割线法在空间桁架几何非线性分析中的应用

Geometrically Non-linear Analysis of 3-D Truss with Secant Method

主要说明割线法在刚度矩阵上的应用。目前国内外有关几何非线性刚度矩阵方面的分析,皆为线性刚度矩阵加上几何刚度矩阵。虽然有关学者已提出许多简易合理的几何刚度矩阵的公式,但它们只适用于桁架、刚架、梁等,若遇到板、壳等较复杂的结构,其几何刚度矩阵将会是个令人困难的地方,因此提出利用割线法的概念,只使用线性刚度矩阵来分析结构的几何非线性行为,从而避免求几何刚度矩阵。虽仅探讨桁架结构,但此成果可供往后续梁柱及板壳等相关研究的参考。

This paper mainly deals with the secant method used on stiffness matrix. In present researches about non-linear analyses, the global matrix of the structure is always linear stiffness matrix added by geometric stiffness matrix. Although many simple and reasonable formulas of geometric stiffness matrix have been presented before, these are only used in trusses, frames, and beams. But if these formulas are used in more complicated structure systems, like plates and shells, the calculations of geometric stiffness matrix are much confusing. So we present an application using secant method to analyze geometrically non-linear of structures without geometric stiffness matrix. This paper is mainly separated in three parts. First, documents retrospect. Second, using secant method to derive formulas. Finally, examples analysis and discussions are presented. Only truss system is dealt with in this paper, but the result can be referred to in correlated researches.