基于扩展逐层法的复合材料层合板的自由振动
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摘要
扩展逐层法结合逐层理论和扩展有限元方法的优点,能同时分析含多层分层和基体裂纹损伤复合材料层合结构的问题。将扩展逐层法应用于复合材料层合板的动态分析,研究含损伤的复合材料层合板的自由振动。在数值算例中,首先研究了扩展逐层法自由振动的收敛性,然后将结果和相关文献及三维实体元结果分别对比,证明扩展逐层法分析有/无基体裂纹的复合材料层合板自由振动问题的正确性;研究了正交各向异性程度、铺层数量、横向裂纹长度在自由振动问题中的影响。
XLWM combines the advantages of layerwise method and XFEM, which is capable to analyze composite laminated structure problems with multiple delamination and matrix crack. XLWM is applied to the dynamic analysis of laminated composite plates to investigate the free vibration of isotropic and laminated composite plates with damage. Free vibration convergence rate of XLWM is investigated through numerical examples,comparing the numerical results with those of previous researches and 3D elastic model, proving the validity of XLMW in composite laminates free vibration analyses with/without matrix crack. In addition, the effects of orthotropy degree, number of layers and crack length on free vibration are investigated.
XLWM combines the advantages of layerwise method and XFEM, which is capable to analyze composite laminated structure problems with multiple delamination and matrix crack. XLWM is applied to the dynamic analysis of laminated composite plates to investigate the free vibration of isotropic and laminated composite plates with damage. Free vibration convergence rate of XLWM is investigated through numerical examples,comparing the numerical results with those of previous researches and 3D elastic model, proving the validity of XLMW in composite laminates free vibration analyses with/without matrix crack. In addition, the effects of orthotropy degree, number of layers and crack length on free vibration are investigated.
引文
[1]REDDY J N.Free vibration of antisymmetric,angle-ply laminated plates including transverse shear deformation by the finite element method[J].Journal of Sound&Vibration,1979,66(4):565-576.
[2]REDDY J N.On the solutions to forced motions of rectangular composite plates[J].Journal of Applied Mechanics,1982,49(2):403-408.
[3]REDDY J N,KUPPUSAMY T.Natural vibrations of laminated anisotropic plates[J].Journal of Sound&Vibration,1984,94(1):63-69.
[4]王云洲,王远功.用高阶位移模式分析复合材料层合板的自由振动[J].上海力学,1994(4):49-57.
[5]胡明勇,王安稳.纤维增强粘弹性复合材料层合板的自由振动和应力分析[J].工程力学,2010,27(8):10-14,20.
[6]NOOR A K.Free vibrations of multilayered composite plates[J].AIAAJournal,1973,11(7):1038-1039.
[7]BERT C W,CHEN T L C.Effect of shear deformation on vibration of antisymmetric angle-ply laminated rectangular plates[J].International Journal of Solids&Structures,1978,14(6):465-473.
[8]OWEN D R J,LI Z H.A refined analysis of laminated plates by finite element displacement methods:II.Vibration and stability[J].Computers&Structures,1987,26(6):915-923.
[9]GHOSH A K,DEY S S.Free vibration of laminated composite plates:a simple finite element based on higher order theory[J].Computers&Structures,1994,52(3):397-404.
[10]KURTARAN H.Geometrically nonlinear transient analysis of moderately thick laminated composite shallow shells with generalized differential quadrature method[J].Composite Structures,2015,125(22):605-614.
[11]ZHENG DINGYANG,KESSISSOGLOU N J.Free vibration analysis of a cracked beam by finite element method[J].Journal of Sound&Vibration,2004,273(3):457-475.
[12]KISA M,GUREL M A.Free vibration analysis of uniform and stepped cracked beams with circular cross sections[J].International Journal of Engineering Science,2007,45(2-8):364-380.
[13]MOGAL S P.Vibration Analysis of Cracked Beam[G].Rourkela:Department of Mechanical Engineering National Insistute of Technology,2009.
[14]LIU JING,SHAO YIMIN,ZHU WEIDONG.Free vibration analysis of a cantilever beam with a slant edge crack[J].Archive Proceedings of the Institution of Mechanical Engineers,Part C:Journal of Mechanical Engineering Science,2016:0954406216631006.
[15]LI DINGHE,LIU YAN,ZHANG XIONG.An extended layerwise method for composite laminated beams with multiple delaminations and matrix cracks[J].International Journal for Numerical Methods in Engineering,2015,101(6):407-434.
[16]LI DINGHE.Delamination and transverse crack growth prediction for laminated composite plates and shells[J].Computers&Structures,2016,177:39-55.
[17]LI DINGHE,ZHANG XIONG,SZE K Y,et al.Extended layerwise method for laminated composite plates with multiple delaminations and transverse cracks[J].Computational Mechanics,2016,58(4):657-679.
[18]DUPONT H L.Extended layerwise method of laminated composite shells[J].Composite Structures,2016,136(3):313-344.
[19]LI DINGHE.Three-dimensional analysis of transverse crack fiber bridging in laminated composite plates[J].Composite Structures,2017,164:277-290.
[2]REDDY J N.On the solutions to forced motions of rectangular composite plates[J].Journal of Applied Mechanics,1982,49(2):403-408.
[3]REDDY J N,KUPPUSAMY T.Natural vibrations of laminated anisotropic plates[J].Journal of Sound&Vibration,1984,94(1):63-69.
[4]王云洲,王远功.用高阶位移模式分析复合材料层合板的自由振动[J].上海力学,1994(4):49-57.
[5]胡明勇,王安稳.纤维增强粘弹性复合材料层合板的自由振动和应力分析[J].工程力学,2010,27(8):10-14,20.
[6]NOOR A K.Free vibrations of multilayered composite plates[J].AIAAJournal,1973,11(7):1038-1039.
[7]BERT C W,CHEN T L C.Effect of shear deformation on vibration of antisymmetric angle-ply laminated rectangular plates[J].International Journal of Solids&Structures,1978,14(6):465-473.
[8]OWEN D R J,LI Z H.A refined analysis of laminated plates by finite element displacement methods:II.Vibration and stability[J].Computers&Structures,1987,26(6):915-923.
[9]GHOSH A K,DEY S S.Free vibration of laminated composite plates:a simple finite element based on higher order theory[J].Computers&Structures,1994,52(3):397-404.
[10]KURTARAN H.Geometrically nonlinear transient analysis of moderately thick laminated composite shallow shells with generalized differential quadrature method[J].Composite Structures,2015,125(22):605-614.
[11]ZHENG DINGYANG,KESSISSOGLOU N J.Free vibration analysis of a cracked beam by finite element method[J].Journal of Sound&Vibration,2004,273(3):457-475.
[12]KISA M,GUREL M A.Free vibration analysis of uniform and stepped cracked beams with circular cross sections[J].International Journal of Engineering Science,2007,45(2-8):364-380.
[13]MOGAL S P.Vibration Analysis of Cracked Beam[G].Rourkela:Department of Mechanical Engineering National Insistute of Technology,2009.
[14]LIU JING,SHAO YIMIN,ZHU WEIDONG.Free vibration analysis of a cantilever beam with a slant edge crack[J].Archive Proceedings of the Institution of Mechanical Engineers,Part C:Journal of Mechanical Engineering Science,2016:0954406216631006.
[15]LI DINGHE,LIU YAN,ZHANG XIONG.An extended layerwise method for composite laminated beams with multiple delaminations and matrix cracks[J].International Journal for Numerical Methods in Engineering,2015,101(6):407-434.
[16]LI DINGHE.Delamination and transverse crack growth prediction for laminated composite plates and shells[J].Computers&Structures,2016,177:39-55.
[17]LI DINGHE,ZHANG XIONG,SZE K Y,et al.Extended layerwise method for laminated composite plates with multiple delaminations and transverse cracks[J].Computational Mechanics,2016,58(4):657-679.
[18]DUPONT H L.Extended layerwise method of laminated composite shells[J].Composite Structures,2016,136(3):313-344.
[19]LI DINGHE.Three-dimensional analysis of transverse crack fiber bridging in laminated composite plates[J].Composite Structures,2017,164:277-290.