Nonlinear static analysis of an axisymmetric shell storage container in spherical polar coordinates with constraint volume

• We develop a model for static analysis of axisymmetric shell with constraint volume.
• The change of pressure may be interpreted as a Lagrange multiplier.
• Varying hydrostatic pressure has no effect on the displacement response of the shell.
• The radius-to-thickness ratio has a major impact on the displacements on the shell.
• The change of pressure is linearly proportional to the linearly hydrostatic pressure.

An axisymmetric membrane shell fully filled with an incompressible fluid is investigated and it is modeled as a half drop shell storage container under hydrostatic pressure subjected to the volume constraint conditions of the shell and contained fluid. The shell geometry is simulated using one-dimensional beam elements described in spherical polar coordinates. Energy functional of the shell expressed in the appropriate forms is derived from the variational principle in terms of displacements and the obtained nonlinear equation can be solved by an iterative procedure. Numerical results of the shell displacements with various water depths, thicknesses, and internal pressures are demonstrated.