US 11,687,692 B2Granted

Method and apparatus for explicit simulation

AssigneeAutodesk, Inc.

InventorLee M. Taylor

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Abstract

A method, apparatus, and system provide the ability to simulate dynamic motion for a computerized model (of finite mesh elements). An element diagonal lumped mass matrix of the mesh, an estimate of a highest element eigenvector and eigenvalue of the mesh, and a kinematic state of the model are computed. Processing iterates until exceeding a time duration. Incremental strain and stress tensors, and hypo-elastic material constants are computed. Within the time duration iteration, eigenvalues are converged, a power-sweep stress field is computed from the strain field using the material constants; divergence of the power-sweep stress field is computed using the current gradient operator; and a power-sweep estimate is computed. Upon convergence, the stability limit is determined and utilized as a time interval for simulating the dynamic motion.

Claims12

Dependent claims

A computer-implemented method for simulating dynamic motion, comprising:

(a) obtaining a computerized model for which dynamic motion will be simulated in a computer, wherein:
(1) the computerized model comprises finite elements in a mesh;
and
(2) the computerized model represents a real-world object;
(b) obtaining an element diagonal lumped mass matrix, M, for the mesh;
(c) obtaining an estimate of a highest element eigenvector (v) of the mesh and a highest eigenvalue of the mesh;
(d) advancing a stress state of the computerized model;
(e) iterating the following without computing a stiffness matrix until a highest natural frequency of the mesh, via the highest eigenvalue of the mesh, converges:
(1) computing a power-sweep strain field (εij) from the highest element eigenvector (v) using a current gradient operator (βij) from a gradient operator matrix (β);
(2) computing a power-sweep stress field (σij) from the strain field (εij) using effective hypo-elastic material constants;
(3) computing a divergence (Fi) of the power-sweep stress field (σij) using the current gradient operator (βij);
(4) computing a power-sweep estimate based on an estimate of the new highest eigenvector and an estimate of a highest eigenvalue based on the new highest eigenvector;
(f) determining a new Courant stability limit based on the new highest eigenvalue;
and
(g) the new Courant stability limit controlling a time interval in which a processor in the computer conducts a finite element analysis (FEA), for every finite element in the mesh, as part of the simulation of the dynamic motion, wherein the simulation simulates a behavior of the real-world object in reaction to real-world physical affects.

12 more elements

A system for simulating dynamic motion, comprising:

(a) a computer comprising a processor;
(b) a dynamic motion simulation application executed by the processor on the computer, wherein the dynamic motion simulation application:
(1) obtains a computerized model for which dynamic motion will be simulated, wherein:
(i) the computerized model comprises finite elements in a mesh;
and
(ii) the computerized model represents a real-world object
(2) obtains an element diagonal lumped mass matrix, M, for the mesh;
(3) obtains an estimate of a highest element eigenvector (v) of the mesh and a highest eigenvalue of the mesh;
(4) advancing a stress state of the computerized model;
(5) iterate the following, without computing a stiffness matrix, until a highest natural frequency of the mesh, via the eigenvalues, converges:
(i) compute a power-sweep strain field (εij) from the highest element eigenvector (v) using a current gradient operator (βij) from a gradient operator matrix (β);
(ii) compute a power-sweep stress field (σij) from the strain field (εij) using effective hypo-elastic material constants;
(iii) compute a divergence (Fi) of the power-sweep stress field (σij) using the current gradient operator (βij);
(iv) compute a power-sweep estimate based on an estimate of the new highest eigenvector and an estimate of a highest eigenvalue based on the new highest eigenvector;
(6) determines a new Courant stability limit based on the new highest eigenvalue;
and
(c) the processor, wherein the new Courant stability limit controls a time interval in which the processor conducts a finite element analysis (FEA), for every finite element in the mesh, as part of the simulation of the dynamic motion in the dynamic motion simulation application, wherein the simulation simulates a behavior of the real-world object in reaction to real-world physical affects.

14 more elements

Dependencies are inferred from the claim text.

Facts

Application: 17/075,333Filed 20 Oct 2020 · continuation
Priority: 19 Jan 2018
Published: US 2021/0034802 A14 Feb 2021
Granted: 27 Jun 2023
Term ends: Not estimatedThe source records don’t support an estimate.

Classification6 codes

G06F 30/23
Design optimisation, verification or simulation: using finite element methods [FEM] or finite difference methods [FDM]
G06F 30/17
Geometric CAD: mechanical parametric or variational design
G06T 17/20
Three-dimensional [3D] modelling for computer graphics: finite element generation, e.g. wire-frame surface description, tesselation
G06F 2119/18
Details relating to the type or aim of the analysis or the optimisation: manufacturability analysis or optimisation for manufacturability

Family

Application15/875,874Parent of this continuation · filed 19 Jan 2018
US 2021/0034802 A1Pre-grant publication · published 4 Feb 2021
US 10,810,335 B2Parent of this continuation
US 2019/0228123 A1Published application
US 11,687,692 B2This patent

From the US filing history. Foreign family members aren’t listed.