M5 Buckling of Laminates

Topic

A thin laminated panel under compression may fail not because the material reaches its limit, but because the panel becomes geometrically unstable: instead of continuing to compress in a straight line, the panel suddenly deflects to the side—a sudden deflection known as buckling. Because the panel deflects in this manner rather than continuing to compress linearly, its failure in this model is classified as a failure due to geometric instability rather than material exhaustion.

The laminate's flexural stiffness matrix—already calculated in another model within this set—directly determines the panel's critical buckling stress: the level of compression at which the panel ceases to remain straight and deflects sideways. A higher flexural stiffness matrix allows the panel to withstand greater compressive stress before buckling, whereas a lower flexural stiffness matrix causes the panel to buckle under lower compressive stress.

This critical buckling stress is also modulated by the panel's slenderness ratio—that is, its length or width relative to its thickness. A higher slenderness ratio (meaning the panel is longer or wider relative to its thickness) results in a lower critical buckling stress, as a more slender panel deflects sideways more easily; conversely, a lower slenderness ratio results in a higher critical buckling stress, as a less slender panel better resists such deflection. For this reason, this model—which addresses the buckling of the laminated panel—depends directly on another model within the same set: the one that calculates the laminate's flexural stiffness matrix. Because that other model determines the flexural stiffness matrix, this model can use it directly—along with the slenderness ratio specific to each panel—to determine the critical buckling load at which that specific panel fails.

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