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文章应用有限曲条-柔度理论对带隔板连续薄壁弯箱梁结构进行力学分析。引入Novozhilov理论,推导了简支有限曲条元刚度矩阵,利用谐函数正交性解决了刚度矩阵元素耦合问题,并联合运用ξ坐标法和Gauss求积法解决了刚度矩阵元素求积问题。研究了内部横隔板和外部支座赘余力问题,应用柔度理论推导了赘余力凝聚矩阵,解决了带隔板连续薄壁弯箱梁结构内外部超静定问题。推导带隔板连续弯箱曲条元整体平衡方程后,给出了求解位移场和应力场的具体计算步骤,编制了相应的计算程序。通过典型算例分析可知,对于带隔板连续薄壁弯箱梁结构,有限曲条-柔度理论是一种较为高效的计算方法,所需单元少且计算过程快速、稳定收敛;对于内部超静定结构,用文章推导的柔度理论求解是适合的。
In this paper, the mechanical analysis of the continuous thin-walled curved box girder with diaphragm is carried out by using the finite curvature-flexibility theory. The Novozhilov theory is introduced to deduce the finite element stiffness matrix of simple finite element. The coupling problem of stiffness matrix element is solved by the orthonormality of harmonic function, and the problem of quadrature integral of stiffness matrix is solved by the combination of ξ coordinate method and Gauss quadrature method. The problem of the excess capacity of the internal diaphragm and the external support was studied. The flexibility matrix was deduced by using the flexibility theory to solve the problem of the indeterminacy of the internal and external of the continuous thin-wall curved box-girder with diaphragm. After deducing the global equilibrium equation of the curved box element with continuous curved boxes, the calculation steps for solving the displacement field and the stress field are given, and the corresponding calculation programs are compiled. The typical example analysis shows that the finite curvature-flexibility theory is a more efficient method for the thin-walled curved box girder with diaphragm, and the required unit is small and the calculation process is fast and stable. For the internal ultra Statically deterministic structure, with the article derived flexibility theory solution is suitable.