The shells differential equation can, in principle, be solved in several ways. Three different methods will here be outlined:
1. The inverse method
By solution after the inverse method, one choose an equation that satisfy the shells differential equation, that is:
2. The semi-inverse method
By solution after the semi-inverse method, one have to assert a certain pattern for the deformation or stress distribution in the shell. From this, a stress function is established. This stress function is then controlled for consistence with the boundary conditions.
3. Serial solutions
The final stress function is made up of a set of weighted functions:
The coefficients Cn are then determined so that the boundary conditions for the problems are fulfilled to the best.
When the stress function are established, the stresses, strains and displacements can be determined from the following equations: