基于新型锯齿理论复合材料层合梁弯曲分析  

Bending Analysis of Composite Laminated Beams Based on a New Zigzag Theory

作　　者：司俊岭[1] Si Junling(College of Engineering,Heilongjiang Bayi Agriculture University,Daqing163319)

机构地区：[1]黑龙江八一农垦大学工程学院,大庆163319

出　　处：《黑龙江八一农垦大学学报》2025年第1期119-126,共8页journal of heilongjiang bayi agricultural university

基　　金：碳纤维增强型复合材料多层结构高性能锯齿理论研究(黑龙江八一农垦大学三纵三横项目:ZRCPY202303)。

摘　　要：首先发展了一种新型的复合材料层合结构锯齿理论,能够较为真实的反映出层合结构的局部特性,即面内位移场沿着层合结构的厚度方向呈现锯齿形分布。该理论与层合梁的整体理论相结合,建立复合材料层合梁初始位移场模型,然后通过层合梁表面剪切应力为零及层间剪切应力连续条件,用整体位移未知变量表示出局部位移未知变量,得到复合材料层合梁最终位移场模型。最后,利用该模型对施加横向分布载荷层合梁进行弯曲分析,通过与精确解数值对比发现,模型能够准确计算复合材料层合梁的力学行为,特别是对层间剪切应力的计算,可以直接从本构方程准确给出有利于该模型在有限元方法中的应用。A new zigzag theory of composite laminated structures was developed firstly.The theory was able to really respond local characteristic of laminated structures,and it was that in-plane displacement field distributed zigzag shape through the thickness of laminated structures.By combining the theory with the global theory of laminated beams,the initial displacement field model could be built.And then the local displacement unknown variables were expressed in terms of the global displacement unknown variables through using the free surface and inter-laminar transverse stress continuity conditions,and the final displacement field model could be obtained.Finally,we introduced a simple-supported laminated beams under transverse distribution force to analyze bending problem of laminated beams.Compared with the exact solutions,the model could give accurate mechanical responds of composite laminated beams.Especially the exact transverse shear stresses were able to obtained from constitutive relations directly,which was benefit for practical applications in the finite element method.

关 键 词：层合梁 锯齿理论 层间连续 形函数 

分 类 号：O343[理学—固体力学]