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 引用本文: 白建涛, 王东禹, 孙鹏飞, 左文杰. 移动车辆激励的内埋膜复合材料桥梁结构动力学计算. 力学学报, 2024, 54(8): 1-12.
Bai Jiantao, Wang Dongyu, Sun Pengfei, Zuo Wenjie. Dynamic computation of composite bridge structures with membrane-embedded model excited by moving vehicle. Chinese Journal of Theoretical and Applied Mechanics, 2024, 54(8): 1-12.
 Citation: Bai Jiantao, Wang Dongyu, Sun Pengfei, Zuo Wenjie. Dynamic computation of composite bridge structures with membrane-embedded model excited by moving vehicle. Chinese Journal of Theoretical and Applied Mechanics, 2024, 54(8): 1-12.

## DYNAMIC COMPUTATION OF COMPOSITE BRIDGE STRUCTURES WITH MEMBRANE-EMBEDDED MODEL EXCITED BY MOVING VEHICLE

• 摘要: 桥梁通常由钢筋混凝土复合材料构成, 钢筋数量众多且以铺层方式埋于混凝土内部. 传统方法通常采用二维梁单元建模, 进行桥梁动力学计算, 虽然具有很高的求解效率, 但计算精度较低. 文章提出了内埋膜复合材料模型, 对钢筋混凝土桥梁结构进行均匀化建模, 建立了移动车辆激励的桥梁结构有限元求解模型, 实现了车桥耦合动力学问题计算. 将钢筋铺层结构等体积等效为膜结构, 分别对混凝土实体结构和膜结构进行有限元离散, 建立了实体单元和膜单元的内埋约束方程, 描述了钢筋和混凝土之间的相互作用关系. 给出了移动载荷的计算方法, 采用射线法识别移动载荷加载单元位置, 推导了实体桥梁与车辆模型的车桥耦合系统动力学方程, 采用HHT-α方法构造了动力学方程求解格式, 通过数值算例验证了方法的有效性. 采用内埋膜方法对桥梁复合材料结构进行精细建模, 可以获得移动车辆激励工况下精确的车辆与桥梁动力学响应, 将在桥梁动力冲击分析、桥梁损伤识别和健康监测等方面有重要应用.

Abstract: Bridges are typically composed of reinforced concrete composite, with numerous rebar embedded in the concrete in a layered manner. Traditional methods often use two-dimensional beam elements to compute bridge dynamics, which have high solving efficiency but low calculation accuracy. In this paper, the membrane-embedded composite model is proposed, the bridge is modeled uniformly, the finite element solution model of the bridge structure excited by moving vehicles is established, and the vehicle-bridge coupling dynamic problem is computed. The volume of rebar layers is equivalently represented as membrane structures. Concrete solid structures and membrane structures are discretized separately using finite elements, with embedded constraint equations established for solid and membrane elements, describing the interaction between rebar and concrete. The method for computing moving loads is provided, the position of the moving load loading element is identified by the ray method, and the dynamic equations of the coupled vehicle-bridge system for solid bridges and vehicle models are derived. The HHT-α method is employed to construct the dynamic equation solving scheme. The effectiveness of the method is validated through numerical examples. In this paper, the embedded membrane method is used to model the bridge composite structure finely, enabling accurate dynamic responses of vehicles and bridges under moving vehicle excitations. It is expected to have significant applications in bridge dynamic impact analysis, bridge damage identification, and health monitoring.

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