A finite element model was produced for both linear eigenvalue buckling and nonlinear large deflection buckling analyses. The graphic to the right illustrates the geometric surface model.
The geometric model of the fuselage was constructed within the ANSYS program with shell thickness and stiffener beam cross sectional attributes attached to the lines and surfaces within the model. Having created the geometric model the finite element mesh was created with the ANSYS automatic meshing capability. The finite element mesh was created with the 4-noded structural nonlinear SHELL43 element, the 2-noded structural BEAM4 and offset BEAM44 elements and 2-noded structural spar elements, LINK8. The active degrees of freedom in the elements are the translatory displacement in the x, y and z directions and the rotational displacements in the rotx, roty and rotz directions. The model consisted of 23,001 elements, 19,437 nodes resulting in a model size of 116,622 degrees of freedom.
A graphic illustrating the finite element mesh used in the analyses can be seen on the left.
Having extracted the buckling critical loads and the mode shapes from an eigenvalue analysis it is possible to correlate these results with testing. It is also possible from this form of analysis to establish the loading increments that would cause the fuselage to start buckling which assists in the loading control of the subsequent nonlinear large deflection buckling analysis.
A graphic showing the out of plane deflection distribution for the panels obtained from the large deflection analysis is shown below at a load increment of 20% of final load. This solution compares very favorably with the experimental data. The FE model actually predicts the onset of buckling at around 13% of final load.
The large deflection solution was run through to a loadof 60% of the final high drag landing load case at which point severe buckling of the fuselage structure was measured experimentally. It should be noted that the aluminium material was assumed to behave elastically during all of this work.
The graphic left shows a closer view of the buckling in the panels at 60% load. This graphic displays the out of plane displacement solution for the critical panels. The graphic shown right displys the same displacement solution at 60% load but from the other side.
It can be seen from this that the fuselage is developing buckled panels which are evolving progressively towards the tail. This matches precisely the shape of the panel buckling experienced during the test and also duplicates the magnitude of load at which this progressive buckling occurs. The analyses were run using SGI Intel based Pentium PC’s.