基于增强型整体-局部高阶理论,构造了四节点四边形单元并分析复合材料自由边拉伸问题。本理论预先满足层合板面内位移和层间应力连续条件及层合板上下自由表面条件,未知变量个数不依赖于层合板的层数。精化四节点四边形单元满足单元间C1弱连续性条件。数值结果表明,基于增强型整体-局部高阶理论构造的四边形单元能够精确分析自由边拉伸问题。层间横向剪切应力能够直接从本构方程中计算得出,而横向法应力则需在一个单元内使用局部三维平衡方程。
Based on the enhanced global-local higher-order theory,a quadrilateral element is proposed to study the free-edge effect problems of laminates.The theory satisfies the continuity condition of displacements and interlaminar stresses as well as free shear traction conditions on the top and the bottom surfaces.In addition,the number of unknown variables in the present model is independent of the number of layers in laminates.The refined four-node quadrilateral element satisfies the requirement of C1 weak-continuity conditions at adjacent elements.Numerical results show that the proposed quadrilateral element based on the enhanced global-local higher-order theory is accurate enough for solving the extension problems of the free-edge in composite laminates.Transverse shear stresses can be computed directly from the constitutive equations without any postprocessing.In order to obtain transverse normal stresses,the local equilibrium equation approach within one element has to be employed.
[1]R L Foye,D J Baker.Design of orthotropic laminates[A].11th Annual AIAA Conf on Structures,Structural Dynamics and Materials[D].Denver CO,1970.
[2]高洪芬,高建中.复合材料层合结构自由边效应实验研究[J].玻璃钢/复合材料,2005(3):3-5.
[3]Wang A S D,Crossman F W.Some new results on edge effect in symmetric composite laminates[J].Compos.Mater,1977(11):92-106.
[4]Spilker R L,Chou S C.Edge effects in symmetric composite laminates:importance of satisfying the traction free-edge condition[J].Compos.Mater,1980(14):2-20.
[5]Gaudenzi P,Mannini A,Carbonaro R.Multi-layer higher-order finite elements for the analysis of free-edges stresses in composite laminates.Int[J].Numer.Methods Eng,1998(41):851-873.
[6]Becker W.Closed-form solution for the free-edge effect in cross-ply laminates.Compos.Struct.,1993(26):39-45.
[7]Tahani M,Nosier A.Free edge stresses analysis of general cross-ply composite laminates under extension and thermal loading[J].Compos.Struct,2003(60):91-103.
[8]姚伟岸,聂臆瞩,肖峰.基于辛对偶体系的层合板自由边效应的分析解[J].应用数学和力学,2011,32(9):1021-1029.
[9]S H Lo,Wu Zhen,Y K Cheung,et al.An enhanced global-local higher-order theory for the free edge effect in laminates[J].Composite and Structures,2007(81):499-510.
[10]Li X Y,Liu D.Generalized laminate theories based on double superposition hypothesis,Int.J.Numer.Methods Eng.,1997(40):1197-1212.
[11]R.Esquej,L Castejon,M Lizaranzu,et al.A new finite element approach applied to the free edge effect on composite materials[J].Composite Structures,2013(98):121-129.
[12]陈万吉.精化直接刚度法与不协调模式[J].计算结构力学及其应用,1995,12(2):127-132.
[13]Wu Zhen,Chen Ronggeng,Chen Wanji.Refined laminated composite plate element based on global-local higher-order shear deformation theory[J].Composite Structures,2005(70):135-152.
