional model as the design space;

obtaining a minimum thickness value for the thickness constraint;

finding an initial surface area of the initial three dimensional model;

calculating an initial volume of material in a hollow three dimensional object having a shape of the initial three dimensional model and a thickness defined by the minimum thickness value; and

setting a target minimum value for the thickness constraint using the unitless ratio of the initial volume and the initial surface area.

17. The non-transitory computer-readable medium of claim 16 , wherein calculating the initial volume comprises multiplying the initial surface area of the initial three dimensional model by the minimum thickness value.

18. The non-transitory computer-readable medium of claim 17 , wherein the overall relationship comprises the unitless ratio normalized with respect to a sphere.

19. The non-transitory computer-readable medium of claim 16 , 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;

measuring the current thickness of the current version of the three dimensional shape using the overall relationship of volume with respect to surface area for the three dimensional shape as a whole;

updating the current version of the three dimensional shape based on the current numerical assessment of the physical response, and based on a difference between the current thickness and a current target minimum value for the thickness constraint, to produce an updated version of the three dimensional shape of the modeled object; and

repeating at least the performing, the measuring 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.

20. The non-transitory computer-readable medium of claim 19 , wherein the updating comprises:

computing shape change velocities for an implicit surface in a level-set representation of the three dimensional shape in accordance with the current numerical assessment and the difference between the current thickness and the current target minimum value for the thickness constraint; and

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

wherein the repeating comprises at least a second portion following a first portion, the second portion of the repeating comprising applying a local thickness constraint using the minimum thickness value, the local thickness constraint having not been applied during the first portion of the repeating.