Nonconforming Approximate Solution to a Specially Orthotropic Axisymmetric ThinShell Subjected to a Harmonic Displacement Boundary Condition

摘要

This report develops an approximate closed form solution to a speciallyorthotropic axisymmetric cylindrical thin shell subjected to a harmonic boundary condition. Modified Love-Timoshenko shell equations forced by a harmonic boundary condition at one end of the shell and grounded by a mechanical spring at the other are used to formulate this boundary value problem. Each modeled shell is subjected to an axial tension, and a steady state approximate solution is then formulated. The solutions derived here are compared to finite element results and to previous models of the thin shell problem. It is shown that the finite element analysis agrees very closely with the equations derived in this study. It is also shown that the earlier models used to analyze specially orthotropic thin shells produce results that do not agree with the model developed here or with the finite element analysis. Shell configurations evaluated include finite length isotropic, finite length specially orthotropic, semi-infinite length specially orthotropic, and damped finite length specially orthotropic.