Finite Elements

Based on mechanics of continuum, a three dimensional solid can be classified in a given category. For a solid with dimensions R, L and t, with t being the thickness, L is the working direction and R is the curvature radius, write:

• If L/t > 20 and R/t > 20: Thin shell assumptions are valid (Kirchhoff or Mindlin shell models)
• If 10 < L/t < 20 and 10 < R/t < 20: Moderately thick shell (Mindlin model)
• If 4 < L/t < 10 and 4 < R/t < 1: Thick shell
• If L/t < 4 or R/t < 4: Solids

An adapted finite element mesh is then applied to each case:

• Shell theory: 2D mesh of the mid-surface
• Thick shell: 3D mesh with constant normal stress assumption
• Solids: 3D mesh without constant normal stress assumption

In Radioss all of these formulations are available. For a given mesh, several kinds of formulations may be available based on:

• The number of integration points
• The stress updating method
• Large or small strain assumption
• Plasticity options for necking and material law integration
• Type of element and hourglass formulation