基于多项式位移分布模式的空间圆弧曲梁单元有限元分析  

FINITE ELEMENT ANALYSIS OF SPATIAL CIRCULAR CURVED BEAM ELEMENTS BASED ON POLYNOMIAL DISPLACEMENT DISTRIBUTION PATTERNS

作　　者：李整[1] 李奥利 陈代海[1] 许世展 杨朝旭 LI Zheng;LI Aoli;CHEN Daihai;XU Shizhan;YANG Chaoxu(School of Civil Engineering,Zhengzhou University,Zhengzhou 450001,China;Henan Expressway Development Company Limited,Zhengzhou 450003,China)

机构地区：[1]郑州大学土木工程学院,郑州450001 [2]河南高速公路发展有限责任公司,郑州450003

出　　处：《力学与实践》2024年第6期1212-1220,共9页Mechanics in Engineering

基　　金：国家自然科学基金项目(51408557);中国博士后科学基金项目(2013M541995);河南省交通运输厅计划项目(2020J-2-6)资助。

摘　　要：为满足曲线梁桥有限元分析的需要,根据有限元分析理论,通过引入多项式位移分布模式构造曲梁单元的位移形函数,利用虚功原理推导局部坐标系下曲梁单元的刚度矩阵和一致质量矩阵表达式,并由曲梁单元空间坐标建立局部坐标系与整体坐标系之间的坐标转换矩阵,运用Fortran语言编制相应的有限元计算程序,对比分析3种模型的静动力性能和自振特性进行验证。研究结果表明,曲梁单元模型与实体模型的计算结果吻合较好,验证了曲梁单元刚度矩阵、质量矩阵的准确性。研究结果为后续曲线梁桥的力学性能分析提供了理论参考,可以为工程实践中的设计和评估提供有力支持。To meet the needs of finite element analysis for curved beam bridges,displacement shape functions for curved beam elements are constructed using polynomial displacement distribution patterns based on the finite element analysis theory.The stiffness matrix and consistent mass matrix expressions for the curved beam element in the local coordinate system are derived using the principle of virtual work.A coordinate transformation matrix between the local and global coordinate systems is established based on the spatial coordinates of the curved beam element.A corresponding finite element calculation program is developed using Fortran language to analyze and compare the static and dynamic performances and resonance characteristics of three models for validation.The results show that the curved beam element model matches well with the solid model's calculation results,confirming the accuracy of the curved beam element stiffness matrix and mass matrix.This study provides theoretical reference for the mechanical performance analysis of future curved beam bridges,and can provide strong support for the design and evaluation of engineering practice.

关 键 词：曲梁单元 多项式位移分布模式 单元刚度矩阵 单元质量矩阵 有限元分析 

分 类 号：O343[理学—固体力学]