Elmer Solver can be used to calculate the deflections, rotations, and stress distributions of thin and moderately thick elastic shells. The shell model is based on a facet approximation of the midsurface, standard plane stress equations (discretized by the standard fem), and the plate model of Reissner and Mindlin (discretization by the stabilized MITC-technique). The normal rotation ("drilling rotation") is introduced as an auxiliary function for user's convenience (discretization by the stabilized method of Hughes and Brezzi).

The surface plot represent the Von Mises stress distribution on the top surface of a simply supported thin hemisphere subject to uniform normal pressure load. The contour plot on the right represents the cartesian stress tensor component Sxx on the mid surface of the shell (in the figures x-axis points to right, y-axis goes up, and z-axis towards the reader). The radius of the sphere is r=1 and the thickness of the midsurface t=0.01. The material was assumed homogeneous and isotropic with Young's modulus E=200E9 and Poisson ration v=0.3. The finite element mesh consisted of 10225 node points and 20448 linear triangular shell elements.

The contour plot represents the absolute displacement of a clamped elastic beam subject to its own weight. The material of the beam is homogeneous and isotropic with Youngs modulus E=207E9, Poisson ratio v=0.3, and density 7800 kg/m3. The length of the beam is 5m, height 2m, and width 1m. The thickness of the material is 1cm. The finite element mesh consists in this case of 6682 linear triangular shell elements and 3452 node points. Note that the displacements are exaggerated.

First eigen mode of the hemisphere

Third eigen mode of the hemisphere

Fourth eigen mode of the hemisphere

Geometry of the hemisphere