M.Sc Student | Eduardo Ejgenberg |
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Subject | Buckling of Laminated Cylindrical Shells |

Department | Department of Civil and Environmental Engineering |

Supervisor | Dr. Goldfeld Yiska |

Full Thesis text |

The stability equations of laminated shells are governed by a set of nonlinear partial differential equations. To simplify the solution procedure and to receive fare and fast prediction of the critical buckling load, the solution procedure can involve some levels of fidelity analysis. Usually the lower levels simplify the solution procedure by the aid of the perturbation technique, by ignoring the nonlinear parts of the pre-buckling state, and eventually by solving a linear set of equations to each state. However, by ignoring the nonlinear pre-buckling deformation and considering only its linear part can completely change the characteristic buckling behavior. It was found that for several special cases, especially for angle-ply laminated shells, the chosen formulation for the solution of bifurcation buckling behavior can lead to inaccurate results.

The main goal of this work is to
investigate the bifurcation buckling behavior of laminated cylindrical shells
obtained by various formulations, thus to find out the reasons for the
obtainable differences. The investigation will focus on the two common
formulations *u-v-w* and *w-F. *A third, mixed, formulation is offered in order to compare and validate the results. The boundary and the field equations for the
three formulations (*w-F*, *u-v-w*, and mixed) are deeply investigated in order to understand the reasons for the inaccuracies in the different formulations.
Special cases that simplify the common *u-v-w* formulation were introduced in order to check the boundary effects in the field equations. Different prebuckling
behaviors are assumed to be: level 1, membrane prebuckling for the three formulations
and level 2, linear axisymmetric prebuckling behavior for the three
formulations. A new non-linear prebuckling behavior is presented for special cases; symmetric angle ply laminates under axisymmetric axial compression for
simply supported cylindrical shells. The buckling behavior achieved under the above assumptions is compared with the linear classical prebuckling assumptions.
The non symmetric nature of the stiffness and the geometric matrices of the
strong form is checked for the *u-v-w* formulation by a simple finite
element code (weak form) for an angle ply cylindrical shell under axisymmetric
buckling behavior.