基于Kirchhoff均匀各向异性板控制方程的等效积分弱形式和对挠度函数采用移动最小二乘近似函数进行插值,进一步研究无网格局部Petrov-Galerkin方法在纤维增强对称层合板弯曲问题中的应用.该方法不需要任何形式的网格划分,所有的积分都在规则形状的子域及其边界上进行,其问题的本质边界条件采用罚因子法来施加.通过数值算例和与其他方法的结果比较,表明无网格局部Petrov-Galerkin法求解层合薄板弯曲问题具有解的精度高、收敛性好等一系列优点.
参考文献
| [1] | Liu G R, Chen X L. Buckling of symmetrically laminated composite plates using the element-free Galerkin method[J]. International Journal of Structural Stability and Dynamics,2002, 2(3): 281-294. |
| [2] | Atluri S N and Zhu T. A new meshless local Petrov-Galerkin(MLPG) approach in computational mechanics [J]. Comput Mech, 1998, 22(1): 117-127. |
| [3] | 龙述尧.弹性力学问题的局部Petrov-Galerkin方法[J].力学学报,2001,33(4):508-518.Long S Y. A local Petrov-Galerkin method for the elasticity problem [J]. ActaMechanica Sinica, 2001, 33(4): 508-518. |
| [4] | Xiong Y B, Long S Y. A meshless local Petrov-Galerkin method for a thin plate [J]. Applied Mathematics and Mechanics(English Edition), 2004, 25(2): 210-218. |
| [5] | Jones R M. Mechanics ofComposite Materials, 2nd ed[M]. Philadelphia: Taylor & Francis Inc, 1999. |
| [6] | 罗祖道,李思简.各向异性材料力学[M].上海:上海交通大学出版社,1994.Luo Z D, Li S J. Mechanics of Anisotropic Materials [M].Shanghai: Shanghai Jiao Tong University Press, 1994. |
| [7] | 梁礼平.各向异性板弯曲分析的一种级数-边界积分法[J].应用数学和力学,1990,11(8):697-703.Liang L P. A series-boundary integral method for bending analysis of an anisotropic plate [J]. Applied Mathematics and Mechanics 1990, 11(8): 697-703. |
| [8] | 张承宗,杨光松.各向异性板结构横向弯曲一般解析解[J].力学学报,1996,28(14):429-440.Zhang C Z, Yang G S. General analytic solutions for transverse bending problem of anisotropic plate structures [J].Acta Mechanica Sinica, 1996, 28(14): 429- 440. |
| [9] | 梁礼平.角铺设层板弯曲问题的一种半解析法[J].复合材料学报,1987,4(1):73-78.Liang L P. A semi-analytic method for bending of angle-ply laminates [J]. Acta Materiae Compositae Sinica , 1987, 4(1): 73-78. |
| [10] | 梁礼平.具有混合边界条件的各向异性板弯曲[A].见:李家宝.解析与数值结合法的理论及其工程应用[C].长沙:湖南大学出版社,1990.609-610.Liang L P. Bending Analysis of Anisotropic Plate with Mixboundary Condition [A]. In: Li Jiabao. The Theory of the Combination Method of Analytic and Numerical Solution and Applications in Engineering [C]. Changsha: Hunan University Press, 1990. 609-610. |
上一张
下一张
上一张
下一张
计量
- 下载量()
- 访问量()
文章评分
- 您的评分：
-
10%
-
20%
-
30%
-
40%
-
50%