适用于“机构施工法”的网格结构划分策略

Strategy for partition of space frames erected by mechanism method

针对以攀达穹顶为代表的"机构施工法",提出对网格结构进行划分以形成机构的几何学策略.以结构中所有杆件伸长量的平方和作为描述结构变形程度的指标,发现该指标可以表示为位移的二次型.考虑到划分后的机构应具备从设计构型到安装面(运动趋势)产生刚体位移的能力,尝试用该二次型矩阵的特征向量来近似构造该刚体位移.理论上发现,选择特征值较小且与运动趋势方向夹角较小的特征向量来构造位移,可以使结构在变形较小的情况下向安装面运动.将运动趋势方向作为初始向量,这些特征向量可以通过求解二次型矩阵逆的里兹向量获得.从设计构型开始,强迫网格结构按所构造的位移方向小幅度运动并逼近安装面,不仅可以控制结构的变形始终处于较低的水平,而且那些相对于设计构型变形较大的区域逐步凸显并成为可实施划分的区域.通过一个立体拱架和一个空间网格结构算例,说明了以上划分策略的有效性.

A geometrical partitioning strategy was proposed to form the mechanism for space frames erected by "mechanism method",typical of Pantadome.The square sum of the elongations of all structural members was adopted as the index to describe the structural deformation and expressed as the quadratic form of nodal displacements.Considering that the partitioned mechanism must implement rigid body displacement from the design configuration to the working surface,i.e.moving trend,the eigenvectors of the quadratic matrix could be used to approximately construct the rigid body displacement.If the displacements which were constantly constructed using those eigenvectors with smaller eigenvalue as well as smaller angle to the moving trend,the structure would theoretically move towards the working surface with small deformations.Taking the direction of moving trend as the initial vector,these eigenvectors could be obtained by solving the Ritz vectors of the inverse of the quadratic matrix. From the design configuration,the space frame was forced to move towards and finally approached the working surface with the estimated displacement.The structural deformation could be generally controlled at a lower level. For the final configuration closest to the working surface,those areas distinctly deformed relative to the design configuration were identified to be the partitioning boundary of the space frame.A vaulted spatial truss and a space frame were adopted as the illustrative examples to prove the validity of the partitioning strategy.