دانلود رایگان مقاله فرمول برای کمانش الاستیک از صفحات مستطیل تحت بارهای تک محوره و برشی

abstract

As thin plates have relatively big thickness ratios, their elastic buckling usually occurs before the yielding. From beginning of the previous century, many researchers have considered various in-plane loading states on thin plates and have strived to find simple equations to predict the buckling load. However, there are few valid equations with negligible errors for a thin plate, when it is under all of in-plane loads. In this paper, using energy method, an applicable formula is suggested for a simply supported rectangular plate, which is under biaxial and shear loads. The biaxial loads can be applied in the compressive/compressive, compressive/tensile, and tensile/tensile states on the plate. Generally, 15 129 examples are considered for this problem. The aspect ratio of plates varies from 1 to 5 and for each case and with the known load ratios, the plate buckling coefficient is calculated. Then, by using the regression techniques and interpolation, it is tried to estimate a simple equation with minimum error to predict the buckling load. The confirmed results show that for the biaxial compression and shear state, the maximum error is 8% and for the compression–tension–shear and biaxial tension and shear states, it increases until 20%.

5. Conclusion

In this paper, using the Rayleigh–Ritz method, the buckling load of a simply supported rectangular plate under biaxial and shear loads was evaluated. The plate aspect ratio was supposed that varies from 1 to 5 and with several loading states, 15 129 examples were considered. Then, applying the regression techniques and interpolation on the obtained data, a concise equation (Eq. (19) or (23)) is approximated to predict the buckling load coefficient. It can be shown that for longer plates (α > 5), the obtained results for α = 5 are applicable with a good accuracy. In Compression–Compression–Shear state, the maximum error in the proposed equation increases when the aspect ratio rises. However, it is always less than 8% (3 ≤ α ≤ 5). In presence of tensile stress(es), right hand of the proposed equation must be always considered unit. When the tensile stress (σy) is applied on the plate length (the longer direction) and the compressive stress, σx ≤ 1.4τ , then a modifier factor (η1) must be applied on the results. Furthermore, if the tensile stress (σx) is applied on the plate width and its value is larger than 40% of the shear stress and also σy ≤ τ , then another modifier factor (η2) must be used. The predicted results by the proposed equation lead to error up to 20% in some states. The proposed equation is directly applicable for Tension– Tension–Shear state, when both of tensile stresses values are less than 40% of the shear stress; otherwise, the modifier factor, η1 should be used to decrease errors. However, the maximum appeared error reaches to 16%. Finally, the achieved results from two methods were compared with those of FEM; thus the maximum difference between the Rayleigh–Ritz method and FEM is about 1.4%.