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EMA 405 - PowerPoint PPT Presentation


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EMA 405. 3-D Elements. Introduction. 3-D elements have 3 degrees of freedom per node ( u x , u y , u z ) The two fundamental shapes are hexahedral and tetrahedral elements. Comments. Mesh generation is easier with tetrahedral elements

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ema 405

EMA 405

3-D Elements

introduction
Introduction
  • 3-D elements have 3 degrees of freedom per node (ux, uy, uz)
  • The two fundamental shapes are hexahedral and tetrahedral elements
comments
Comments
  • Mesh generation is easier with tetrahedral elements
  • Tetrahedral elements tend to produce more degrees of freedom in a given model
  • Try mapped meshing if you want to use hex elements
20 node hexahedral element
20-node Hexahedral element

Quadratic Strain

Not compatible with 10-node tetrahedral elements

boundary conditions
Boundary Conditions
  • We have to restrict 3 translational rigid body modes and 3 rotational rigid body modes
  • We can restrict a single node in all 3 directions to take care of the translational modes
  • Rotations are trickier
boundary conditions continued
Boundary Conditions continued
  • Consider a 2-D case
  • With one node restricted in all directions, rotation about z-axis is possible
  • Restricting one node on x-axis in y-direction will prevent rotation about z
  • Do similar things to restrict rotations about x and y

y

Restrict in y

Restrict in x and y

x

example hollow cylinder with hole
Example – hollow cylinder with hole
  • E=100 Gpa, =0.3
  • L=80 mm
  • Pressure load=1 Mpa (applied on end faces)
  • Inner radius=7.5 mm
  • Outer radius=10 mm
  • Radius of hole=2.5 mm
  • Theory says peak stress is 3.65 MPa