各向异性修正偶应力理论Reddy层合板稳定和有限元法

发布时间：2018-01-06 21:38

本文关键词：各向异性修正偶应力理论Reddy层合板稳定和有限元法　出处：《沈阳航空航天大学》2017年硕士论文　论文类型：学位论文

【摘要】：各向异性修正偶应力理论适用于分析细观各向异性材料的相关问题。Reddy高阶理论和一阶理论含有相同未知变量个数,但前者不仅满足自由表面条件,并且能够不用剪切修正因子就可以求解横向剪切应力,具有更高的预测精度。本文分别用解析法和有限元法研究了基于各向异性修正偶应力理论复合材料Reddy型层合板稳定性尺寸效应问题。具体工作为:1.详细介绍了各向异性修正偶应力理论,并且重写了该理论的本构关系,通过虚功原理,构建了只包含一个细观材料尺寸参数的各向异性修正偶应力理论正交铺设Reddy型层合板的稳定性模型。研究了微尺度正交铺设四边简支层合方板在不同铺设角和轴向载荷作用时临界失稳载荷的细观尺寸效应,并且与一阶剪切变形和Kirchhoff板理论结果对比。结果表明,各向异性修正偶应力Reddy型层合板模型的预测精度更高,更适合分析较厚的层合板稳定性问题。2.基于九参数非协调单元BCIZ和修正九参数三角形薄板弯曲单元RT9提出了横向位移函数满足0C连续和1C弱连续条件的三结点三角形板单元。为了验证该单元的准确性和实用性,使用该单元计算了各向异性修正偶应力Reddy型层合板在不同边界条件下、不同铺设角及不同几何形状下的临界失稳载荷。结果显示,有限元解呈快速一致收敛于解析解结果,并且能够成功捕捉在不同工况下层合板的稳定性尺寸效应。
[Abstract]:The anisotropy of the modified couple stress theory is applicable to the analysis of related problems of.Reddy high order theory of meso anisotropic materials and first-order theory contains the same number of unknown variables, but the former not only satisfies the free surface conditions, and can not shear correction factor can solve the transverse shear stress, has higher prediction accuracy. Method and finite element method of anisotropic Reddy should be modified couple stress theory for stability of composite laminates based on size effect were used in this paper. The specific work is as follows: 1. introduces anisotropic modified couple stress theory, and the constitutive relationship of rewriting theory, through the principle of virtual work, the building contains only an anisotropic material meso size parameters of the modified couple stress theory for cross ply composite laminates Reddy stability model. On the micro scale cross ply laminated simplysupported square plate in The meso size effect of different ply angles and axial loads when the critical buckling load, and compared with the first-order shear deformation plate theory and Kirchhoff results. The results show that the prediction accuracy of anisotropic modified couple stress force of Reddy laminate model is better, more suitable for the analysis of stability of thick.2. laminates based on nine parameter nonconforming element BCIZ and modified nine parameter triangular plate bending element RT9 presents transverse displacement function satisfying the 0C continuous and 1C weak continuity condition of three node triangular plate element. In order to verify the accuracy and practicability of the unit, the unit to calculate the anisotropy of the modified couple stress type Reddy laminated plates under different boundary conditions different, the laying of the critical buckling loads of different angle and geometry. The result shows that the finite element solution was rapidly converge to the analytical results, and can be caught in different The stability size effect of the laminate under working conditions.

【学位授予单位】：沈阳航空航天大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TB33

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