正交各向异性带钢瓢曲变形行为样条有限元研究

BUCKLING ANALYSIS OF ORTHOTROPIC STEEL STRIPS BY THE SPLINE FINITE ELEMENT METHOD

带钢在轧制过程由于晶粒的择优取向而产生各向异性,为了研究这种各向异性对带钢板形瓢曲行为的影响规律,针对生产中常见的板形瓢曲缺陷,根据正交各向异性薄板小挠度理论和屈曲问题的驻值势能原理,建立了带钢在纵向延伸塑性应变(初应变)作用下以样条函数为基础的前屈曲样条有限元计算模型,获得了屈曲临界塑性应变、临界波长与带钢各向异性程度的关系;根据大挠度理论和虚功原理,应用样条有限元获得了正交各向异性带钢后屈曲路径。计算分析了带钢正交各向异性程度对中浪、边浪、四分之一浪、边中复合浪屈曲变形前屈曲临界条件及后屈曲变形过程的影响规律。

Steel strips exhibit orthotropy due to the orientational preference of the crystalline structure in the rolling processes. The influence of the orthotropy on the buckling behavior of steel strips is investigated in this study. On the basis of the small deflection theory and the principle of stationary potential energy for orthotropic thin plates, the computational model of common flatness for pre-buckling deformation is established by the spline finite element method under plastic strain(initial strain). The relationships among the degree of anisotropy, the critical plastic strain and the critical wavelength are formulated. According to the large deflection theory and the virtual work principle, the path of post-buckling of steel strips is obtained by using the spline finite element method. The buckling behavior of center wave, edge wave, composite wave and quarter wave is analyzed under different degrees of orthotropy. The effect of othotropy on pre-buckling critical conditions and post-buckling deformation processes are also evaluated.