中文摘要：

针对增量-迭代技术背景下几何非线性分析耗时长、代价大的问题,通过颠倒U.L.（更新的拉格朗日）列式隐含的自然变形-刚性运动过程,建立了平面梁全新势能列式,由卡氏定理推导了显式增量割线刚度矩阵.与U.L.列式相比,割线刚度矩阵不仅使表达式得到简化且具有通过刚体运动检验、免于薄膜闭锁和保持对称性等特点.应用增量割线刚度作为几何非线性分析典型迭代步＂预测＂和＂校正＂算子,建立了基于柱面弧长约束方程的直接迭代算法,提出了非比例加载下荷载因子取舍算法.算例表明：增量割线刚度法追踪较陡路径能有效地避免路径回溯及迭代发散问题;与牛顿-拉夫逊法相比,减少了增量步数和机时,提高了分析效率.

英文摘要：

The existing methods of geometric nonlinear analysis is generally considered as time-consuming and computational intensive under the framework of the incremental-iterative scheme.By assuming an inverse deformationprocess of the U.L.（updated Lagrangian）approach i.e.,natural deformation to rigid body motion,apotential energy formulation was presented and applied to the planar beam member as an illustration.An explicit incremental secant stiffness matrix was correspondingly developed via the Castigliano′s theorem.The derived secant stiffness matrix was rigid body motion test qualified,membrane locking free and symmetric as well as simple in form as compared with the one obtained by the U.L.approach making it suitable for a general use in the solutions of geometrical nonlinear problems.By applying the incremental secant stiffness matrix to both the ‘predictor＇and‘corrector＇phases of a typical iteration of geometric nonlinear analysis,a direct iteration procedure making use of the cylindrical arc-length constraint equation was proposed for tracing complete equilibrium path.Meanwhile,a root selection algorithm which was capable of successfully giving correct solution direction was presented for specifically dealing with the general cases of non-proportional loading.The results of numerical validations demonstrate that the proposed method can reliably avoid the‘turning back＇of solution direction and the phenomenon of divergence during iterative process even in the case of tracing prudent equilibrium path.In comparison of the Newton-Raphson method,a reduction in the total number of incremental steps and computation time can be achieved to effectively im-prove the analysis efficiency.