Winkler地基上连续裂纹梁的弯曲解析解

doi:10.12066/j.issn.1007-2861.2495

摘要/Abstract

摘要： 解除连续裂纹梁的内部支座约束,代之以未知约束反力,将连续裂纹梁转化为带未知反力的单跨裂纹梁,基于梁中横向贯穿开裂纹的等效线性扭转弹簧模型,采用Laplace变换及其逆变换,得到了Winkler基础上具有任意开裂纹数目连续裂纹Euler-Bernoulli梁弯曲挠度的解析通解.在利用Abaqus有限元软件验证解析解正确性的基础上,数值分析了地基反力系数、裂纹深度、位置及梁长高比等参数对连续裂纹梁弯曲变形的影响.研究结果表明:随着地基反力系数的增大,Winkler地基上连续裂纹梁的挠度减小;随着裂纹深度的增大,裂纹处的梁挠度尖点和截面转角跳跃明显,挠度增幅显著;裂纹位置、深度及数目对Winkler地基裂纹连续梁的弯曲影响较大;当地基反力较大时,裂纹对地基连续梁弯曲变形的影响逐渐减弱.这些成果对工程设计和结构健康检测具有一定指导意义.

关键词: Winkler基础, 连续裂纹Euler-Bernoulli梁, 广义函数, 解析解, 参数研究

Abstract: Removing constraints of internal supports of continuous cracked beam and instead of them with unknown reaction forces, the continuous cracked beam was simplified as a single span with unknown reaction forces. Based on the linear torsional spring model of transverse crack in beam, the general analytical solution of continuous Euler-Bernoulli beam with arbitrary number of open cracks on Winkler foundation was presented by Laplace transform and its inverse transformation. On the basis of verifying the correctness of the analytical solution using Abaqus finite element software, the influences of the foundation reaction coefficient, crack depth and location as well as beam length-height ratio on the bending deformation of continuous cracked beam were analyzed numerically. It is revealed that the deflection of the continuous cracked beam on Winkler foundation decreases with the foundation reaction coefficient increase. And the deflection cusp and rotation angle jump of beam at the crack location become more remarkable with increase of the crack depth; The influences of location, depth and numbers of the crack on the bending of cracked beam on Winkler foundation are remarkable. Furthermore, when the foundation reaction coefficient is larger, the influence of the crack on bending deformation of continuous beam on Winkler foundation diminishes gradually. These conclusions can provide certain guiding significance for structure design and structural health detection and monitoring.

Key words: Winkler foundation, continuous cracked Euler-Bernoulli beam, generalized function, analytical solution, parameter study

中图分类号:

TU223
TU317

杨骁, 刘昕, 冷蓉. Winkler地基上连续裂纹梁的弯曲解析解[J]. 上海大学学报(自然科学版), 2025, 31(6): 1023-1034.

YANG Xiao, LIU Xin, LENG Rong. Analytical solution of bending of the continuous cracked beam on winkler foundation[J]. Journal of Shanghai University（Natural Science Edition）, 2025, 31(6): 1023-1034.

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