LMS HMESHER - Automatic Mesh Generation for Complex CAD Assemblies

Slide 1:LMS HMESHER - Automatic Mesh Generation for Complex CAD Assemblies

Iulian Grindeanu, LMS International Hideaki Ozaki, Honda R&D Co., Ltd., Automobile R&D Center

Slide 2:Outline

HMesher history Integration in Virtual Lab HMesher basic flow Zonal meshing Examples

Slide 3:HMesher Development

Started from PolyFEM mesher. PolyFEM is a p-type finite element tool Some attributes of PolyFEM mesher Start from CAD geometry Conforming meshes in CAD assemblies Relatively coarse mesh, associated with geometric boundary Agglomeration of tetras into hexas and pentas. QT connections are allowed by PolyFEM solver HMesher as opposite to p-mesher (for an h-type FE) Designed for NASTRAN Sought properties: hexa meshing Coarse mesh Conformity to geometry

Slide 4:HMesher Integration

Part of LMS Virtual.Lab LMS Virtual.Lab is a software suite used to simulate the performance of mechanical systems in terms of structural integrity, noise and vibration, durability, system dynamics, ride and handling LMS Virtual.Lab is based on CAA V5, the open middleware for PLM from Dassault Systèmes. There are other meshers available in Catia V5 Octtree mesher, INRIA mesher The actual meshing process is done outside CATIA, but geometry extraction and importing of the mesh are done using API tools, CAA interfaces.

Slide 5:HMesher Integration (Cont)

The integration allows for accurate geometry representation, we use CGM tools Local mesh control can be done at the edge and face levels After importing the mesh, we take advantage of the mesh visualization tools, preparation of the input file for subsequent Finite Element Analyses (FE drivers), import of the results and post-processing (FE interfaces), available in Virtual Lab Associativity between mesh and geometry ensure easy application of boundary conditions for FE analysis

Slide 6:Main Analysis and Design Flow

Slide 7:How to build a mesh for something like this?

13 parts 5 assemblies 1 master assembly All parts are in contact Need a conforming mesh for modal analysis

Slide 8:Geometry Extraction

Top-down assembly organization: CATProduct documents CATPart documents Bodies within Part documents Domains Volumes Volumes have a manifold geometry, boundary representation. A topology scan is performed to extract boundary faces, edges and vertices In the end, geometry file is a collection of BRep volumes, that can be in contact along faces, edges Penetrating volumes are not allowed! CATIA geometric tolerance: 0.001 mm

Slide 9:Geometry Extraction: UV parametrization

Each face sits on a surface, which has a uv parametrization. The boundary of each face is represented as a collection of uv curves. 3D Edges have 3 representations: as a segment on a 3D curve, and as 2 uv curves in adjacent faces

Slide 10:Geometry Extraction

Surface types supported by HMesher are PLANE, CANONICAL (Cylinder, Sphere, Torus, Cone) and NURBS. Not all CATIA surfaces are supported by the HMesher. The surfaces that have no correspondent are converted to the NURBS format, using CATIA operators, with a default tolerance of 0.01 mm.

Slide 11:Basic Flow of HMesher

Slide 12:Multiple Solid Processing

Needed for volumes in contact, for conforming mesh an important advantage for finite element analysis, as there are no linkage elements needed. The solids will share nodes, edges and faces of mesh elements

Slide 13:Multiple Solid Processing

Intersection is done in UV space of one of the faces in contact New faces are created with the intersection edges, vertices

Slide 14:Multiple Solid Processing

Face that is common to both solids after multiple solids processing: Non manifold geometry

Slide 15:Multiple Solid Processing: Final mesh

Mesh is compatible along contact face between solids

Slide 16:Basic Flow of HMesher

Slide 17:Facetting: Surface Meshing

Start with breaking the boundary geometry edges Performed on each boundary face Constrained Delaunay mesh on each face is mapped on 3D geometry

Slide 18:Surface meshing

Scaled uv space Constrained 2d Delaunay 2d refinement points added in layers

Slide 19:Surface mesh violations

Due to curvature and feature proximity, surface mesh from different faces can intersect, resulting in surface mesh violations mesh size reductions are performed in those cases, to eliminate violations

Slide 20:Basic Flow of HMesher

Slide 21:Surface Mesh Simplification (Blurring)

The most effective way of eliminating the small edges, thin faces and other small features

Slide 22:Solid Meshing. Interior Point Generation

Interior points are roughly on the normals from the closest boundary Normal direction for layer generation Boundary points Points are added in layers from boundary, and are averaged when fronts collide

Slide 23:3D Delaunay

Classic 3d Delaunay , we insert all the points of the surface mesh and interior points in a large enough tetra

Slide 24:Trimming / Untrimming

Conforming Delaunay is performed next: add “trimming” points on the faces and edges until all faces and edges are part of tetrahedralization. Remove outside tetrahedrons Untrimming: Eliminate trimming points if possible, maintaining the topology of the model, but do not consider anymore Delaunay property

Slide 25:Trimming / Untrimming

zoom

Slide 26:Untrimming (Delaunay relaxation)

Slide 27:Trimming / Untrimming explained in 2D

Slide 28:Basic Flow of HMesher

Slide 29:Curve Recovery

Input: Tetrahedralization of the points, and the curved representation of the model. Output: Curved representation of the Tetrahedralization Algorithm: Repeatedly perform the following For each edge on the model boundary, map using the original curve. For each edge on the face interior, map using a geodesic curve, maintaining angles with neighbors For each edge in the interior, map only if necessary to maintain validity Interpolate the interior faces.

Slide 30:Curve Recovery

Slide 31:Hybrid Meshing

[1] Meshkat, S. , Talmor, D. , “Generating a Mixed Mesh of Hexahedra, Pentahedra and Tetrahedra from an Underlying Tetrahedral Mesh”, International Journal for Numerical Methods in Engineering. Volume 49, Issue 1-2 , Pages 17 – 30, July 2000

Slide 32:Hybrid Meshing

Uses a subgraph of the topological dual graph Tetrahedron – vertex in dual graph Interior face – solid edge in dual graph Quadrilateral face on a merged element – dotted edge in dual graph Extended RF graph for a pyramid

Slide 33:Hybrid Meshing

Extended RF graph for a pentahedra (triangular prism)

Slide 34:Hybrid Meshing

Some interesting properties RF Graphs for penta or hexa decomposition are planar The RF-graph of all tetrahedral decompositions of a hexahedron into six tetrahedra has exactly one cycle. The decomposition into five tetrahedra contains no cycles In a tetrahedral decomposition of a hexahedron, a tetrahedron with 3 boundary faces cannot be connected to another tetrahedron with 2 or 3 boundary faces

Slide 35:Hybrid Meshing

Extended RF graphs for hexahedron: there is 1 RF graph for 5-tetrahedron decomposition

Slide 36:Hybrid Meshing

Extended RF graphs for hexahedrons: 5 different graphs for 6-tetrahedron decompositions

Slide 37:Hybrid Meshing

Extended RF graphs for hexahedrons: 5 different graphs for 6-tetrahedron decompositions

Slide 38:Hybrid Meshing

Extended RF-graphs are compact way of storing conceptual templates for a tetrahedral decomposition. Since finding hexahedra and pentahedra in a tetrahedrization involves finding a subgraph that matches a given graph, the use of a graph is somewhat inefficient. Instead, for a given graph, all possible search trees are constructed, one for each root node. These six RF-graphs are converted into 14 search trees in total The algorithm uses actually 31 search trees, for hexahedrons that are composed from more than 6 tetrahedrons (up to 13)

Slide 39:Hybrid Meshing

RF graphs are converted to search trees: example of 2 search trees corresponding to 3-cycle RF graph The solid lines depict the tetrahedra that share a face, whereas dashed lines represent the constraint to find a quadrilateral pair.

Slide 40:Hybrid Meshing

The RF-graph only establishes graph-theoretical conditions for existence of a given polyhedron, i.e. hexahedron or pentahedron. Additional geometry criteria are necessary to ensure the validity of the polyhedron. A backtrack algorithm is involved to find possible search trees for tetrahedrons in the mesh A best solution is committed early if found The process is expensive (60%-80% of total CPU time) Unless there are at least 2 layers of hexas/pentas on the boundary, the mesh cannot be used for stress analysis

Slide 41:Hybrid Meshing

Quality measures: Percentage of volume of boundary bricks/wedges M1 ~90% Percentage of volume of all bricks/wedges M3 ~70% Percentage of number of boundary bricks/wedges M4 ~55% Percentage of number of boundary bricks M5 ~30% Percentage of number of all bricks M6 ~20% Percentage of number of boundary quads M7 ~60% For a good stress analysis, all these measures should be closer to 100%. Nevertheless, this meshes can be used successfully for modal analysis.

Slide 42:Zonal Meshing

In order to mesh large assemblies of relatively complex models, like engine blocks, transmission cases, a modular approach is introduced; we call it zonal meshing. With zonal approach, design changes are not propagated past the contacts between zones The contact surfaces are processed first, then parts are meshed independently, while preserving the surface mesh in the contact area. The most difficult problem is to ensure the compatibility of meshes between parts, at the contact surfaces, effectively constraining the solid mesh to be compatible to the mesh at the common surface. There are theoretical guarantees of when the Delaunay mesh can be constrained (Jonathan Shewchuk): Edge protection criteria

Slide 43:Zonal Meshing

First, create a compatible surface mesh

Slide 44:Zonal Meshing

The final mesh is compatible between solids

Slide 45:Zonal Meshing: Imprint feature

Imprint feature: impose a surface mesh pattern on a face of the solid

Slide 46:Engine Block Example

13 parts 5 assemblies 4 zonal interfaces 10000 faces 28000 edges

Slide 47:Engine Block Example

Define zonal Interfaces

Slide 48:Engine Block Example

Zonal surface mesh

Slide 49:Engine Block Example

Slide 50:Engine Block Hybrid Mesh

Slide 51:Future Work

Efficiency needs to be increased Merging measures closer to 100% Memory management Robustness and quality will always be issues with coarse meshes

Slide 52:Acknowledgements

Many thanks to Honda R&D Co., Ltd., for continuous support and for driving the whole process forward. Thanks to LMS International for the opportunity to work on the HMesher Thank you for your attention!