Multi-scale mesh modeling software products and controllers

Patent metadata

Field	Value
Publication number	US-2016321384-A1
Application number	US-201415105683-A
Country	US
Kind code	A1
Filing date	Dec 19, 2014
Priority date	Dec 19, 2013
Publication date	Nov 3, 2016
Grant date	—

Abstract

Simulation systems, manufacturing systems, software products and controllers are provided with multi-scale modeling in which a coarse mesh and a fme mesh that models a stimulus are decoupled. The fine mesh can be moved within the coarse mesh with a cut and paste operation. The coarse mesh is updated by sparsely propagated effects through the coarse mesh. Simulations of the invention can be conducted in real-time, and be used as controllers in manufacturing systems, such as additive manufacturing systems. A number of efficient methods are provided for solving meshing determinations that arise from movement of a stimulus modeled within a fine mesh.

First claim

1 . A modeling and simulation software product in a control system for a manufacturing process, comprising code stored on a non-transient medium, the product comprising code for:
generating a coarse scale mesh to model at least a portion of an article being manufacturing; generating a fine scale mesh to model the article in an area of a stimulus that affects the article within the boundaries of the coarse scale mesh; conducting a dynamic feed forward multi-scale refinement and de-refinement operation within the coarse scale mesh in response to movement or changes of the stimulus, wherein the fine scale mesh includes the area of the simulus where energy is added to the material and corresponding thermo-mechanical stiffness matrices are implemented to avoid re-computation of nodal connectivity each time the fine mesh region moves or changes.

2 . The product of claim 1 , further comprising generating a fine scale mesh to model geometry, internal features and microstructures of the article.

3 . The product of claim 1 , comprising code for solving directional finite element problems to determine an effect of the stimulus on the coarse scale mesh using a numerical technique for dimensional reduction of physical field variable/tensor problems by computing Eigenmodes of a transformed non-dispersive stiffness matrix.

4 . The product of claim 3 , wherein the transformed non-dispersive stiffness matrix comprises a functional form of a B −1 A equation where B indicates the stiffness matrix between successive planes perpendicular to the direction in which the stimulus has been applied and A indicates the in-plane stiffness matrix of the corresponding plane.

5 . The product of claim 4 , comprising for conducting multiscale homogenization of the coarse scale and fine scale meshes using periodic and higher order boundary conditions (PHOBC) at scale of the fine mesh based on dominant Eigenmodes computed at scale of the coarse mesh.

6 . The product of claim 3 , comprising for conducting multiscale homogenization of the coarse scale and fine scale meshes using periodic and higher order boundary conditions (PHOBC) at scale of the fine mesh based on dominant Eigenmodes computed at scale of the coarse mesh.

7 . The product of claim 6 , wherein the PHOBCs are calculated from a Taylor expansion of dominant Eigenmodes.

8 . The product of claim 7 , further comprising computing a homogenized thermomechanical constitutive model computed from the PHOBCs.

9 . The product of claim 8 , wherein the constitutive model is used to iteratively determine the effect of the stimulus on the coarse scale to model macroscopic Eigenmodes for multi-scale and/or non-linear phenomena.

10 . The product of claim 1 , wherein said conducting a dynamic feed forward multi-scale refinement and de-refinement comprises solving simultaneous equations by:
calculating a stiffness matrix for initial material properties of the article; assigning an approximate initial tolerance based on existing values in the stiffness matrix; calculating an E matrix, which has information about significant values in a Cholesky decomposition, using different criteria to compute each successive value in the Cholesky matrix such that the E matrix has information of which addresses in L are significant to compute; recording insignificant numerical operations and determining a tolerance of significant to insignificant operations to compute; determining a number of computer iterations required with the tolerance used; optimizing the tolerance by adjusting the tolerance until error is within a predetermined acceptable limit while the number of computer iterations is minimized; and subsequently using the E matrix and the information stored about significant numerical operations for a next iteration for the same or different stiffness matrices for the same coarse mesh with different material properties in case of any nonlinearity.

11 . A manufacturing system including the product of claim 1 , wherein the manufacturing system includes a tool to apply the stimulus, and a controller controlled by the product of claim 1 to move and/or modify output of the tool.

12 . The system of claim 1 , wherein the system is an additive manufacturing system, and the tool is a laser.

13 . The system of claim 12 , wherein the fine mesh characterizes a melt pool region of the article.

14 . The system of claim 13 , comprising code for determining thermo-mechanical stiffness matrices without re-computing nodal connectivity each time the fine mesh region moves.

15 . The system of claim 14 , comprising Eigensolvers that predict thermo-mechanical variables away from the melt pool region.

16 . The system of claim 15 , wherein the Eigensolvers further predict areas where thermomechanical gradients are substantially lower than the area of stimulus.

17 . The system of claim 15 , comprising a banded vectorization that truncates a neighborhood of any nodal point used for computation of thermomechanical fields by extracting a lower triangular matrix from a stiffness matrix such that row-wise multiplication of any two lower triangular matrix vectors is less than a predetermined threshold then an entity corresponding to the lower triangular matrix is assumed to be zero and is not computed.

18 . A material or space modeling system for modeling material or space subjected to a stimulus or a process that uses a stimulus upon the material or space, the system including:
means for obtaining physical property data about the material or space; and a simulator for multi-scale meshing the material or space to characterize an effect of the stimulus on the material or space, the simulator executing the following operations,
defining the material or space with a coarse mesh having a bounded extremities;
defining a fine mesh motif within the coarse mesh based upon the material data property and properties of the stimulus;
removing coarse grid nodes in a region of the stimulus;
pasting the fine mesh motif in a region of the stimulus; and
assembling the fine mesh motif and the coarse mesh while sparsely propagating effects of the stimulus through the coarse mesh using stiffness matrices characterizing the coarse mesh.

19 . In a material or space modeling system, a method for finite element mesh solving conducted by software having knowledge of thermal and mechanical properties of material or space being modeled in a process, the system comprising code for:
characterizing the material or space with a finite element mesh; setting and solving an Eigenvalue problem of the thermomechanical propagator matrices to determine the orthogonal basis functions (Eigenvectors) for thermomechanical fields of the material or space in response to a stimulus event; truncating fields in mesh in planes distant from the stimulus event; propagating the thermomechanical field through the finite element mesh.

20 . In a material or space modeling system, a method for decomposing a finite element mesh conducted by software having knowledge of thermal and mechanical properties of material or space being modeled, the system comprising code for:
calculating Eigenmodes of the mesh to find periodicity and higher order modes; updating a fine mesh within the mesh to track a stimulus, while limiting the fine mesh to a boundary that is defined by dominant Eigenmodes determined during said calculating; and decoupling the fine mesh from the remaining mesh.

21 . The system of claim 20 , wherein the system comprises c

Assignees

• Univ Louisville Res Found Inc
• Univ Of Louisville Reasearch Found Inc

Inventors

• Pal Deepankar
• Patil Nachiket
• Stucker Brent

Classifications

• G05B19/4099 Primary

  Surface or curve machining, making three-dimensional [3D] objects, e.g. desktop manufacturing · CPC title

• G06F2119/18

  Manufacturability analysis or optimisation for manufacturability · CPC title

• B33Y50/02 Primary

  for controlling or regulating additive manufacturing processes · CPC title

• G06F30/23

  using finite element methods [FEM] or finite difference methods [FDM] · CPC title

• G05B2219/49007

  Making, forming 3-D object, model, surface · CPC title