复合材料球形阵列结构压入力学模型及弯曲变形协调机制
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摘要
为了从结构力学角度揭示集中载荷作用下复合材料球形阵列结构的弯曲变形协调机制,建立了该结构典型局部板格的压入力学模型,采用载荷叠加法将集中载荷作用下四角点弹性支承且四边受等弯矩正交各向异性矩形板线性弯曲的中心点挠度分为2个部分:集中载荷作用下四角点弹性支承且四边自由的板的挠度,以及四边受等弯矩的板的挠度.前者可进一步分解为集中载荷作用下四角点弹性支承刚性板的挠度和集中载荷作用下四角点刚性支承线弹性板的挠度,后者可进一步分解为左右边简支上下边受相同弯矩的板的挠度以及上下边简支左右边受相同弯矩的板的挠度.将相同厚度的板在不同载荷情况下的挠度计算结果与有限元分析结果进行比较,进一步开展了试验验证,验证了解析解的正确性.
In order to reveal the deformation coordination mechanism of the composite spherical array sandwich structure from the view of structural mechanics, the indentation mechanical model of the typical local plate lattice for the structure was established under a concentrated load.For a rectangular plate with elastic support of four points and equal moment constraints of four edges, the elastic bending deflection under a concentrated load was treated as the superposition of deflections under two cases, a concentrated load with elastic support of four points and free boundary of four edge sadded to equal moments along four edges. The former was further decomposed into the deflection of rigid plate with elastic support of four points and elastic plate with rigid support of four points and free boundary of four edges under the same concentrated load.The latter was also further decomposed into the deflection of the elastic plate with equal moments along two opposite edges and along the other two opposite edges with the same simply supported boundary. The analytical solutions of three plates with different spans and concentrated force positions were compared with finite element method results, demonstrating the accuracy of the proposed solution. Results show that the mechanical model effectively can effectively reveal the bending deformation mechanism and guide the parametric design of the composite spherical array sandwich structure.
In order to reveal the deformation coordination mechanism of the composite spherical array sandwich structure from the view of structural mechanics, the indentation mechanical model of the typical local plate lattice for the structure was established under a concentrated load.For a rectangular plate with elastic support of four points and equal moment constraints of four edges, the elastic bending deflection under a concentrated load was treated as the superposition of deflections under two cases, a concentrated load with elastic support of four points and free boundary of four edge sadded to equal moments along four edges. The former was further decomposed into the deflection of rigid plate with elastic support of four points and elastic plate with rigid support of four points and free boundary of four edges under the same concentrated load.The latter was also further decomposed into the deflection of the elastic plate with equal moments along two opposite edges and along the other two opposite edges with the same simply supported boundary. The analytical solutions of three plates with different spans and concentrated force positions were compared with finite element method results, demonstrating the accuracy of the proposed solution. Results show that the mechanical model effectively can effectively reveal the bending deformation mechanism and guide the parametric design of the composite spherical array sandwich structure.
引文
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[9] 刘杰.中心荷载角点支承矩形板的弯曲[J].株洲工学院学报,1996,10(4):61-64.Liu Jie.The flexure of center point load of anguler-point strutting rectangular plate [J].Journal of Zhuzhou Institute of Technology,1996,10(4):61-64.(in Chinese)
[10] 陈英杰,李志航,付宝连.应用混合变量余能原理求解不同载荷作用下四边简支矩形板的弯曲[J].计算力学学报,2015,32(2):287-292.Chen Yingjie,Li Zhihang,Fu Baolian.Apply the principles of complementary energy with mixed variables to solve the bending of the rectangular plate with simply supported on four sides under different loads [J].Chinese Journal of Computational Mechanics,2015,32(2):287-292.(in Chinese)
[2] Mc Shane G J,Deshpande V S,Fleck N A.The underwater blast resistance of metallic sandwich beams with prismatic lattice cores[J].Journal of Applied Mechanics,ASME,2007,74(2):352-364.
[3] 徐芝纶.弹性力学 [M].北京:高等教育出版社,2006.Xu Zhilun.Elastic mechanics [M].Beijing:Higher Education Press,2006.(in Chinese)
[4] 陈英杰,宋小惠.应用修正的功的互等法求解大挠度矩形薄板弯曲问题[J].塑性工程学报,2018,25 (2):175-182.Chen Yingjie,Song Xiaohui.Problem of the bending of large deflection rectangular thin plate solved by applying corrected reciprocal method [J].Journal of Plasticity Engineering,2018,25 (2):175-182.(in Chinese)
[5] 龚永庆.四边简支矩形薄板集中力作用中心弯矩影响面[J].山西建筑,2010,36(2):84-85.Gong Yongqing.The central bending moment influence surface of the concentrated force of the rectangular thin plate[J].Shanxi Architecture,2010,36(2):84-85.(in Chinese)
[6] 王春玲,张海霞,吴艳红.半空间地基与正交异性矩形中厚板相互作用解析解[J].北京理工大学学报,2012,32(6):556-560.Wang Chunling,Zhang Haixia,Wu Yanhong.Analytic solution of interaction between half-space foundation and orthotropic rectangular middle thick plate [J].Transactions of Beijing Instituteof Technology,2012,32(6):556-560.(in Chinese)
[7] 王小成,张庆明,乔继延,等.局部均布载荷作用下双凹槽简支板的承载特性 [J].北京理工大学学报,2006,26(11):949-952.Wang Xiaocheng ,Zhang Qingming,Qiao Jiyan,et al.Load carrying characteristics of simply supported rectangular plate with two flutes under partial symmetrical load [J].Transactions of Beijing Instituteof Technology,2006,26(11):949-952.(in Chinese)
[8] 肖闪闪,陈普会.集中载荷下四边固支正交各向异性矩形板的线性弯曲问题[J].工程力学,2015,32(6):28-32.Xiao Shanshan,Chen Puhui.Analytical solutions for bending of clamped orthotropic rectangular plates under a concentrated force [J].Journal of Engineering Mechanics,2015,32(6):28-32.(in Chinese)
[9] 刘杰.中心荷载角点支承矩形板的弯曲[J].株洲工学院学报,1996,10(4):61-64.Liu Jie.The flexure of center point load of anguler-point strutting rectangular plate [J].Journal of Zhuzhou Institute of Technology,1996,10(4):61-64.(in Chinese)
[10] 陈英杰,李志航,付宝连.应用混合变量余能原理求解不同载荷作用下四边简支矩形板的弯曲[J].计算力学学报,2015,32(2):287-292.Chen Yingjie,Li Zhihang,Fu Baolian.Apply the principles of complementary energy with mixed variables to solve the bending of the rectangular plate with simply supported on four sides under different loads [J].Chinese Journal of Computational Mechanics,2015,32(2):287-292.(in Chinese)