新修正偶应力理论Reddy型层合板稳定分析
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摘要
基于新修正偶应力理论建立了一个Reddy型复合材料层合板稳定性模型。该理论中曲率张量不对称,而偶应力矩张量对称。Reddy型层合板模型能够满足横向剪切应力为0的自由表面条件,而且横向剪切为二次函数,避免了常剪力一阶理论需要引入的剪力修正系数。为了便于工程应用,通过虚功原理推导了只含纤维材料尺度参数正交铺设的Reddy型层合板偶应力模型的稳定性方程,并以微尺度正交铺设四边简支层合方板为例,分析了不同铺设角和轴向载荷作用时临界载荷的细观尺度效应,并且与一阶剪切变形和Kirchhoff板理论结果对比。结果表明,本文建立的新修正偶应力Reddy型层合板模型更适合分析较厚的复合材料层合板稳定性的尺度效应。
In this paper,a model of composite laminated Reddy plate is established based on the new modified couple stress theory which contains asymmetric curvature tensor and symmetry couple stress tensor for stability analysis.The model of composite laminated Reddy plate can satisfy the free surface condition.At the same time,the transverse shear stress shows a quadratic parabola distribution without the correction factor which introduced in First-Order Shear Deformation Theory.For the convenience of engineering application,the stability equation of cross-ply composite laminated Reddy plate which merely involves the material length scale parameter of fiber derived by means of the virtual work principle.Moreover,a simply supported cross-ply composited laminated simple square plate is used to analyse the scale effect with different angle-plies and axial loads and the results are compared with the results from Mindlin and Kirchhoff plate theories.Numerical results show that the present model is more appropriate for capturing scale effects in the stability analysis of thicker composite laminated plate.
In this paper,a model of composite laminated Reddy plate is established based on the new modified couple stress theory which contains asymmetric curvature tensor and symmetry couple stress tensor for stability analysis.The model of composite laminated Reddy plate can satisfy the free surface condition.At the same time,the transverse shear stress shows a quadratic parabola distribution without the correction factor which introduced in First-Order Shear Deformation Theory.For the convenience of engineering application,the stability equation of cross-ply composite laminated Reddy plate which merely involves the material length scale parameter of fiber derived by means of the virtual work principle.Moreover,a simply supported cross-ply composited laminated simple square plate is used to analyse the scale effect with different angle-plies and axial loads and the results are compared with the results from Mindlin and Kirchhoff plate theories.Numerical results show that the present model is more appropriate for capturing scale effects in the stability analysis of thicker composite laminated plate.
引文
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[9]Chen W J,Li L,Xu M.A modified couple stress model for bending analysis of composite laminated beams with first order shear deformation[J].Composite Structures,2011,93(11):2723-2732.
[10]李莉,陈万吉,郑楠.修正偶应力理论层合薄板稳定性模型及尺度效应[J].工程力学,2013,30(5):1-7.(LI Li,CHEN Wan-ji,ZHENG Nan.Model of composite laminated thin plate based on modified couple stress theory and buckling analysis of scale effects[J].Engineering Mechanics,2013,30(5):1-7.(in Chinese))
[11]Chen W J,Li X P.Size-dependent free vibration analysis of composite laminated Timoshenko beam based on new modified couple stress theory[J].Archive of Applied Mechanics,2012,83:431-444.
[12]Chen W J,Yang S Q,Li X P.A study of scale effect of composite laminated plates based on new modified couple stress theory by finite element method[J].International Journal for Multiscale Computational Engineering,2014,12(6):507-527.
[13]任晓辉,陈万吉.C0型高阶锯齿理论及复合材料厚梁热应力分析[J].计算力学学报,2015,32(1):77-82.(REN Xiao-hui,CHEN Wan-ji.Thermal stress analysis of thick composite beams based on C0-type higher-order zig-zag theory[J].Chinese Journal of Computational Mechanics,2015,32(1):77-82.(in Chinese))
[14]Koiter W T.Couple-stresses in the theory of elasticity:I and II[A].Proceedings of the Koninkliske Nederlandse Akademie van Wetenschappen[C].1964.
[15]Pagano N J.Exact solutions for rectangular bi-directional composites and sandwich plates[J].Compos Mater,1970,4:20-34.
[2]McFarland A W,Colton J S.Role of material microstructure in plate stiffness with relevance to microcantilever sensors[J].Journal of Micromechanics and Microengineering,2005,15(5):1060-1067.
[3]Kouzeli M,Mortensen A.Size dependent strengthening in particle reinforced aluminium[J].Acta Materialia,2002,50(1):39-51.
[4]Mindlin R D.Influence of couple stresses on stress concentrations[J].Experimental Mechanics,1963,3(1):1-7.
[5]Yang F,Chong A C M,Lam D C C,et al.Couple stress based strain gradient theory for elasticity[J].International Journal of Solids and Structures,2002,39(10):2731-2743.
[6]Tsiatas G C.A new Kirchhoff plate model based on a modified couple-stress theory[J].International Journal of Solids and Structures,2009,46(13):2757-2764.
[7]Lin Y,Qian Q,Wang L,et al.Vibration analysis of micro-scale plates based on modified couple stress theory[J].Acta Mechanica Solid Sinca,2010,23(5):386-392.
[8]Simsek M,Reddy J N.Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory[J].International Journal of Engineering Science,2013,64:37-53.
[9]Chen W J,Li L,Xu M.A modified couple stress model for bending analysis of composite laminated beams with first order shear deformation[J].Composite Structures,2011,93(11):2723-2732.
[10]李莉,陈万吉,郑楠.修正偶应力理论层合薄板稳定性模型及尺度效应[J].工程力学,2013,30(5):1-7.(LI Li,CHEN Wan-ji,ZHENG Nan.Model of composite laminated thin plate based on modified couple stress theory and buckling analysis of scale effects[J].Engineering Mechanics,2013,30(5):1-7.(in Chinese))
[11]Chen W J,Li X P.Size-dependent free vibration analysis of composite laminated Timoshenko beam based on new modified couple stress theory[J].Archive of Applied Mechanics,2012,83:431-444.
[12]Chen W J,Yang S Q,Li X P.A study of scale effect of composite laminated plates based on new modified couple stress theory by finite element method[J].International Journal for Multiscale Computational Engineering,2014,12(6):507-527.
[13]任晓辉,陈万吉.C0型高阶锯齿理论及复合材料厚梁热应力分析[J].计算力学学报,2015,32(1):77-82.(REN Xiao-hui,CHEN Wan-ji.Thermal stress analysis of thick composite beams based on C0-type higher-order zig-zag theory[J].Chinese Journal of Computational Mechanics,2015,32(1):77-82.(in Chinese))
[14]Koiter W T.Couple-stresses in the theory of elasticity:I and II[A].Proceedings of the Koninkliske Nederlandse Akademie van Wetenschappen[C].1964.
[15]Pagano N J.Exact solutions for rectangular bi-directional composites and sandwich plates[J].Compos Mater,1970,4:20-34.