A MATHEMATICAL METHOD TO INVESTIGATE DIFFERENT PROFILES ON DEFORMATION OF CYLINDRICAL SHELLS WITH VARIABLE THICKNESS

A mathematical formulation is presented to investigate the effect of different profiles on deformation of the cylindrical sells with variable thickness. The shells are subjected to the axial and radial constant pressures. The displacement field is predicted by using the first order shear deformation theory. The kinematics of the problem is defined by the von-Karman theory and the constitutive equation obeys the Hooke’s law. By applying the virtual work principle, the governing equations which are a system of nonlinear differential equations with variable coefficients are extracted. The matched asymptotic expansion method of the perturbation technique is used to solve the governing equations and then the effects of geometrical parameters on the displacements are studied. Also, a comparison with the finite elements method is performed.