具有初始几何缺陷加劲板的动态屈曲

Dynamical buckling of stiffened plates with initial geometrical imperfection

针对工程中常用的加劲板,研究了动态屈曲的求解方法。将加劲板分为母板与加劲肋两个部分考虑,其中母板按经典薄板理论计算,加劲肋视为Euler梁。假定加劲板的位移,利用Hamilton原理结合系统能量和振型叠加法建立了加劲板的动态屈曲特征方程。最后,选择四边简支加劲板进行数值分析,分析中考虑初始几何缺陷的影响,并讨论了初始几何缺陷、加劲肋的数量及其刚度的变化对动态屈曲临界荷载的影响。结果表明:一阶模态的初始几何缺陷对加劲板的临界荷载影响很大,而增加加劲肋的数量及其刚度可以提高加劲板的抗动态屈曲能力。研究结果也为加劲板的结构设计方法提供一定的参考。

An approach was presented to study the dynamical buckling of stiffened plates.The stiffened plate was divided into one plate and some stiffeners,with the plate analyzed based on the classical thin plate theory,and the stiffeners taken as Euler beams.Assuming the displacements of the stiffened plate,the Hamilton principle and modal superposition method were used to derive the eigenvalue equations of the stiffened plate according to the energy of the system.Numerical examples of simply supported stiffened plates were presented to study the critical loads with the initial geometrical imperfection considered.A detailed discussion on how the initial geometrical imperfection,the number and the flexural rigidity of stiffeners influence the critical load was carried out.The results show the initial geometrical imperfection in the 1st mode shape has a great effect on the critical load,and the increase of the number and the flexural rigidity of stiffeners can strengthen the dynamical buckling capacity.These conclusions can also provide references to the engineering design of stiffened plates.