Methods for modelling variations of repeating parts of a component
A computer-implemented method for modelling variations of repeating parts of a component is disclosed herein. The method includes providing parameter sets for part configurations of a plurality of different of parts, wherein the parameters of each parameter set respectively define the part configuration of a part; selecting a selection of the part configurations; providing a part model for each part configuration of the selection, wherein the part model relates forces and displacements to locations of the respective part; and building an approximator, wherein the approximator is provided for interpolating the part models to approximate a part model of a part configuration that does not belong to the selection of the part configurations.
1 . A computer-implemented method for improving an efficiency and an accuracy of a physical simulation of three-dimensional (3D) components with repeating parts by modelling variations of repeating parts of a 3D component, the method comprising:
providing, by a processor, parameter sets for part configurations of a plurality of different parts, wherein parameters of each parameter set define a respective part configuration of a part of the plurality of different parts of the 3D component;
selecting, by the processor, a selection of the part configurations from a defined parameter space of configurations;
providing, by the processor, a part model for each part configuration of the selection, wherein the part model relates forces and displacements to locations of the respective part;
building, by the processor, a computational approximator, wherein the computational approximator is provided for interpolating the part models to approximate a part model of a part configuration that does not belong to the selection of the part configurations within the defined parameter space;
generating a reduced component model, using the computational approximator, for several parts of the 3D component, therein providing an improved efficiency and accuracy when a physical simulation of a 3D component is performed without the computational approximator; and
manufacturing the 3D component using the reduced component model.
2 . The method of claim 1 , wherein the providing of the part model comprises:
meshing a mesh of the part with solid elements;
generating a preliminary part model of the meshed part by relating forces and displacements to locations defining the solid elements through a first part stiffness matrix;
identifying constraints reducing a number of exterior degrees of freedom of movement by constrained degrees of freedom; and
generating the part model by reducing the model order of the preliminary part model to the remaining exterior degrees of freedom by eliminating the constrained degrees of freedom of the first part stiffness matrix resulting in a reduced stiffness matrix, and
wherein the building of the approximator comprises interpolating the reduced stiffness matrixes to extract the reduced stiffness matrix of a part that does not belong to the selection of the part configurations.
3 . The method of claim 2 , wherein the repeating parts are joints of a lattice structure.
4 . The method of claim 3 , wherein the selecting of the selection of the part configurations is a random selection.
5 . The method of claim 3 , wherein the reducing the model order is done using a Guyan reduction resulting in the reduced stiffness matrix.
6 . The method of claim 3 , wherein the interpolating of the reduced stiffness matrices of the part models uses Canonical Polyadic Decomposition.
7 . The method of claim 3 , further comprising:
combining resulting reduced stiffness matrices of the several parts of the 3D component with other models of elements of the 3D component.
8 . The method of claim 1 , wherein the repeating parts are joints of a lattice structure.
9 . The method of claim 1 , wherein the selecting of the selection of the part configurations is a random selection.
10 . The method of claim 2 , wherein the reducing the model order is done using a Guyan reduction resulting in a reduced stiffness matrix.
11 . The method of claim 1 , wherein the interpolating of the reduced stiffness matrices of the part models uses Canonical Polyadic Decomposition.
12 . The method of claim 1 , further comprising:
combining resulting reduced stiffness matrices of the several parts of the 3D component with other models of elements of the 3D component.
13 . An additive manufacturing method for generating a three-dimensional (3D) component with variations of repeating parts, the method comprising:
providing, by a processor, parameter sets for part configurations of a plurality of different parts, wherein parameters of each parameter set define a respective part configuration of a part of the plurality of different parts of the 3D component;
selecting, by a processor, a selection of the part configurations from a defined parameter space of configurations;
providing, by a processor, a part model for each part configuration of the selection, wherein the part model relates forces and displacements to locations of the respective part;
building, by the processor, a computational approximator, wherein the computational approximator is provided for interpolating the part models to approximate a part model of a part configuration that does not belong to the selection of the part configurations within the defined parameter space;
generating a reduced component model, using the computational approximator, for several parts of the 3D component, therein providing an improved efficiency and accuracy when a physical simulation of a 3D component is performed without the computational approximator; and
generating the 3D component using the reduced component model.
14 . A computer system for improving an efficiency and an accuracy of a physical simulation of a three-dimensional (3D) component with repeating parts by modeling variations of repeating parts of the 3D component, the computer system comprising:
a processor; and
a memory,
wherein the memory and the processor are configured to:
provide parameter sets for part configurations of a plurality of different parts, wherein parameters of each parameter set define a respective part configuration of a part of the plurality of different parts of the 3D component;
select a selection of the part configurations from a defined parameter space of configurations;
provide a part model for each part configuration of the selection, wherein the part model relates forces and displacements to locations of the respective part;
build a computational approximator, wherein the computational approximator is provided for interpolating the part models to approximate a part model of a part configuration that does not belong to the selection of the part configurations within the defined parameter space;
generate a reduced component model, using the computational approximator, for several parts of the 3D component, therein providing an improved efficiency and accuracy when a physical simulation of a 3D component is performed without the computational approximator; and
generate the 3D component using the reduced component model.
15 . The method of claim 1 , further comprising:
outputting, by the processor, the computational approximator for use in the manufacturing of the 3D component.