Transcript Document
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 1 TWO POSSIBLE REPRESENTATIONS OF A PLATE 2 CAN YOU IDENTIFY THESE ELEMENTS? Note: all these elements would be way too large for analysis 3 SW TERMINOLOGY Draft Quality – first order element High Quality – second order element 4 FINITE ELEMENT MESH Mesh compatibility Mesh quality Mesh adequacy 5 MESH COMPATIBILITY Compatible elements Incompatible elements The same displacement shape function along edge 1 and edge 2 The same displacement shape function along edge 1 and edge 2 6 MESH COMPATIBILITY 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. 7 MESH COMPATIBILITY Tetrahedral solid elements Hexahedral solid elements Tetrahedral solid elements and hexahedral solid elements combined in one model. 8 MESH COMPATIBILITY Shell elements Solid elements 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. 9 Exaggerated stress concentration may appear along the link lines. MESH QUALITY Elements before mapping Elements after mapping 10 MESH QUALITY aspect ratio angular distortion ( skew ) angular distortion ( taper ) curvature distortion midsize node position warpage 11 MESH QUALITY Element distortion: aspect ratio Element distortion: warping 12 MESH QUALITY Element distortion: tangent edges 13 MESH ADEQUACY This stress distribution need to be modeled This is what is modeled with one layer of first order elements 14 MESH ADEQUACY cantilever beam, model 1 terribly bad cantilever beam, model 2 also terribly bad cantilever beam model 3 a good beginning ! cantilever beam, model 4 an acceptable model cantilever beam size: modulus of elasticity: load: beam theory maximal deflection: beam theory maximal stress: 10" x 1" x 0.1" 30,000,000 PSI 150 lb. f = 0.2" = 90,000 PSI our definition of the discretization error : ( beam theory result - FEA result ) / beam theory result model # FEA deflection [in] deflection error [%] FEA stress [ PSI ] stress error [%] 1 0.1358 32 1,500 98 2 0.1791 10 39,713 56 3 0.1950 2.5 65,275 27 4 0.1996 0.2 80,687 10 15 MESH ADEQUACY Two layers of second order solid elements are generally recommended for modeling bending. Shell elements adequately model bending. 16 MESH ADEQUACY Incorrect shell elements meshing using automatically generated mid-surface 17