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EMA 405

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

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  1. EMA 405 3-D Elements

  2. Introduction • 3-D elements have 3 degrees of freedom per node (ux, uy, uz) • The two fundamental shapes are hexahedral and tetrahedral elements

  3. 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

  4. 4-node Tetrahedral element Constant Strain

  5. 10-node Tetrahedral element Linear Strain

  6. 8-node Hexahedral element Linear Strain

  7. 20-node Hexahedral element Quadratic Strain Not compatible with 10-node tetrahedral elements

  8. 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

  9. 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

  10. 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

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