基于共旋坐标法的几何非线性裂纹梁单元  

Geometric Non-linearity of Cracked Beam Element Based on Co-rotational Procedure

作　　者：董正方[1] 吴名豪 王淼 李运华[1] DONG Zheng-fang;WU Ming-hao;WANG Miao;LI Yun-hua(School of Civil Engineering and Architecture,Henan University,Kaifeng 475004,China;Shanghai Municipal Engineering Design Institute(Group)Co.,Ltd.,Shanghai 200092,China)

机构地区：[1]河南大学建筑工程学院,开封475004 [2]上海市政工程设计研究总院(集团)有限公司,上海200092

出　　处：《科学技术与工程》2024年第28期11979-11990,共12页Science Technology and Engineering

基　　金：河南省自然科学基金(242300421433);中国博士后科学基金资助项目(2024M750780)。

摘　　要：现有有限元软件模拟裂纹结构主要采用指派裂纹的实体和壳单元,但缺少梁单元。因此,在弹性梁单元的曲率函数中引入Dirac-δ函数表征局部损伤的曲率变化,得到位移分布函数;推导出应变矩阵和单元刚度矩阵,提出了裂纹梁单元。基于共旋坐标法理论进一步发展了考虑裂纹损伤的几何非线性裂纹梁单元,给出了单元的具体算法及流程。利用课题组开发的有限元求解框架,在程序中实现了裂纹梁单元及共旋列式裂纹梁单元。经过典型算例,对比分析了裂纹位置、裂纹深度及外荷载对裂纹梁弯曲性能的影响。结果表明:该单元能够准确描述裂纹结构的挠度变化,同时与现有模拟裂纹结构弯曲变形的单元相比,提出的裂纹梁和共旋列式裂纹梁在精度分别提高了约1%和4%,并且能够退化成无损伤的梁单元和几何非线性梁单元。The existing finite element software mainly uses solid and shell elements of the preset crack to simulate the bending effect of the crack structure but not the beam element.Therefore,in the simplified computational model based on the Euler-Bernoulli theory,the Dirac-δfunction was introduced into the beam element’s curvature function to represent the crack,the displacement distribution function were obtained.Then,the cracked beam element was proposed by deriving the strain matrix and the element stiffness matrix.Based on the theory of co-rotational coordinate method,the geometric nonlinear crack beam element considering crack damage was further developed,and the specific algorithm and process of the element were given.Using the finite element solution framework developed by the research group,the crack beam element and the co-rotational crack beam element were realized in the program.Through typical examples,the effects of crack location,crack depth and external load on the bending performance of cracked beams were compared and analyzed.The results show that the element can accurately describe the deflection change of the crack structure.At the same time,compared with the existing elements that simulate the bending deformation of the crack structure,the accuracy of the proposed crack beam and the co-rotational crack beam is improved by about 1%and 4%respectively,and can be degraded into a non-destructive beam element and a geometric nonlinear beam element.

关 键 词：共旋坐标法 裂纹 梁单元 刚度矩阵 几何非线性 

分 类 号：O342[理学—固体力学]