Numerical studies on combined (compression and shear) buckling

The compression and shear buckling analysis is made only for thin plates (with material characteristics presented in previous chapter). The geometry of the plates is square one, having the side length of 320mm, and total thickness of 4.96mm. The orthotropic directions (a), thickness of the macro-layers (t) and plate lay-up are presented in Table AA1.

The constrains are considered according to plates type b from the previous chapter. The loading acting on the plate is according to figure AA9. For analysis the parametric calculus was done for various ratios a=q/p, that is {0.2; 0.4; 0.6; 0.8; 1}.

The all types of amplitude of initial transversal deformation are analysed.

In the table AA3 the buckling loads so for perfect and for imperfect plates are presented. Only the cases of a=0.2 and a=0.4 are presented in figure AA10. As it is seen in figure AA10, according to the graphical method, the buckling loads for the all three imperfect plates are in the range 0.134MPa < pcr < 0.288MPa.

Fig. 17.9. Plate in shearing and compression

 a=q/p w0=0 w0=1.06 mm w0=3.2 mm w0=9.6mm 0.2 41.765 0.288 0.222 0.134 0.4 41.561 0.266 0.111 0.087 0.6 41.007 0.288 0.088 0.071 0.8 40.167 0.277 0.111 0.071 1 39.119 0.305 0.124 0.081

 a=q/p Failure mode Perfect plate w0=1.06 mm w0=3.2 mm w0=9.6mm 0.2 Tension 2.499 0.706 0.605 0.403 Compression – 1.413 1.312 1.211 0.4 Tension 2.499 0.706 0.504 0.403 Compression – 1.311 1.211 0.999 0.6 Tension 1.874 0.504 0.504 0.302 Compression – 0.908 0.876 0.802 0.8 Tension 1.562 0.403 0.403 0.302 Compression – 0.806 0.706 0.706 1 Tension 1.249 0.302 0.302 0.302 Compression – 0.706 0.563 0.563