双轴受压小刚度加劲厚板的极限强度计算

Calculation of ultimate strength for slightly stiffened thick panels under biaxial compression

对于中厚钢板,柔性加劲比刚性加劲更具技术和经济优势,小刚度加劲厚板的极限强度计算则是中厚板柔性加劲设计的理论依据。基于整体屈曲模态,将加劲板等效成单块的正交异性板,根据板的大挠度理论方程,推导得到同时适用于单轴、双轴均匀受压的小刚度加劲厚板的极限强度计算公式。加劲板模型可包含多种加劲肋形状,推导过程中计入焊接残余变形的影响。初始变形和受荷变形均假定为正弦函数分布,并可按照需要进行应力修正。在对可能发生屈服的区域依据VonMises屈服准则进行极限状态判定之后,采用单纯形直接搜索的最优化方法并借助MATLAB优化工具箱实现了复杂方程的高效求解。计算结果得到有限元法的验证,可为中厚板的柔性加劲设计提供理论基础。

For plates of moderate thickness, flexible stiffeners have more advantages over rigid stiffeners both in fabrication and in cost saving. Calculation of ultimate strength for slightly stiffened thick panels is the theoretical basis of flexible stiffener design of plates of moderate thickness. By transforming the stiffened panel to an equivalent orthotropic plate, ultimate strength formulations for slightly stiffened panels subject to uniaxial or biaxial compressive loads are derived based on large deflection theory and overall buckling mode. The panel can be composed of various shapes of stiffeners. Post-weld initial deflection is considered during the process. Both initial and added deflection modes are simplified as trigonometric functions and the stress distribution can be revised if necessary. The yield regions are determined according to von Mises yield criterion, and efficient solution of the complex formations is executed by adopting nonlinear programming theory and MATLAB~ optimization tool box. The calculation results are checked by that of FEM analysis.