梁系结构冗余度及其特性分析

Redundancy and properties of beam-composed structures

对梁系结构冗余度及其特性进行研究,将“超静定数反映结构整体冗余程度”概念扩展到单元层面。首先,根据变形形式的势能方程,推导并定义平面梁单元与空间梁单元的单元冗余度。其次,通过刚度矩阵凝聚,推导不同约束条件下平面梁的单元冗余度并通过MATLAB实现。最后,通过算例分析,讨论构件参数和约束条件对单元冗余度的影响。分析结果表明,平面梁系结构的单元冗余度变化范围为0～3;杆件的单元冗余度随刚度的增大而减小;约束条件由刚接变铰接时会引起结构整体冗余度的减小。所提出的单元冗余度可以较好地反映梁系结构几何构造、刚度分布情况以及约束情况等结构特性。

This paper presents the concept of redundancy of beam-composed structures, and extends it to the element level ,which reflects the properties of the topology and stiffness of these structures. Based on the potential energy equation, the parameters defining the element-redundancy are attained, which represent the physical properties of plane and spatial beams. The plane beam＇ s element-redundancy on various constraint conditions are derived through the stiff matrix coagulation. The effect of element properties and constraint conditions on the element-redundancy are revealed through case studies implemented with the MATLAB program. The result shows that the element-redundancy of plane beam-composed structures ranges from 0 to 3; with the increase of the element stiffness, the element- redundancy decreases ; the redundancy of structures decreases when some rigid joints become hinged joints, indicating that the element-redundancy is an effective parameter to evaluate the structural behavior, such as the geometry, stiffness distribution and constraint conditions.