利用网壳结构的整体受力以及平面内刚度较大的特点，提出基于曲面插值的未测节点位置推算方法.通过对节点偏差的统计分析来判断结构的变形程度；基于回归分析理论，采用回归方程推算节点位置的水平坐标；基于数值计算理论，由已测量节点插值计算网壳曲面，进而推算出未测节点位置的竖向坐标；同时，采用实际网壳结构对基于曲面插值的未测节点位置推算方法进行验证.结果表明，基于曲面插值的未测节点位置推算方法比传统方法的计算结果更符合实际.
A new method was proposed to reckon the nodal positions of an existing grid shell structure using surface interpolation, based on the structural characteristics of the high in-plane stiffness and overall capacity of load bearing. In the proposed method, the degree of structural deformation is estimated firstly by statistical analysis of nodal deviations. Then horizontal nodal coordinates are calculated by regression equations from statistic regression analysis theory. Lastly, vertical nodal coordinates can be determined by the structural shape and interpolation from the measured nodal positions according to surface interpolation theory. By applying the proposed method to the practical grid shell structures, it was concluded that the method can give realistic results and is effective for the assessment of existing structures.
［1］中华人民共和国住房和城乡建设部. 高耸与复杂钢结构检测与鉴定标准: GB 51008—2016 ［S］. 北京: 中国计划出版社, 2016.
Ministry of Housing and Urban-Rural Construction of the People’s Republic of China. Technical standard for inspection and appraisal of high-rising and complex steel structures: GB 51008—2016［S］. Beijing: China Planning Press, 2016.
［2］罗永峰. 国家标准《高耸与复杂钢结构检测与鉴定技术标准》编制简介［J］. 钢结构, 2014, 29(4): 44-49.
LUO Yongfeng. Brief introduction of composition of technical standard for inspection and appraisal of high-rising and complex steel structures［J］. Steel Construction, 2014, 29(4): 44-49.
［3］ISO Technical Committee. Bases for design of structures—Assessment of existing structures: ISO 13822—2010 ［S］. Geneva: International Organization for Standardization, 2010.
［4］BULENDA T, KNIPPERS J. Stability of grid shells［J］. Computers & Structures, 2001, 79(12): 1161-1174.
［5］刘慧娟, 罗永峰, 杨绿峰, 等. 单层网壳结构稳定性分析的随机缺陷模态迭加法［J］. 同济大学学报(自然科学版), 2012, 40(9): 1294-1299.
LIU Huijun, LUO Yongfeng, YANG Lüfeng, et al. Stochastic imperfection mode superposition method for stability analysis of single-layer lattice domes［J］. Journal of Tongji University (Natural Science), 2012, 40(9): 1294-1299.
［6］BRUNO L, SASSONE M, VENUTI F. Effects of the equivalent geometric nodal imperfections on the stability of single layer grid shells［J］. Engineering Structures, 2016, 112: 184-199.
［7］LIU H J, ZHANG W, YUAN H. Structural stability analysis of single-layer reticulated shells with stochastic imperfections［J］. Engineering Structures, 2016, 124: 473-479.
［8］罗立胜, 罗永峰, 郭小农. 考虑节点几何位置偏差的既有网壳结构稳定计算方法［J］. 湖南大学学报(自然科学版), 2013, 40(3): 26-30.
LUO Lisheng, LUO Yongfeng, GUO Xiaonong. Overall stability of existing reticulated shells consi-dering the effect of geometric position deviation of joints［J］. Journal of Hunan University (Natural Science), 2013, 40(3): 26-30.
［9］罗永峰, 刘俊. 既有空间结构位形推算的随机偏差方法［J］. 同济大学学报(自然科学版), 2017, 45(6): 791-798.
LUO Yongfeng, LIU Jun. Stochastic deviation method of calculating nodal positions of existing spatial structures［J］. Journal of Tongji University (Natural Science), 2017, 45(6): 791-798.
［10］CHEN G B, ZHANG H, RASMUSSEN K J R, et al. Modeling geometric imperfections for reticulated shell structures using random field theory［J］. Engineering Structures, 2016, 126: 481-489.
［11］陈希孺. 高等数理统计学［M］. 合肥: 中国科学技术大学出版社, 2009.
CHEN Xiru. Advanced mathematical statistics［M］. Hefei: Press of University of Science and Technology of China, 2009.
［12］赖金涛, 傅建中, 沈洪垚, 等. 基于NURBS曲面敏感点的曲面检测测点优化［J］. 浙江大学学报(工学版), 2015, 49(7): 1201-1207.
LAI Jintao, FU Jianzhong, SHEN Hongyao, et al. Measuring points optimization in machining error inspection based on reconstruction of NURBS control points driven by sensitive points［J］. Journal of Zhejiang University (Engineering Science), 2015, 49(7): 1201-1207.
［13］RAVARI A N, TAGHIRAD H D. Reconstruction of B-spline curves and surfaces by adaptive group testing［J］. Computer-Aided Design, 2016, 74: 32-44.
［14］LANCASTER P, SALKAUSKAS K. Curve and surface fitting: An introduction［M］. London: Academic Press, 1986.
［15］CONKLIN J D. Applied logistic regression［J］. Technometrics, 2012, 34(3): 358-359.
