纤维增强聚合物加固黏弹性Timoshenko裂纹梁的弯曲变形
|
摘要
将裂纹的缝隙效应和FRP加固作用等效为黏弹性组合弹簧,推导出Laplace变换域内FRP加固黏弹性裂纹梁的等效抗弯刚度.基于标准线性固体本构关系和Laplace变换,获得了具有任意开闭裂纹数目FRP加固黏弹性梁弯曲的解析解.数值算例说明,AFRP布可有效地削弱裂纹效应,且裂纹梁的变形与跨高比成反比例关系;受AFRP布加固作用影响,裂纹深度和荷载的改变对梁变形的影响并不明显.
Considering the effects of crack gap and strenghening with Fibre Reinforcement Polymer( FRP) as a viscoelastic combination spring,the equivalent flexural rigidity of the cracked beam bonded with FRP sheet in Laplace transformed domain is presented. By using the standard linear solid viscoelastic constitutive relation and Laplace's transformation method,the explicit analytical solutions in time domain for the bending of the viscoelastic beam with an arbitrary number of cracks and FRP sheet reinforcement are derived. By numerical examples,it is stated that FRP sheet has an weakening influence on the crack effect,and the bending solution is inversely proportional to the slender ratio; Strenghened with AFRP sheet reiforcement,the fluctuation of the crack depth and load have less influence on the cracked beam bending.
Considering the effects of crack gap and strenghening with Fibre Reinforcement Polymer( FRP) as a viscoelastic combination spring,the equivalent flexural rigidity of the cracked beam bonded with FRP sheet in Laplace transformed domain is presented. By using the standard linear solid viscoelastic constitutive relation and Laplace's transformation method,the explicit analytical solutions in time domain for the bending of the viscoelastic beam with an arbitrary number of cracks and FRP sheet reinforcement are derived. By numerical examples,it is stated that FRP sheet has an weakening influence on the crack effect,and the bending solution is inversely proportional to the slender ratio; Strenghened with AFRP sheet reiforcement,the fluctuation of the crack depth and load have less influence on the cracked beam bending.
引文
[1]CHRISTENSEN R M. Theory of viscoelasticity:An introduction[M]. 2nd Edition. New York,USA:Academic Press,1982.
[2]YAHYAEI MOAYYED M,TAHERI F. Experimental and computational investigations into creep response of AFRP reinforced timber beams[J]. Composite Structures,2011,93(2):616-628.
[3]CHEN L,PENG L,ZHANG A,et al. Transverse vibration of viscoelastic Timoshenko beam-columns[J]. Journal of Vibration and Control,2015,23(10):1572-1584.
[4]CICIRELLO A,PALMERI A. Static analysis of Euler-Bernoulli beams with multiple unilateral cracks under combined axial and transverse loads[J]. International Journal of Solids and Structures,2014,51(5):1020-1029.
[5]YANG X,HUANG J,OUYANG Y. Bending of Timoshenko beam with effect of crack gap based on equivalent spring model[J]. Applied Mathematics and Mechanics(English Edition),2016,37(4):513-528.
[6]STEVENS K K,EVAN IWANOWSKI R M. Parametric resonance of viscoelastic columns[J]. International Journal of Solids and Structures,1969,5(7):755-765.
[7]付超,杨骁.基于等效黏性弹簧的黏弹性Timoshenko裂纹梁弯曲解析解[J].力学季刊,2018,39(1):90-106.FU Chao,YANG Xiao. Analytical bending solution of viscoelastic Timoshenko cracked beam based on equivalent viscoelastic spring[J]. Chinese Quarterly of Mechanics,2018,39(1):90-106.
[8]欧阳煜,江勇,周磊.纤维增强聚合物布加固黏弹性木梁弯曲的解析解[J].上海大学学报(自然科学版),2017,23(4):609-622.OUYANG Yu,JIANG Yong,ZHOU Lei. Analytical solution of bending of viscoelastic timber beam reinforced with fibre reinforcement polymer(FRP)sheet[J]. Journal of Shanghai University(Natural Science),2017,23(4):609-622.
[9]谭英辉. FRP布加固黏弹性Timoshenko木梁弯曲变形的解析解[D].上海:上海大学,2016.TAN Yinghui. Analytical solution for bending deformation of FRP sheet-reinforced viscoelastic Timoshenko timber beam[D].Shanghai:Shanghai University,2016.
[10]CHEN T M. The hybrid Laplace transform/finite element method applied to the quasi-static and dynamic analysis of viscoelastic Timoshenko beams[J]. International Journal for Numerical Methods in Engineering,1995,38:509-522.
[2]YAHYAEI MOAYYED M,TAHERI F. Experimental and computational investigations into creep response of AFRP reinforced timber beams[J]. Composite Structures,2011,93(2):616-628.
[3]CHEN L,PENG L,ZHANG A,et al. Transverse vibration of viscoelastic Timoshenko beam-columns[J]. Journal of Vibration and Control,2015,23(10):1572-1584.
[4]CICIRELLO A,PALMERI A. Static analysis of Euler-Bernoulli beams with multiple unilateral cracks under combined axial and transverse loads[J]. International Journal of Solids and Structures,2014,51(5):1020-1029.
[5]YANG X,HUANG J,OUYANG Y. Bending of Timoshenko beam with effect of crack gap based on equivalent spring model[J]. Applied Mathematics and Mechanics(English Edition),2016,37(4):513-528.
[6]STEVENS K K,EVAN IWANOWSKI R M. Parametric resonance of viscoelastic columns[J]. International Journal of Solids and Structures,1969,5(7):755-765.
[7]付超,杨骁.基于等效黏性弹簧的黏弹性Timoshenko裂纹梁弯曲解析解[J].力学季刊,2018,39(1):90-106.FU Chao,YANG Xiao. Analytical bending solution of viscoelastic Timoshenko cracked beam based on equivalent viscoelastic spring[J]. Chinese Quarterly of Mechanics,2018,39(1):90-106.
[8]欧阳煜,江勇,周磊.纤维增强聚合物布加固黏弹性木梁弯曲的解析解[J].上海大学学报(自然科学版),2017,23(4):609-622.OUYANG Yu,JIANG Yong,ZHOU Lei. Analytical solution of bending of viscoelastic timber beam reinforced with fibre reinforcement polymer(FRP)sheet[J]. Journal of Shanghai University(Natural Science),2017,23(4):609-622.
[9]谭英辉. FRP布加固黏弹性Timoshenko木梁弯曲变形的解析解[D].上海:上海大学,2016.TAN Yinghui. Analytical solution for bending deformation of FRP sheet-reinforced viscoelastic Timoshenko timber beam[D].Shanghai:Shanghai University,2016.
[10]CHEN T M. The hybrid Laplace transform/finite element method applied to the quasi-static and dynamic analysis of viscoelastic Timoshenko beams[J]. International Journal for Numerical Methods in Engineering,1995,38:509-522.