专题:海洋工程装备智能化

基于谱位移格式的复杂切口功能梯度板自由振动等几何分析

  • 杨少伟 ,
  • 孙贤波 ,
  • 蔡志勤 ,
  • 卢海龙 ,
  • 杨志勋
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  • 1. 大连理工大学工程力学系, 大连 116024;
    2. 哈尔滨工程大学机电工程学院, 哈尔滨 150001
杨少伟,博士研究生,研究方向为等几何分析,电子信箱:qinchao98998@mail.dlut.edu.cn;蔡志勤(通信作者),教授,研究方向为动力学与控制,电子信箱:zhqcai@dlut.edu.cn

收稿日期: 2023-06-02

  修回日期: 2023-07-09

  网络出版日期: 2024-08-01

基金资助

国家自然科学基金项目(52271269,52001088,U2241263,U1906233)

Isogeometric analysis for free vibration of functionally graded plates with complex cutouts using spectral displacement formulation

  • YANG Shaowei ,
  • SUN Xianbo ,
  • CAI Zhiqin ,
  • LU Hailong ,
  • YANG Zhixun
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  • 1. Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China;
    2. College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, China

Received date: 2023-06-02

  Revised date: 2023-07-09

  Online published: 2024-08-01

摘要

为分析具有复杂切口的功能梯度板自由振动响应,基于一种新的准三维高阶剪切变形理论(谱位移格式)的等几何分析方法被用来预测带切口板的动力特性。谱位移格式将未知位移场展开为厚度方向上特殊形式的切比雪夫级数,具有精度高,以及避免剪切闭锁问题的特性,对薄厚板的分析具有很好的通用性。利用达朗贝尔原理和虚功原理推导了功能梯度板自由振动的控制方程,并利用等几何方法对方程进行离散和求解。通过对数值算例的计算,以及与现有参考结果的比较,证明了提出的分析方法能够准确有效地分析具有复杂切口的功能梯度板自由振动问题。

本文引用格式

杨少伟 , 孙贤波 , 蔡志勤 , 卢海龙 , 杨志勋 . 基于谱位移格式的复杂切口功能梯度板自由振动等几何分析[J]. 科技导报, 2024 , 42(13) : 36 -47 . DOI: 10.3981/j.issn.1000-7857.2023.09.01364

Abstract

This paper aims to analyze the free vibration response of functionally graded plates with complex cutouts. An isogeometric analysis method based on a novel quasi-three-dimensional higher-order shear deformation theory called the spectral displacement formulation (SDF) is employed to predict the free vibration characteristics of the plates. The SDF can deal with the three-dimensional elasticity solution and naturally avoid the shear-locking problem, making it suitable for plates with varying thicknesses. The governing equations for free vibration of the plates are derived using the D'Alembert principle and the principle of virtual work, and the equations are discretized using isogeometric method. The results of several numerical examples are compared with existing reference solutions. It is concluded that the proposed analysis method can accurately and effectively analyze the free vibration of functionally graded plates with complex cutouts.

参考文献

[1] Xu F X, Zhang X, Zhang H. A review on functionally graded structures and materials for energy absorption[J]. Engineering Structures, 2018, 171:309-325.
[2] Saleh B, Jiang J H, Fathi R, et al. 30 Years of functional-ly graded materials:An overview of manufacturing meth-ods, applications and future challenges[J]. Composites Part B:Engineering, 2020, 201:108376.
[3] Guedes Soares C, Shenoi R A. Analysis and design of ma-rine structures[M]. London:CRC Press, 2009.
[4] Sahoo S. Laminated composite stiffened shallow spherical panels with cutouts under free vibration-A finite element approach[J]. Engineering Science and Technology, an In-ternational Journal, 2014, 17(4):247-259.
[5] Ovesy H R, Fazilati J. Buckling and free vibration finite strip analysis of composite plates with cutout based on two different modeling approaches[J]. Composite Struc-tures, 2012, 94(3):1250-1258.
[6] Natarajan S, Deogekar P S, Manickam G, et al. Hygrother-mal effects on the free vibration and buckling of laminat-ed composites with cutouts[J]. Composite Structures, 2014, 108:848-855.
[7] Fantuzzi N, Tornabene F, Viola E. Four-parameter func-tionally graded cracked plates of arbitrary shape:A GDQ-FEM solution for free vibrations[J]. Mechanics of Ad-vanced Materials and Structures, 2016, 23(1):89-107.
[8] Ansari R, Torabi J, Hassani R. A comprehensive study on the free vibration of arbitrary shaped thick functionally graded CNT-reinforced composite plates[J]. Engineering Structures, 2019, 181:653-669.
[9] Liu G R, Chen X L. A mesh-free method for static and free vibration analyses of thin plates of complicated shape[J]. Journal of Sound and Vibration, 2001, 241(5):839-855.
[10] Nguyen K D, Nguyen-Xuan H. An isogeometric finite el-ement approach for three-dimensional static and dynam-ic analysis of functionally graded material plate struc-tures[J]. Composite Structures, 2015, 132:423-439.
[11] Hughes T J R, Cottrell J A, Bazilevs Y. Isogeometric analysis:CAD, finite elements, NURBS, exact geometry and mesh refinement[J]. Computer Methods in Applied Mechanics and Engineering, 2005, 194(39/40/41):4135-4195.
[12] Thai H T, Kim S E. A review of theories for the model-ing and analysis of functionally graded plates and shells[J]. Composite Structures, 2015, 128:70-86.
[13] Jha D K, Kant T, Singh R K. A critical review of recent research on functionally graded plates[J]. Composite Structures, 2013, 96:833-849.
[14] Carrera E, Brischetto S, Cinefra M, et al. Effects of thickness stretching in functionally graded plates and shells[J]. Composites Part B:Engineering, 2011, 42(2):123-133.
[15] Zenkour A M. Benchmark trigonometric and 3-D elastic-ity solutions for an exponentially graded thick rectangu-lar plate[J]. Archive of Applied Mechanics, 2007, 77(4):197-214.
[16] Matsunaga H. Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory[J]. Composite Structures, 2008, 82(4):499-512.
[17] Matsunaga H. Free vibration and stability of functionally graded shallow shells according to a 2D higher-order deformation theory[J]. Composite Structures, 2008, 84(2):132-146.
[18] Neves A M A, Ferreira A J M, Carrera E, et al. A quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates[J]. Composite Structures, 2012, 94(5):1814-1825.
[19] Neves A M A, Ferreira A J M, Carrera E, et al. Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique[J]. Composites Part B:Engineering, 2013, 44(1):657-674.
[20] Neves A M A, Ferreira A J M, Carrera E, et al. Buck-ling analysis of sandwich plates with functionally graded skins using a new quasi-3D hyperbolic sine shear defor-mation theory and collocation with radial basis functions[J]. ZAMM-Journal of Applied Mathematics and Me-chanics, 2012, 92(9):749-766.
[21] Mantari J L, Guedes Soares C. Generalized hybrid quasi-3D shear deformation theory for the static analysis of ad-vanced composite plates[J]. Composite Structures, 2012, 94(8):2561-2575.
[22] Mantari J L, Soares C G. A quasi-3D tangential shear deformation theory with four unknowns for functionally graded plates[J]. Acta Mechanica, 2015, 226(3):625-642.
[23] Thai H T, Kim S E. A simple quasi-3D sinusoidal shear deformation theory for functionally graded plates[J]. Composite Structures, 2013, 99:172-180.
[24] Thai H T, Vo T P, Bui T Q, et al. A quasi-3D hyperbol-ic shear deformation theory for functionally graded plates[J]. Acta Mechanica, 2014, 225(3):951-964.
[25] Hebali H, Tounsi A, Houari M S A, et al. New quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates[J]. Journal of Engineering Mechanics, 2014, 140(2):374-383.
[26] Bessaim A, Houari M S, Tounsi A, et al. A new higherorder shear and normal deformation theory for the static and free vibration analysis of sandwich plates with func-tionally graded isotropic face sheets[J]. Journal of Sand-wich Structures&Materials, 2013, 15(6):671-703.
[27] Bennoun M, Houari M S A, Tounsi A. A novel five-vari-able refined plate theory for vibration analysis of func-tionally graded sandwich plates[J]. Mechanics of Ad-vanced Materials and Structures, 2016, 23(4):423-431.
[28] 黎梦真.功能梯度板高阶剪切变形理论建模方法与力学特性研究[D].武汉:武汉理工大学, 2021.
[29] Van Do V N, Lee C H. Free vibration analysis of FGM plates with complex cutouts by using quasi-3D isogeo-metric approach[J]. International Journal of Mechanical Sciences, 2019, 159:213-233.
[30] Huang W H, Xue K, Li Q H. Three-dimensional solu-tion for the vibration analysis of functionally graded rect-angular plate with/without cutouts subject to general boundary conditions[J]. Materials, 2021, 14(22):7088.
[31] Yin S H, Yu T T, Bui T Q, et al. A cutout isogeometric analysis for thin laminated composite plates using level sets[J]. Composite Structures, 2015, 127:152-164.
[32] Tran L V, Abdel Wahab M, Kim S E. An isogeometric fi-nite element approach for thermal bending and buckling analyses of laminated composite plates[J]. Composite Structures, 2017, 179:35-49.
[33] Thai C H, Zenkour A M, Abdel Wahab M, et al. A sim-ple four-unknown shear and normal deformations theory for functionally graded isotropic and sandwich plates based on isogeometric analysis[J]. Composite Structures, 2016, 139:77-95.
[34] Zang Q S, Liu J, Ye W B, et al. Static and free vibration analyses of functionally graded plates based on an isogeometric scaled boundary finite element method[J]. Composite Structures, 2022, 288:115398.
[35] 钟锐,胡双卫,秦斌,等.功能梯度开孔平行四边形板的等几何振动分析[J].哈尔滨工程大学学报, 2022, 43(7):999-1005.
[36] Sun X B, Gao R X, Zhang Y H. Spectral stochastic isogeometric analysis of bending and free vibration of porous functionally graded plates[J]. Applied Mathemati-cal Modelling, 2023, 116:711-734.
[37] Yang S W, Sun X B, Cai Z Q, et al. High-precision isogeometric static bending analysis of functionally grad-ed plates using a new quasi-3D spectral displacement formulation[J]. Applied Sciences, 2023, 13(11):6412.
[38] Szilard R. Theories and applications of plate analysis:Classical, numerical and engineering methods[J]. Ap-plied Mechanics Reviews, 2004, 57(6):B32-B33.
[39] Cottrell J A, Hughes T J R, Bazilevs Y. Isogeometric analysis:Toward integration of CAD and FEA[M]. NJ, USA:John Wiley&Sons, 2009.
[40] Piegl L, Tiller W. The NURBS book[M]. Berlin, Germa-ny:Springer Science&Business Media, 1996.
[41] Cox D A, Little J, O'Shea D. Ideals, varieties, and algo-rithms:An introduction to computational algebraic geom-etry and commutative algebra[M]. Berlin:Springer Cham, 2015.
[42] Babuška I. The finite element method with penalty[J]. Mathematics of Computation, 1973, 27(122):221-228.
[43] Fernández-Méndez S, Huerta A. Imposing essential boundary conditions in mesh-free methods[J]. Computer Methods in Applied Mechanics and Engineering, 2004, 193(12/13/14):1257-1275.
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