1 TYPICAL ELEMENTS Triangular shell element 6 D.O.F. per node Tetrahedral solid element 3 D.O.F. per node First order elements Linear displacement distribution Constant stress distribution Second order elements Second order displacement distribution Linear stress distribution

2 TWO POSSIBLE REPRESENTATIONS OF A PLATE

3 CAN YOU IDENTIFY THESE ELEMENTS? Note: all these elements would be way too large for analysis

4 Draft Quality – first order element High Quality – second order element SW TERMINOLOGY

5 FINITE ELEMENT MESH Mesh compatibility Mesh quality Mesh adequacy

6 MESH COMPATIBILITY Compatible elements The same displacement shape function along edge 1 and edge 2 Incompatible elements The same displacement shape function along edge 1 and edge 2

7 Model of flat bar under tension. There is an incompatibility along the mid-line between the left and the right side of the model. The same model after analysis. Due to incompatibility a gap has formed along the mid-line. MESH COMPATIBILITY

8 Tetrahedral solid elements and hexahedral solid elements combined in one model. Hexahedral solid elements Tetrahedral solid elements MESH COMPATIBILITY

9 Shell elements and solid elements combined in one model. Shell elements are attached to solid elements by links constraining their translational D.O.F. to D.O.F. of solid elements and suppressing their rotational D.O.F. This way nodal rotations of shells are eliminated and nodal translations have to follow nodal translations of solids. Unintentional hinge will form along connection to solids if rotational D.O.F. of shells are not suppressed. Exaggerated stress concentration may appear along the link lines. MESH COMPATIBILITY Shell elements Solid elements

10 Elements before mappingElements after mapping MESH QUALITY

11 MESH QUALITY aspect ratio angular distortion ( skew ) angular distortion ( taper ) curvature distortion midsize node position warpage

12 Element distortion: aspect ratio Element distortion: warping MESH QUALITY

13 Element distortion: tangent edges MESH QUALITY

14 MESH ADEQUACY This stress distribution need to be modeled This is what is modeled with one layer of first order elements

15 cantilever beam size:10" x 1" x 0.1" modulus of elasticity:30,000,000 PSI load:150 lb. beam theory maximal deflection:f = 0.2" beam theory maximal stress:  = 90,000 PSI our definition of the discretization error : ( beam theory result - FEA result ) / beam theory result MESH ADEQUACY

16 MESH ADEQUACY Two layers of second order solid elements are generally recommended for modeling bending. Shell elements adequately model bending.

17 MESH ADEQUACY Incorrect shell elements meshing using automatically generated mid-surface