کمانش تجزیه و تحلیل حساسیت از صفحات نازک ترک خورده تحت تنش غشاء و یا در حال بارگذاری فشرده سازی

Thin-walled structural components such as plates and shells are commonly used in practical applications such as aerospace, naval, nuclear power plant, pressure vessels, mechanical and civil engineering structures and so on, and the safety assessment of such structures must carefully consider all the phenomena which can decrease the bearing capacity of such elements. Among them, the presence of cracks in thin-walled structures can heavily affects their safety factor with respect to the more common modes of failure such as buckling or fracture. For very thin plate, buckling collapse under compression or even under tension, apart fracture or plastic failure in this last case, can easily take place: the presence of flaws such as through-the-thickness cracks can sensibly modify such ultimate loads. In the paper the effects of cracks’ length and orientation on the buckling loads of rectangular elastic thin-plates – characterised by different boundary conditions and by various Poisson's ratio – under tension and compression, is considered. For tensioned flawed plates a fracture-buckling and a plastic-buckling collapse maps are obtained. After a short explanation of the buckling phenomena in plates, several FE numerical parametric analyses results are presented in terms of critical load multiplier in compression or in tension in cracked plates. The obtained results are discussed and some interesting and useful conclusions regarding the sensitivity to cracks’ presence of buckling loads of thin plates under compression or tension (or fracture in this last case) are explained. The interesting case of tensioned cracked plates is considered by studying the easiest collapse between fracture, plastic flow and buckling: in such cases some failure-type maps are finally determined.

The knowledge of the buckling phenomena in elastic thin-wall structures, such as plates, under tension and compression is essential in many engineering fields for their structural safety assessment. In the present paper the buckling and fracture behaviour of variously cracked and restrained rectangular elastic thin-plates has been considered. The influence of several geometrical and mechanical parameters on the buckling load of compressed or tensioned plates has been investigated by the numerical Finite Element Method (FEM): in particular the effects of the relative crack length, crack orientation, Poisson's ratio of the plate's material and of the boundary conditions on the buckling phenomena have been quantitatively investigated. The obtained results have shown that the crack's effects on the buckling phenomena under compressive stress heavily depends on the plate's boundary conditions, while they are almost independent for tension cases. Crack length slightly reduces the buckling load in compressed plates with all supported or clamped edges, especially for cracks nearly parallel to the loading direction (θ > π/3); surprisingly the buckling behaviour shows some improvements with respect to the uncracked case (buckling load increases up to 10%), when cracks are transversal to the loading direction. In tensioned plates the crack always reduce the buckling critical load with respect to the undamaged case. The tension critical load multipliers λ+ are always higher than the corresponding compressive ones. In such cases buckling loads tend to decrease rapidly by increasing the crack length and decreasing the crack orientation angle. The presence of cracks in tensioned plates lying orthogonal to the loading direction (θ = 0°) can be considered to be the most dangerous ones. Poisson's ratio variation has shown to reduce (to increase) the buckling load for compressed (tensioned) plates, but significant effects can be appreciated only for cracked plates under tension. Finally, in tensioned cracked plates the possibility of fracture or plastic failure instead of buckling collapse has been studied. By evaluating the lowest collapse load by considering different failure's mode, regions of buckling or plastic collapse in the domain of the considered parameters have been determined for different fracture toughness and material's yield stress values. Usually buckling rupture easily occurs instead of fracture or plastic flow for long cracks oriented nearly transversal to the loading direction; for very tough materials a secondary buckling collapse region can be identified as corresponding to cracks oriented nearly parallel to the loading axis and with not excessive extension (small cracks).