Truss structure optimization techniques
View Patent ↗Design of a 3-D truss structure, including a plurality of coupling nodes and a plurality of struts, is optimized by performing a quantitative optimization of an objective function corresponding to a figure of merit of the design. The quantitative optimization includes: generating a finite element analysis model, the analysis model a 3-D lattice mesh of strut-like finite elements; computing, with the finite element analysis model, a value for the objective function; and optimizing the objective function by executing at least two cycles of an optimization loop. The optimization loop includes a) computing a respective parameter of each strut-like finite element; b) deleting, from the finite element analysis model, selected finite elements for which a resulting mechanical property is less than a threshold; (c) computing an updated value for the objective function; and repeating the optimization loop until the objective function is within a desired tolerance of the specified value.
1. A structure supporting at least one component, the structure comprising:
a truss-like frame structure including an arrangement design of at least four coupling nodes and at least six physical strut elements (struts) connected at a plurality of joints, each strut being disposed between and attached with a respective pair of the plurality of coupling nodes; wherein
the arrangement design results from performing a quantitative optimization of an objective function corresponding to a system performance characteristic of the arrangement design, the system performance characteristic having a specified value and being one or more of stiffness, strength, or coefficient of thermal expansion of the arrangement design, the quantitative optimization comprising:
generating a finite element analysis model, the analysis model including boundary conditions and an initial dense 3-D lattice mesh of strutlike finite elements, each strutlike finite element having a respective set of one or more assumed mechanical properties that model a respective simulated strut element, the boundary conditions including one or more input load parameters, and one or more of a mass, a moment of inertia and a thermal characteristic of at the at least one component;
computing, with the finite element analysis model, a value for the objective function;
optimizing the objective function by executing, on a processor, at least two cycles of an optimization loop, the optimization loop comprising:
(a) computing a respective parameter of each strut-like finite element;
(b) adjusting the finite element analysis model by: (i) decrementing the assumed mechanical property of a first subset of the finite elements, each element in the first subset having a respective computed parameter that is less than a first threshold; and (ii) deleting, from the finite element analysis model, any finite element in the first subset for which a resulting mechanical property is less than a second threshold;
(c) computing, with the adjusted finite element analysis model, an updated value for the objective function; and
determining, when the updated value for the objective function is within a desired tolerance of the specified value, that the adjusted finite element analysis model represents a sufficiently optimized arrangement design, and, when the updated value for the objective function is outside the desired tolerance, repeating steps (a) through (c).
2. The structure of claim 1 , wherein adjusting the finite element analysis model includes incrementing the assumed mechanical property of a second subset of the finite elements, each element in the second subset having a respective computed parameter that exceeds a third threshold.
3. The structure of claim 1 , wherein adjusting the finite element analysis model includes smoothing the resulting finite element analysis model.
4. The structure of claim 3 , wherein smoothing the resulting finite element analysis model includes replacing two or more respective simulated strut-like finite elements with a single simulated strut-like finite element.
5. The structure of claim 4 , wherein the two or more respective strut-like finite elements are respectively nonlinear.
6. The structure of claim 1 , wherein each set of one or more assumed mechanical properties includes one or more of stiffness, strength, diameter, length, and a thermal characteristic of the respective simulated strut element.
7. The structure of claim 6 , wherein, for at least the sufficiently optimized arrangement design, each set of one or more assumed mechanical assumed properties models a respective one of the plurality of physical strut elements.
8. A method for optimizing an arrangement design of a 3-D truss structure supporting at least one component, the arrangement design at least four coupling nodes and at least six physical strut elements (struts) connected at a plurality of joints, each strut being disposed between and attached with a respective pair of the plurality of coupling nodes, the method comprising:
performing a quantitative optimization of an objective function corresponding to a system performance characteristic of the arrangement design, the system performance characteristic having a specified value and being one or more of stiffness, strength, or coefficient of thermal expansion of the arrangement design, the quantitative optimization comprising:
generating a finite element analysis model, the analysis model including boundary conditions and a 3-D lattice mesh of strut-like finite elements, each strut-like finite element having a respective set of one or more assumed mechanical properties that model a respective simulated strut element, the boundary conditions including one or more input load parameters, and one or more of a mass and a moment of inertia of at the at least one component;
computing, with the finite element analysis model, a value for the objective function;
optimizing the objective function by executing, on a processor, at least two cycles of an optimization loop, the optimization loop comprising:
a) computing a respective parameter of each strut-like finite element;
b) adjusting the finite element analysis model by: (i) decrementing the assumed mechanical property of a first subset of the finite elements, each element in the first subset having a respective computed parameter that is less than a first threshold; and (ii) deleting, from the finite element analysis model, any finite element in the first subset for which a resulting mechanical property is less than a second threshold;
(c) computing, with the adjusted finite element analysis model, an updated value for the objective function; and
determining, when the updated value for the objective function is within a desired tolerance of the specified value, that the adjusted finite element analysis model represents a sufficiently optimized arrangement design, and, when the updated value for the objective function is outside the desired tolerance, repeating steps (a) through (c).
9. The method of claim 8 , further comprising incrementing the assumed mechanical property of a second subset of the finite elements, each element in the second subset having a respective computed parameter that exceeds a third threshold.
10. The method of claim 8 , further comprising smoothing the resulting finite element analysis model.
11. The method of claim 10 , wherein smoothing the resulting finite element analysis model includes replacing two or more respective simulated strut-like finite elements with a single strut-like finite element.
12. The method of claim 11 , wherein the two or more respective strut-like finite elements are respectively nonlinear.
13. The method of claim 8 , wherein each set of one or more assumed mechanical properties includes one or more of stiffness, strength, diameter, length, and a thermal characteristic of the respective simulated strut element.
14. The method of claim 13 , wherein, for at least the sufficiently optimized arrangement design, each set of one or more assumed mechanical assumed properties models a respective one of the plurality of physical strut elements.
15. A non-transitory computer readable medium having software stored thereon, the software including instructions for causing a computer to optimize an arrangement design of a 3-D truss structure supporting at least one component, the arrangement design including at least four coupling nodes and at least six physical strut elements (struts) connected at a plurality of joints, each strut being disposed between and attached with a respective pair of the plurality of coupling nodes, the software including instructions for:
performing a quantitative optimization of an objective function corresponding to a system performance characteristic of the arrangement design, the system performance characteristic having a specified value and being one or more of stiffness, strength, or coefficient of thermal expansion of the arrangement design, the quantitative optimization comprising:
generating a finite element analysis model, the analysis model including boundary conditions and a 3-D lattice mesh of strut-like finite elements, each strut-like finite element having a respective set of one or more assumed mechanical properties that model a respective simulated strut element, the boundary conditions including one or more input load parameters, and one or more of a mass and a moment of inertia of at the at least one component;
computing, with the finite element analysis model, a value for the objective function;
optimizing the objective function by executing, on a processor, at least two cycles of an optimization loop, the optimization loop comprising:
a) computing a respective parameter of each strut-like finite element;
b) adjusting the finite element analysis model by: (i) decrementing the assumed mechanical property of a first subset of the finite elements, each element in the first subset having a respective computed parameter that is less than a first threshold; and (ii) deleting, from the finite element analysis model, any finite element in the first subset for which a resulting mechanical property is less than a second threshold;
(c) computing, with the adjusted finite element analysis model, an updated value for the objective function; and
determining, when the updated value for the objective function is within a desired tolerance of the specified value, that the adjusted finite element analysis model represents a sufficiently optimized arrangement design, and, when the updated value for the objective function is outside the desired tolerance, repeating steps (a) through (c).
16. The computer readable medium of claim 15 , wherein each set of one or more assumed mechanical properties includes one or more of stiffness, strength, diameter, length, and thermal characteristic of the respective simulated strut element.
17. The computer readable medium of claim 16 , wherein, for at least the sufficiently optimized arrangement design, each set of one or more assumed mechanical assumed properties models a respective one of the plurality of physical strut elements.