基于同伦随机有限元方法的梁结构边界约束静力模型修正  

Boundary constraint static model modification of beam structure based on homotopy stochastic finite element method

作　　者：胡建伟 祁灿 朱礼平 吴志峰[4,5] 黄斌 陈学龙[1,4] HU Jianwei;QI Can;ZHU Liping;WU Zhifeng;HUANG Bin;CHEN Xuelong(WSGRI Engineering&Surveying Incorporation Limited,Wuhan 430080,China;China Gezhouba Group Corporation of Power Company,Yichang 443002,China;WISDRI Wuhan Architecture Design Co.,Ltd.,Wuhan 430000,China;School of Civil Engineering and Architecture,Wuhan University of Technology,Wuhan 430070,China;School of Civil and Hydraulic Engineering,Huazhong University of Science and Technology,Wuhan 430074,China)

机构地区：[1]中冶武勘工程技术有限公司,武汉430080 [2]中国葛洲坝集团电力有限责任公司,宜昌443002 [3]中冶南方武汉建筑设计有限公司,武汉430000 [4]武汉理工大学土木工程与建筑学院,武汉430070 [5]华中科技大学土木与水利工程学院,武汉430074

出　　处：《机械强度》2025年第2期138-146,共9页Journal of Mechanical Strength

基　　金：国家自然科学基金(51978545)。

摘　　要：考虑到结构边界条件的不确定性,基于同伦随机有限元方法,提出了一种梁结构边界约束静力模型修正方法。基于不确定的静力测量数据,实现了梁身单元与边界单元的整体修正。静力凝聚方法能够保证计算自由度与测量自由度相匹配。正则化方法可以减少随机模型修正方程病态解的问题。概率残差最小化法实现同伦系数的最优选择,保证了边界约束的精确识别和整体修正的精度。最后,通过变截面混凝土梁数值算例和铝合金梁的静力加载试验,验证了该方法的有效性。Considering the uncertainty associated with structural boundary conditions,a method for modifying the boundary constraint static model of beam structures was proposed based on the homotopy stochastic finite element method.The overall modification of both the beam body elements and boundary elements was achieved using uncertain static measurement data.By employing the static condensation method,computational degrees of freedom were ensured to match measured degrees of freedom.Regularization methods were applied to mitigate ill-conditioned solutions in modification equations for stochastic models.The probabilistic residual minimization method enables optimal selection of homotopy coefficients,ensured accurate identification of boundary constraints and precise overall modification.Finally,simulations on variable-section concrete beams and static loading tests on aluminum alloy beams were conducted to verify the effectiveness of this approach.

关 键 词：同伦随机有限元 边界约束 模型修正 静力测量误差 静力凝聚 

分 类 号：TH114[机械工程—机械设计及理论]