摘要
将梁中裂纹等效为无质量线性扭转弹簧,研究了温克勒(Winkler)基础上具有任意开裂纹数目Timoshenko梁的弯曲变形.利用Delta广义函数和Heaviside函数以及Laplace变换,给出了Winkler基础上具有任意裂纹数目Timoshenko梁弯曲变形的解析通解.在此基础上,研究了Winkler基础上受均布荷载作用简支裂纹Timoshenko梁的弯曲变形,数值分析了裂纹数目和位置以及深度、梁剪切刚度和基础反力系数等对裂纹Timoshenko梁弯曲变形的影响.结果表明:在裂纹处,梁挠度存在尖点,转角存在跳跃;梁挠度随着裂纹深度和数目的增加而增加,但横截面弯矩和转角减小;随着基础反力系数的增加,梁挠度、弯矩和转角减小;随着剪切刚度的增加,梁挠度减少,弯矩和转角增大.
Regarding the crack in a beam as a massless linear torsional spring,the bending deformation of Timoshenko beam with an arbitrary number of open cracks on Winkler foundation was studied.A general analytical solution for bending deformation of Timoshenko beam with an arbitrary number of open cracks on Winkler foundation was derived by using Delta generalized function,Heaviside function and Laplace Transform.Then,the bending deformation of a simply-supported cracked Timoshenko beam on Winkler foundation subjected to uniformly distributed loading was investigated.The influences of the number,position and depth of cracks,as well as the shear stiffness and foundation spring stiffness on bending deformation of cracked Timoshenko beam were analyzed numerially.It is shown from the numerical results that,at the crack position,there exist a cusp on the deflection curve and a jump on the rotational angle curve;With the increase of the depth and number of the cracks,the deflection increases while the bending moment and the rotational angle decrease;With the increase of the foundation spring stiffness,the deflection,the bending moment and the rotational angle decrease.Furthermore,with the increase of the shear stiffness,the deflection decreases while the bending moment and the rotational angle increase.
作者
杨骁
施文祥
郑超引
YANG Xiao;SHI Wenxiang;ZHENG Chaoyin(Shanghai Customs College,Shanghai 201204,China;School of Mechanics and Engineering Science,Shanghai University,Shanghai 200444,China)
出处
《力学季刊》
CAS
CSCD
北大核心
2022年第1期159-170,共12页
Chinese Quarterly of Mechanics
基金
上海市自然科学基金(18ZR1414500)。
