摘要
虽然关于几何非线性分析的空间梁单元研究成果较多,但这些单元均是基于几何一致性得到的单元刚度矩阵,而基于场一致性的单元研究则较少,该文基于局部坐标系(随转坐标系)下扣除结构位移中的刚体位移得到的结构变形与结构坐标系下的总位移的关系,直接利用微分方法导出两者增量位移之间的关系,再基于场一致性原则,最终获得空间梁单元在大转动、小应变条件下的几何非线性单元切线刚度矩阵,在此基础上根据带铰梁端受力特征,导出了能考虑梁端带铰的单元切线刚度矩阵表达式,利用该文的研究成果编制了程序,对多个梁端带铰和不带铰的算例进行了空间几何非线性分析,计算结果表明这种非线性单元列式的正确性,实用价值较强。
In the previous study for the geometric nonlinear analysis of a 3-D beam element, the element tangential stiffness matrix is generally acquired by the geometric consistency rather than by field consistency. In this paper, a differentiation method is directly employed to derive the relationship of the incremental displacements between the structural deformation in a local coordinate system and the total displacement in an integral coordinate system. The field consistency is then used to achieve the element tangential stiffness matrix of the 3-D beam element under the conditions of large rotation and small strain. Moreover, according to the mechanical characteristics of a hinged beam, an explicit expression of the non-linear tangent stiffness matrix is derived to consider the effect of the hinged beam. A computer program is developed to analyze the geometrical nonlinear behavior of several classic examples with and without hinges. The results demonstrate the accuracy of the proposed innovative element, and illustrate promising practical value.
出处
《工程力学》
EI
CSCD
北大核心
2013年第1期91-98,共8页
Engineering Mechanics
基金
国家自然科学基金项目(51008037)
关键词
空间梁元
铰
场一致性
几何非线性
切线刚度矩阵
3-D beam element
hinge
field consistency
geometric nonlinear
tangent stiffness matrix
