Optimal Design of an Isotropic Porous-Cellular Cylindrical Shell

The paper outlines the effects on an isotropic porous-cellular cylindrical shell when subjected to a combined load: of axial force and external pressure. Metal porosity varies across the thickness of the shell wall. A dimensionless porosity parameter is introduced to compensate for this. Nonlinear hypothesis of deformation of the flat cross section of the shell wall is formulated. A system of five differential equations is defined on the basis of the theorem of the minimum of total potential energy. This system of equations is then analytically solved with Galerkin’s method. Critical loads for a family of porous shells are numerically determined based on the analytical solution. The optimization problem considers two criteria: minimum of mass and maximum of critical load on the shell. Optimal porosity variability for the cylindrical shell is determined numerically. An optimal dimensionless porosity parameter is then defined. Moreover, a comparative analysis for selected cylindrical shells with the use of FEM is performed. Results of the calculation are shown in respective figures. Finally, the results of the investigation for porous cylindrical shells are compared to the corresponding results for isotropic homogeneous shells.