几何可变体系大变形机构模态的二元体构建法

针对仅有一个自由度的几何可变体系,基于大变形机构模态的特性,提出常变、瞬变的判断方法,进而对常变体系提出大变形机构模态的二元体构建算法。该算法将问题简化为类似于一元二次方程的求解,无须求解非线性超越方程组,可给出完备的模态解答和完整的解答路径及其分叉点。本法具有原理直观、公式简洁、解答完备的优点,可作为结构力学几何构造分析教学的补充内容。

CONSTRUCTION OF MECHANISM MODES OF GEOMETRICALLY UNSTABLE SYSTEMS IN LARGE DEFORMATION

Based on the characteristic of mechanism mode in large deformation, this paper proposes a method for determining whether a geometrically unstable system of a single degree of freedom is constantly unstable or instantaneously unstable, and in the former case the paper further proposes a bi-element construction method to build the mechanism mode in large deformation. The method is nearly as simple as solving a quadratic equation without the need for solving transcendental equations and moreover the method can give complete solutions for modes, solution paths, limit points and bifurcation points. The method is found to be intuitive in theory, simple in formulation and complete in solutions. The method can be used as a supplement or extension to analysis of geometrical stability in structural mechanics course.