弹性膜结构几何非线性分析的刚体准则法

THE RIGID BODY RULE FOR THE NONLINEAR ANALYSIS OF MEMBRANE STRUCTURES

提出了一种新型弹性空间膜结构几何非线性分析方法。根据刚体准则的思想,初始受力平衡的单元在经历刚体位移后,其单元结点力方向随单元发生转动而大小不变,单元仍保持平衡。建立了新型三角形空间膜单元,该膜单元由三根空间杆件组成铰接三角形,并在中间张拉薄膜而成,杆件的材料与薄膜相同。所建立的空间膜单元的整体位形由杆单元空间铰接三角形确定,而膜单元的有限弹性变形由内部张拉的薄膜变形确定。由满足刚体准则的杆单元几何刚度矩阵推导了空间膜单元的几何刚度矩阵。根据刚体准则思想,认为膜单元在变形过程中,其刚体位移对其整体变形的贡献较大,而单元的弹性变形贡献较小。采用更新的拉格朗日格式的增量迭代法,在分析的每个阶段充分考虑刚体转动效应,利用小变形线性化理论处理自然变形的剩余效应。该方法几何刚度矩阵推导简单,无需引入对单元大变形的人为假定,可容易地退化为平面膜单元,增量迭代计算过程充分考虑刚体准则,对若干典型空间膜结构算例的分析及与已有方法的比较,验证了所建单元与方法的准确性以及计算效率。

A new geometric non-linear analysis method for elastic space membrane structures is proposed.According to the rigid body rule,when an initial stressed element undergoes rigid body displacement,the directions of the nodal forces at the element will change with the rigid rotation of the element while the magnitude of the nodal forces will remain unchanged in order to keep the element in balance.A new triangular space membrane element is presented.This membrane element is composed of three bars to form a pin-joint triangle with a triangle film stretched inside.The material of the bars is assumed the same as that of the film.The geometric stiffness matrix of the proposed membrane element is derived by the geometric stiffness matrix of a spatial bar element of rigid body rule qualified.According to the rigid body rule,it is considered that the rigid body motion has the major contribution to the total deformation of the membrane element than that of the element elastic deformation.By rooting the rigid body rule into the UL incremental-iteration method,the effect of rigid body rotation is fully considered in each stage of analysis and the residual effects of natural deformation is treated by the linearization.The derivation of the geometric stiffness matrix of the proposed membrane element is quite clear without introducing any assumption on the large deformation of the membrane element and can be easily degenerated into a plane membrane element.The accuracy and efficiency of the present membrane element as well as the rigid-body-rule-rooted nonlinear analysis method are proved by the analysis of several typical space membrane structures and by the comparison with the results of other methods.