J.Cugnoni LMAF / EPFL 2012

Vertices (0D): ◦ Coordinates & coordinate system

Edges (1D): ◦ several Vertices => line / curve

Surfaces (2D): ◦ closed loop of edges (shared vertices),

parametric 2D space, normal = orientation Volumes (3D):

◦ a closed set of surfaces (shared edges), unified normal orientation

3D CAD volume: all edges are shared between boundary faces =>no « free » edges => surface is closed => it’s a volume!

3D CAD volume: all edges are shared between boundary faces =>no « free » edges => surface is closed => it’s a volume!

Several formats are supported by Abaqus CAE:◦ STEP : universal format, good for volumes & assemblies◦ IGES : universal format, good for surfaces, ok for volumes◦ SAT : ACIS engine, native geometry format of Abaqus

CAE, good for nearly everything◦ CATPart: CATIA v5 format, can be imported with a

specific module (1 licence)

Always check the geometry:◦ Free edges / invalid entities: tools => query => geom.

diagnostic◦ If free edges, stitch the surfaces: tools => geom. repair

=> part => stitch◦ If meshing problems, convert to « precise »: tools =>

geom. repair => part => convert to precise◦ Check the dimensions / units !!◦ If you have problems with geometric operations (like

partition), try to Convert to Precise and Convert to Analytical representation

Mesh generation in 3D is based on the same

hierarchy as the CAD model:◦1D: meshing of the edges, starting from a

user-defined element size / distribution

◦2D: propagation of 1D mesh to 2D surface;

structured or free (advancing front or

medial axis).

◦3D: propagation of 2D mesh to the 3D volume;

structured, semi-structured (sweep), free

Method:◦ Use the curvilinear parameter to distribute nodes

along edges => create 1D elements Definition:

◦ Constant size: number of elements on edge or element size

◦ Variable size: number of elements and bias Bias = ratio of largest to smallest elem. size Pick the edge close to the end to be refined

Constant element

sizeDefault (global)

element size

Biased element size distribution

Methods:◦ Propagate 1D mesh on the surface◦ Curved surface:

Nearly planar: use projection on the best plane General: mesh in Parameter space

◦ Algorithms: Structured / mapped meshing Delaunay triangulation Advancing front meshing Medial axis

Definition:◦ Just select the meshing algorithm◦ Automatically inherits the mesh size from the

edges

Mapped meshing (works for surfaces having 3 to 5 corners)

Advancing front meshing Medial axis meshing

Methods: Propagate 2D mesh in the volume Algorithms:

Structured / mapped meshing : map volume to a simple case (hexa)

Semi-structured: « extrusion » / « sweep » of a free 2D mesh (tri or quad) Generates either hexa or prisms (wedges)

Free meshing: Delaunay or Advancing Front tetrahedralization

Definition: Just select the meshing algorithm Automatically inherits the mesh size from the surfaces

& edges

Mapped meshing for hexa: any extrusion of mapped quad. mesh

Mapped meshing for hexa: « simple » 3D primitives here 1/8 of a sphere

Sweep meshing for hexa.: free quad mesh + extrusion

Sweep meshing for wedges : free tri. mesh + extrusion

Free tetrahedral meshing: free advancing front 2D meshing + 3D adv. front tetrahedralization the most general meshing algorithm in Abaqus/CAE

Goal◦ Decompose the geometry into simpler volumes / faces

Method:◦ Cut edges, faces or volumes by planes, extrusions,

sketch… Useful to:

◦ Use structured or sweep meshing on certain region of the part

◦ Enhance mesh quality & assign local refinements◦ Create new faces / edges for boundary conditions or

output Drawback:

◦ If not used correctly: create a lot of small faces and edges => generate very small elements of bad quality

Example: see demo & tutorial

Continuous Displacement field => need congruent mesh on the boundaries with shared nodes at the interface

Continuous mesh if and only if shared face or edge => When working with “imported” geometry, need to « merge  » boundary faces & edges!! => always check for “Free edges” !!

Incompatible meshing methods can create “hanging” nodes or displacement jumps which are not linked across boundary; for example, linear to quadratic or tetra to hexa transitions are not “compatible” => discontinuous displacement

If not possible to have shared boundaries, one need to impose displacement compatibility through kinematic constraints => additional equations (to avoid whenever possible!!)

Two disconnected CAD regions

Presence of two bounding faces=> Duplicated nodes & no continuity of displacement

Two connected CAD regions

only one shared bounding face=> shared nodes so displacement is continuous at nodes

Duplicated bounding

face / edge

Duplicated bounding

face / edge

Shared bounding

face / edge

Shared bounding

face / edge

QuadraticTetrahedral

Mesh

Linear Hexahedra

l mesh

Linear Quadrangular

facesQuad.

Triangular faces

Hanging nodes!!

Tetrahedral mesh regions can only be linked to prismatic (wedge) regions.

Prismatic regions can be linked to both hexa (along structured faces) and tetra.

Criteria◦ Geometry : Distortion ,aspect ratio, minimum angle,

maximum angle, …◦ FE-based: jacobian

Influence:◦ Low quality = bad mesh convergence◦ Large stress field discontinuities ◦ Some elements may « lock » for high aspect ratio◦ Create numerical « round-off » errors & singularities◦ May completely « crash » the solver if jacobian is

negative ! Advice:

◦ It is usually better to have « good quality » quadratic tetrahedra than « highly deformed » hexahedra !!

◦ Small edges & nearly tangent junction surfaces can be problematic because they require too small or too sharp elements => use virtual topology

In CAD: ◦ Create CLEAN parts for FEA:

Avoid creating small surfaces & edges Avoid « tangent » connections (very small angles) Try to minimize the number of faces present in the

model Prefer a single « sweep » / « loft » to complex cut /

extrude operations (=> can use structured meshing)◦ Remove unsignificant geometric details:

ask yourself what is important (abstraction) for the goal of the modelling !!!

Typical details: fillets / chamfers, small holes, unsignificant components (bolts & nuts, rivets)

For complex parts / assemblies, it is usualy very time consuming to try to « fix » the geometry & meshing problems, you should better

completely reconstruct a clean 3D CAD model just for FE analysis

In FEA pre-processor / mesher:◦ Always check imported geometry (free edges?)◦ If necessary: repair geometry or try a different

format◦ Partition to create simpler volumes

( symmetries ? )◦ Choice of meshing method (if possible): Hex

structured > Hex swept > Wedges swept > Tetra free

◦ Use compatible meshes at the interface !!!◦ Check mesh quality: at least no Analysis Error◦ Define local refinements where necessary◦ Use virtual topology if necessary