Basic assumptions

The basic assumptions that are assumed by rambshell for the shell analysis are the following:

  1. Small displacements

  1. Lineal elasticity of the materials
  1. Superposition of loads (Consequence of point 2)
  1. Shear deformation is considered for shells

The analysis of shells is based on simplifying the representation of a real solid, with one of its dimensions much smaller than the other two, with its medium plane.

The Reissner-Mindlin hypotesis:

  1. All the points belonging to one normal to the medium plane have the same vertical displacement (in z’ sense).
  1. Normal stress σz is negligible.
  1. The points that before the deformation belonged to one normal to the medium plane, after deformation continue belonging to one straight line, not being this, necessarily, orthogonal to the deformed medium plane.

From these assumptions it is possible to extract the following equations:

where

are the 5 degrees of freedom that, adding the 6th degree
that comes from joining the shells in the space, give the total 6 degrees of freedom that every node has.

where α is the coefficient to correct the transversal tangential work.

From here it is possible to define the strengths on the shell, which are defined as:

where t is the thickness of the shell.