西安建筑科技大学学报(自然科学版)

本文开展了集中荷载作用下FRP圆弧拱的面内弹性失稳理论研究,基于能量变分原理建立了拱的非线性平衡方程,提出了FRP拱修正长细比计算公式,推导了拱失稳临界荷载解析解.通过有限元数值解验证了理论公式的正确性,着重分析了铺层角度、铺层厚度及矢跨比等设计参数对FRP拱失稳临界荷载的影响.研究结果表明,铺层方向显著影响拱的失稳临界荷载; 对于单种角度铺层的截面,保证铺层总厚度不变条件下,仅增加铺层数量并不会引起失稳临界荷载量值的变化; 拱矢跨比在1/10～1/3范围内变化时,失稳临界荷载随着矢跨比的增大而增大,且随着矢跨比的增加,增长速率逐渐下降.

This paper presents an analytical investigation of the in-plane elastic buckling of FRP arches subjected to a central concentrated load. The nonlinear buckling equilibrium equation is established based on energy variation principle. A new slenderness ratio formula is further proposed and the theoretical buckling load of FRP circular shallow fixed arch is derived. consequently. Numerical simulation and additional experiment are implemented to verify the accuracy of the analytical solutions derived in this context. A parametric study is then conducted to analyze the effect of ply orientation, laminated thickness, and the rise-span ratio on in-plane bucking critical load for laminated fixed circular shallow arch. It is found that the pavement condition significantly impact the buckling critical load. Increasing the number of layer only will not change the value of the critical load, with the thickness of laminated arch being constant. When the rise-span ratio varies from 1/10 to 1/3, the critical load of instability increases with the increase of span ratio, whereas the growth rate decreases with the increase of span ratio.

引言
1 新解析推导
2 数值验证
3 结语

图1 FRP拱结构的工程应用<br/>Fig.1 Engineeringapplication of FRP arch structure

图1 FRP拱结构的工程应用
Fig.1 Engineeringapplication of FRP arch structure

图2 纤维复合材料拱的力学简图(注意边界)<br/>Fig.2 FRP fixed circular arch subjected to a central concentrated load

图2 纤维复合材料拱的力学简图(注意边界)
Fig.2 FRP fixed circular arch subjected to a central concentrated load

图3 FRP圆弧拱有限元模型<br/>Fig.3 FE Model of FRP arches

图3 FRP圆弧拱有限元模型
Fig.3 FE Model of FRP arches

表1 T300B/WP2300型纤维复合材料特性表<br/>Tab.1 Material properties of the laminates

表1 T300B/WP2300型纤维复合材料特性表
Tab.1 Material properties of the laminates

图4 有限元与理论对比图<br/>Fig.4 Comparison of FE and theoretical result

图4 有限元与理论对比图
Fig.4 Comparison of FE and theoretical result

图5 铺层角度、铺层厚度及矢跨比对失稳临界荷载的影响<br/>Fig.5 The effects of ply-orientation, ply-thickness, and rise-span ratios on the buckling load of FRP arch

图5 铺层角度、铺层厚度及矢跨比对失稳临界荷载的影响
Fig.5 The effects of ply-orientation, ply-thickness, and rise-span ratios on the buckling load of FRP arch

表2 铺层数量对失稳临界荷载的影响<br/>Tab.2 The effects of layers on the buckling load

表2 铺层数量对失稳临界荷载的影响
Tab.2 The effects of layers on the buckling load

[1] MYERS G J. Composite structure design[M]. New jersey, USA:John Wiley & Sons, Inc., 1978.4.
[2] SOBRINO J A, PULIDO M. Towards advanced composite material footbridges[J]. Structural Engineering International, 2002, 12(2): 84-86.
[3] LUKASZ Pyrzowski, MISKIEWICZ M. Modern GFRP composite footbridges[C]// Environmental Engineering. 10th International Conference, Wilno: Vilnius Gediminas Technical University, 2017.
[4] USHAKOV A, KLENIN Y, OZEROV S. Development of modular arched bridge design[C]// Proceedings of 5th Inter national Engineering and Construction Conference(IECC 5). USA: CA, Irvine, 2008: 95-101.
[5] 叶列平, 冯鹏. FRP在工程结构中的应用与发展[J]. 土木工程学报, 2006, 39(3):24-36.
[6] 冯鹏. 复合材料在土木工程中的发展与应用[J]. 玻璃钢/复合材料, 2014(9):99-104.
[7] 冯鹏, 叶列平, 金飞飞,等. FRP桥梁结构的受力性能与设计方法[J]. 玻璃钢/复合材料, 2011(5):12-19.
[8] LUU A T, KIM N I, LEE J. Bending and buckling of general laminated curved beams using NURBS-based isogeometric analysis[J]. European Journal of Mechanics-A/Solids, 2015, 54: 218-231.
[9] FRATERNALI F, SPADEA S, ASCIONE L. Buckling behavior of curved composite beams with different elastic response in tension and compression[J]. Composite Structures, 2013, 100: 280-289.
[10]SONAWANE M. Buckling analysis of singly curved shallow bilayered arch under concentrated loading[D]. State of Texas: Texas A & M University,2010.
[11]KIM D, Chaudhuri R A. Postbuckling behavior of symmetrically laminated thin shallow circular arches[J]. Composite Structures, 2009, 87(1): 101-108.
[12]LIU A, BRADFORD M A, PI Y L. In-plane nonlinear multiple equilibria and switches of equilibria of pinned-fixed arches under an arbitrary radial concentrated load[J]. Archive of Applied Mechanics, 2017, 87(11): 1909-1928.
[13]PI Y L, BRADFORD M A, LIU A. Nonlinear equilibrium and buckling of fixed shallow arches subjected to an arbitrary radial concentrated load[J]. International Journal of Structural Stability & Dynamics, 2017, 17(8):1750082.
[14]LIU A, YANG Z, LU H, et al. Experimental and analytical investigation on the in-plane dynamic instability of arches owing to parametric resonance[J]. Journal of Vibration & Control, 2017(1):107754631772621.
[15]LIU A, LU H, PI Y L, et al. Out-of-plane parametric resonance of arches under an in-Plane central Harmonic load[J]. Singapor and Hangzhou: Sprirger Nature Singapore Pte.Ltd and Zhejiang University Press,2018.
[16]LIU A, LU H, PI Y L, et al. Out-of-Plane Parametric Resonance of Arches Under an In-Plane Central Harmonic Load[M]//Environmental Vibrations and Transportation Geodynamics. Singapore:Springer 2018:45-51.
[17]LIU A, LU H, FU J, et al. Lateral-torsional buckling of fixed circular arches having a thin-walled section under a central concentrated load[J]. Thin-Walled Structures, 2017, 118:46-55.
[18]LIU A, LU H, FU J, et al. Lateral torsional buckling of circular steel arches under arbitrary radial concentrated load[J]. Journal of Structural Engineering, 2017, 143(9):1-13.
[19]DENG J, LIU A, HUANG P, et al. Interfacial mechanical behaviors of RC beams strengthened with FRP[J]. Structural Engineering & Mechanics, 2016, 58(3):577-596.
[20]刘爱荣, 李晶, 黄永辉. 拱的静动力稳定性研究进展[J]. 广州大学学报(自然科学版), 2016, 15(5):1-12.
[21]HUANG Y, YANG Z, LIU A, et al. Nonlinear buckling analysis of functionally graded graphene reinforced composite shallow arches with elastic rotational constraints under uniform radial load[J]. Materials, 2018, 11(6): 910.
[22]Gibson R F. Principles of Composite Material Mechanics[M]. 4th ed. Boca Raton USA: CRC Press, Taylor and Francis, 2011.

备注

引言

1 新解析推导

2 数值验证

3 结语

期刊信息