TOPOLOGY OPTIMIZATION WITH LOCALLY DIFFERENTIABLE COMPLEMENT SPACE CONNECTIVITY
One or more physical constraints are selected from a plurality of physical constraints for a part. The physical constraints are for use by a physics solver and define a physical performance of the part. One or more connectivity constraints are defined for use by the physics solver. The connectivity constraints enforce connectivity to or from at least one region over a complement space of the part. The connectivity constraints include locally differentiable violation measures that are modeled after at least one of the physical constraints. A topology of the part is optimized in the physics solver by enforcing the physical constraints and the connectivity constraints while satisfying a primary objective function that optimizes the physical performance of the part. A computer-aided design of the part is produced based on the optimized topology.
1 . A method of designing a part, comprising:
defining one or more physical constraints selected from a plurality of physical constraints for the part, the one or more physical constraints for use by a physics solver defining a physical performance of the part;
defining one or more connectivity constraints for use by the physics solver, the one or more connectivity constraints enforcing connectivity to or from at least one region over a complement space of the part, the one or more connectivity constraints comprising locally differentiable violation measures that are modeled after at least one of the physical constraints;
optimizing a topology of the part in the physics solver by enforcing the one or more physical constraints and the one or more connectivity constraints while satisfying a primary objective function that optimizes the physical performance of the part; and
producing a computer-aided design of the part based on the optimized topology, the computer-aided design used to produce the part via a manufacturing instrument.
2 . The method of claim 1 , wherein the connection is between an inner region of the part and a boundary of the part.
3 . The method of claim 1 , wherein the connection is between two inner regions of the part.
4 . The method of claim 1 , wherein the connectivity constraints comprise a virtual load applied on a boundary of the region.
5 . The method of claim 1 , wherein the connectivity constraints comprise a thermal boundary condition applied on a boundary of the region.
6 . The method of claim 1 , wherein the one or more connectivity constraints comprise a virtual energy function or a virtual compliance of a hypothetical structure representing the complement space of the part.
7 . The method of claim 6 , wherein enforcing the one or more connectivity constraints comprises minimizing the virtual energy function.
8 . The method of claim 6 , wherein the connectivity constraints comprises both Neumann and Dirichlet boundary conditions.
9 . The method of claim 1 , wherein optimizing the topology further comprises representing the part and the complement space as respective super-level and sub-level sets of a density field.
10 . The method of claim 1 , further comprising assigning different weights to each of the one or more connectivity constraints and the one or more physical constraints to emphasize one of the physical performance of the part or the connectivity.
11 . The method of claim 1 , wherein the one or more connectivity constraints ensure accessibility of a manufacturing machine when manufacturing the part.
12 . The method of claim 1 , wherein the one or more connectivity constraints ensure channels exist in the part.
13 . The method of claim 12 , wherein the channels are configured for at least one of:
routing wires through the part;
removing powder from the part after a manufacturing process; and
flowing coolant through the part during use of the part.
14 . The method of claim 1 , wherein the physics solver comprises a finite element solver.
15 . A system comprising a memory storing instructions and a processor, the processor operable via the instructions to perform the method of claim 1 .
16 . A method of designing a part, comprising:
defining a physical constraint for the part, the physical constraint for use by a physics solver defining a physical performance of the part;
defining a connectivity constraint for use by the physics solver, the connectivity constraint enforcing connectivity to or from a region over a hypothetical structure that represents a complement space of the part, the connectivity constraint comprising locally differentiable violation measures that are modeled after one or more physical constraints;
for each intermediate design of the part in an optimization loop:
evaluating a real response based on the physical performance of the part;
evaluating a virtual response based on the connectivity constraints applied to the complement space;
defining a first and second sensitivity fields based respectively on the real response and the virtual response;
weighting the first and second sensitivity fields to relatively emphasize one of the physical performance of the part or the connectivity;
updating the intermediate design based on optimizing an objective function that relates to the physical performance of the part, the optimizing the objective function based on the weighted first and second sensitivity fields; and
determining a convergence criterion that indicates that the updated intermediate design approaches an optimized topology of the part, and terminating the optimization loop with a final design if the convergence criterion meets a threshold; and
after the termination of the optimization loop, producing a computer-aided design of the part based on the final design, the computer-aided design used to produce the part via a manufacturing instrument.
17 . The method of claim 16 , wherein the connectivity constraint comprises a virtual energy function or a virtual compliance of the hypothetical structure.
18 . The method of claim 16 , wherein the one or more connectivity constraints ensure channels exist in the part.
19 . The method of claim 16 , wherein the physics solver comprises a finite element solver.
20 . A system comprising a memory storing instructions and a processor, the processor operable via the instructions to perform the method of claim 16 .