Finite Element Method for 3D Solids

  • Maria Augusta Neto
  • Ana Amaro
  • Luis Roseiro
  • José Cirne
  • Rogério Leal


A three-dimensional (3D) solid element is the most general finite element because all the displacement variables are dependent in x1, x2 and x3 coordinates. The formulation of 3D solids elements is straightforward, because it is basically an extension of 2D solids elements. All the techniques described in 2D solids can be utilized, except that all the variables are now functions of special coordinate.


Shape Function Strain Matrix Nodal Displacement Vector Tetrahedron Element Natural Coordinate System 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Maria Augusta Neto
    • 1
  • Ana Amaro
    • 1
  • Luis Roseiro
    • 2
  • José Cirne
    • 3
  • Rogério Leal
    • 3
  1. 1.CEMUC - Centre for Mechanical EngineeringUniversity of CoimbraCoimbraPortugal
  2. 2.Department of Mechanical EngineeringPolytechnic Institute of CoimbraCoimbraPortugal
  3. 3.Department of Mechanical EngineeringUniversity of CoimbraCoimbraPortugal

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