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中文字数:2509,中文页数:6 英文字数:1556 页数:7 ABSTRACT: A second-order nonlinear analysis of steel space structures has been presented. Of the two types of nonlinearities, material and geometric, only geo-metric nonlinearity has been considered. The material of the structure steel has been assumed to be linearly elastic. In geometric nonlinearity, the effects of instability produced by axial forces, the bowing of the deformed members, and finite deflections have all been included. For this purpose, the secant stiffness matrix in the deformed state and the modified kinematic matrices along with the geometric matrix necessary for formulating the tangent stiffness matrix, have been developed. These matrices are used in the analysis, which is carried out by the displacement method through an iterative-incremental procedure based on Newton-Raphson technique. The iterations that take into account the latest geometry are repeated until the unbalanced loads become negligible and equilibrium is obtained. The equilibrium equations are solved by Cholesky's method. Results of an illustrative example and conclusion based on them are also given. 空间钢结构的非线性分析 摘要：随着二阶非线性分析大跨空间结构理念的提出，对两种类型的非线性、材料和几何分析中，几何非线性已被考虑，非线性分析才能被认可。同时需要假设钢结构的材料为线弹性。在几何非线性的影响下，所产生不稳定的轴向力、弯曲变形产生的弯矩,以及有限制的偏移量均包括在内。为了达到这个目的，制定刚度矩阵修正后的变形状态和动态矩阵与几何矩阵所需的切线刚度矩阵，这样才能更好的去分析。在这些矩阵中使用分析方法，,通过牛顿迭代法进行位移法来实现。在迭代过程中,考虑几何变化是重复,直到最后结果的变化已经微乎其微，可以看作是达到了平衡，这样做的误差很小，能满足要求。通过这样的方程进行求解的方法是实用的。与此同时，平衡方程求解Cholesky的方法就是在这种结论的基础上给出的，从而进一步说明了这种分析方法的可行性。 |
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