Elastic buckling of thin plates with holes in compression or bending

Closed-form expressions for approximating the influence of single or multiple holes on the critical elastic buckling stress of plates in bending or compression are developed, validated and summarized. The expressions are applicable to plates simply supported on 4 sides and plates simply supported on 3 sides, commonly called stiffened and unstiffened elements in design. The expressions serve as a convenient alternative to shell finite element eigen-buckling analysis, which requires commercial software not typically accessible to the engineering design community. The forms of the expressions are founded on classical plate stability approximations, and are developed and validated with parametric studies employing shell finite elements. The finite element parametric studies demonstrate that holes may create unique buckling modes, and can either decrease or increase a plate's critical elastic buckling stress depending on the hole geometry and spacing. The validated closed-form expressions and their associated limits are intended to be general enough to accommodate the range of hole shapes, locations, and spacings common in engineering practice, while at the same time also defining regimes where explicit use of shell finite element analyses is still needed for adequate accuracy.