FEM Modeling: Mesh, Loads

Transcription

1 8 FEM Modeling: Mesh, Loads and BCs IFEM Ch 8 Slide 1

2 Topics in Chapter 8 General Modeling Rules Finite Element Mesh Layouts Distributed Loads Displacement BCs suppressing rigid body motions taking advantage of symmetry and antisymmetry IFEM Ch 8 Slide 2

3 General FEM Modeling Rules Use the simplest elements that will do the job Never, never, never use complicated or special elements unless you are absolutely sure of what you are doing Use the coarsest mesh that will capture the dominant behavior of the physical model, particularly in design situations 3 word summary: Keep It Simple IFEM Ch 8 Slide 3

4 Another Justification for Simplicity In product design situations several FEM models of increasing refinement will be set up as design evolves Ergo, do not overkill at the beginning IFEM Ch 8 Slide 4

5 Where Finer Meshes Should be Used entrant corners Cutouts Cracks weld Vicinity of concentrated (point) loads, and sharp contact areas Load transfer (bonded joints, welds, anchors, reinforcing bars, etc.) Abrupt thickness changes Material interfaces IFEM Ch 8 Slide 5

6 Avoid 2D/3D Elements of Bad Aspect Ratio Good Bad IFEM Ch 8 Slide 6

7 Elements Must Not Cross Interfaces No OK Physical interface IFEM Ch 8 Slide 7

8 Element Geometry Preferences Other things being equal, prefer in 2D: Quadrilaterals over Triangles in 3D: Bricks over Wedges Wedges over Tetrahedra (Elements do not file discrimination suits) IFEM Ch 8 Slide 8

9 Node by Node (NbN) Distributed Load Lumping Nodal force f 3 at 3 is set to P, the magnitude of the crosshatched area under the load curve. This area goes halfway over adjacent element sides f = P 3 Distributed load intensity (load acts downward on boundary) Boundary Finite element mesh IFEM Ch 8 Slide 9

10 Element by Element (EbE) Distributed Load Lumping Force P has magnitude of crosshatched area under load curve and acts at its centroid. (e) (e) 2 f P f (e) 3 Distributed load intensity (load acts downward on boundary) centroid C of crosshatched area Boundary (e) f 2 = (b/l)p C 2 P 3 a b L=a+b (e) f 3 = (a/l)p Details of element force computations Finite element mesh IFEM Ch 8 Slide 10

11 Boundary Conditions (BCs) The most difficult topic for FEM program users Two types Essential Natural IFEM Ch 8 Slide 11

12 Boundary Conditions Essential vs. Natural Recipe: 1. If a BC involves one or more DOF in a direct way, it is essential and goes to the Left Hand Side (LHS) of Ku = f 2. Otherwise it is natural and goes to the Right Hand Side (RHS) of Ku = f IFEM Ch 8 Slide 12

13 Department of Engineering Mechanics Minimum Support Conditions to Suppress Rigid Body Motions in 2D (a) A B (b) A y B x (c) y B A x IFEM Ch 8 Slide 13

14 Minimum Support Conditions to Supress Rigid Body Motions in 3D z B A y C D x IFEM Ch 8 Slide 14

15 Visualizing Symmetry and Antisymmetry Conditions in 2D (a) Symmetry line (b) Antisymmetry line loads A' A' A A" A A" displacement vectors IFEM Ch 8 Slide 15

16 Example of Application of Symmetry BCs (a) y A C B D x (b) A C B D IFEM Ch 8 Slide 16

17 Example of Application of Antisymmetry BCs y (a) A B C D x A (b) C B D Vertical (y) motion of one node such as C or D may be constrained to suppress y-rbm IFEM Ch 8 Slide 17

18 "Breaking Up" Point Loads at Symmetry BCs (a) y P A C B D P x (b) P/2 P/2 P/2 P/2 (c) P/2 IFEM Ch 8 Slide 18

19 "Breaking Up" Point Loads at Antisymmetry BCs (A trickier problem) y P A C B D P x 2P?? IFEM Ch 8 Slide 19