A Direct Approach to Skeletal Structures Statics and Dynamics

Abstract

Abstract: Abstract： The precision of finite element method is restricted by mesh density. To solve this problem, an analytical method for arbitrary complex bar system was proposed based on the nodal method. The nodal compatibility equation of displacement and the equilibrium equation of internal force were considered. The spectral coefficients were treated as the unknowns. The deformation and internal section force were described by the exact solutions of corresponding problems. The process of the construction of the coefficient matrix of the equation of the system was illustrated in an algebraic symbolic way, providing basis for general program development. Two special modelling procedures, distributed load and hinge joint, were investigated and given. A plane steel frame buckling analysis and a space pipe line harmonic analysis were launched. The results confirm that the present method is highly precise and requires a small number of elements. The method is well suited for the requirement of analytical solutions.

Key words: analytical solution, nodal method, frame, bar system, beam

CLC Number:

TU 32

ZHOU Juna，RAO Zhushib，TA Naa. A Direct Approach to Skeletal Structures Statics and Dynamics [J]. Journal of Shanghai Jiaotong University, 2016, 50(01): 52-58.

References

［1］冯康, 秦孟兆. Hamilton动力体系的Hamilton算法［J］. 自然科学进展, 1991(2):102112. ［2］SHARIYAT M, ASEMI K. 3D Bspline finite element nonlinear elasticity buckling analysis of rectangular FGM plates under nonuniform edge loads, using a micromechanical model［J］. Composite Structures, 2014, 112: 397408. ［3］袁驷, 王永亮, 徐俊杰. 二维自由振动的有限元线法自适应分析新进展［J］. 工程力学, 2014, 31(1):1522. YUAN Si, WANG Yongliang, XU Junjie. New progress in selfadaptive FEMOL analysis of 2D free vibration problems［J］. Engineering Mechanics, 2014, 31(1):1522. ［4］李艳, 王媛, 汤琴, 等. 考虑结合部耦合的结构梁的边界元解析方法研究［J］. 机械强度, 2015, 37(2):300306. LI Yan, WANG Yuan, TANG Qin, et al. Study on boundary element method analysis of structural beam with coupled joints［J］. Journal of Mechanical Strength, 2015, 37(2):300306. ［5］谷超豪, 李大潜, 陈恕行, 等. 数学物理方程［M］. 2版. 北京:高等教育出版社, 2002: 165170. ［6］LIU G R, ZHANG G Y, ZONG Z, et al. Meshfree cellbased smoothed alpha radial point interpolation method (CSα RPIM) for solid mechanics problems［J］. International Journal of Computational Methods, 2013, 10(4): 1350020. ［7］CHALLAMEL N, WANG C M, ELISHAKOFF I. Discrete systems behave as nonlocal structural elements: Bending, buckling and vibration analysis［J］. European Journal of Mechanics, A/Solids, 2014, 44:12535. ［8］董宇, 杨翊仁, 鲁丽. 基于微分求积法的轴向流作用下叠层板的稳定性和模态分析［J］. 振动工程学报, 2015, 28(2):197202. DONG Yu, YANG Yiren, LU Li. Buckling and modal analysis of coupled parallel flexible plates in an axial flow using the differential quadrature method［J］. Journal of Vibration Engineering, 2015, 28(2):197202. ［9］ABBAS L K, BESTLE D, RUI X T. Transfer matrix method for the determination of the free vibration of two elastically coupled beams［J］. Applied Mechanics and Materials, 2013, 372: 301304. ［10］沈小璞. 工程结构分析的状态空间理论及其应用［D］.合肥:合肥工业大学研究生院,2009. ［11］黄修长, 徐时吟, 章振华, 等. 利用波动法研究曲梁结构中的波形转换和能量传递［J］. 振动与冲击, 2012, 31(8):3846. HUANG Xiuchang, XU Shiyin, ZHANG Zhenhua, et al, Application of wave approach in wave mode conversion and energy transmission of curved beams［J］. Journal of Vibration and Shock, 2012, 31(8):3846. ［12］张娇, 聂国华. 带有全铰节点的三维杆系结构静力分析的回传波射矩阵法研究［J］. 力学季刊, 2013, 34(2):199206. ZHANG Jiao, NIE Guohua. Method of reverberationray matrix for static analysis of 3d barsystem structures containing completely hinged joints［J］. Chinese Quarterly of Mechanics, 2013, 34(2):199206. ［13］袁驷, 叶康生, Williams F W, 等. 杆系结构自由振动精确求解的理论和算法［J］. 工程力学, 2005, 22(增刊):16. YUAN Si, YE Kangsheng, WILLIAMS F W, et al. Theory and algorithm of the exact method for free vibration problems of skeletal structures［J］. Engineering Mechanics, 2005, 22(Sup):16. ［14］Shirmohammadi F, Bahrami S, Saadatpour M M，et al. Modeling wave propagation in moderately thick rectangular plates using the spectral element method［J］. Applied Mathematical Modelling, 2015, 39(12): 34813495. ［15］周俊, 塔娜, 饶柱石. 杆系结构振动计算的解析节点法［C］//第十届全国振动理论及应用学术会议论文集. 南京:南京航空航天大学出版社, 2011: 625634.

[1]	HE Qinglin, ZHAO Hongyu, CHEN Yuxuan, HOU Xianghao. Design of Distributed Underwater Acoustic Tracking Algorithm for Aerial Targets Based on CRLB [J]. Air & Space Defense, 2025, 8(1): 86-94.
[2]	ZHOU Lian, ZHANG Kai, XU Han, WANG Feiliang, ZHANG Yiping, TANG Lina, YANG Jian. Experimental Study on Bearing Behavior and Debonding Damage of Hidden Frame Glass Curtain Walls Under Negative Wind Pressure [J]. Journal of Shanghai Jiao Tong University, 2024, 58(7): 1130-1138.
[3]	JIANG Yilin^{1, 2∗}(蒋伊琳), LI Xiang^{1, 2} (李向), ZHANG Haoping³ (张昊平). Emitter Beam State Sensing Based on Convolutional Neural Network and Received Signal Strength [J]. J Shanghai Jiaotong Univ Sci, 2024, 29(6): 1017-1022.
[4]	WANG Shuang^1∗ (王爽), WANG Dengfeng² (王登峰), NING Zhanjin¹(宁占金), HU Zhongjian¹(胡中建). Frame Optimization Design Based on Improved Grey Relational Analysis [J]. J Shanghai Jiaotong Univ Sci, 2024, 29(6): 1071-1080.
[5]	BAYOUMI EL-Said Abd-Allah^{1, 2∗} , MAHMOUD Mahmoud Hassan³ , ARIF Mohammed ^{1, 4}. Flexural Behavior of Cross-Connected Brick Masonry Infill Wall Panels Supported on Reinforced Concrete Beam Grids [J]. J Shanghai Jiaotong Univ Sci, 2024, 29(5): 889-899.
[6]	HUANG Heyuan1, QIU Jiangliang1, LI Zhongsheng1, LIU Jinjian2. Hydrodynamic Study on the Probes of Expendable Bathythermograph [J]. Ocean Engineering Equipment and Technology, 2024, 11(4): 67-74.
[7]	JIANG Ruitao(姜瑞涛), YANG Xing(杨星), DENG Youming(邓又铭)，LENG Yongbin(冷用斌). Diagnostic Method for Beam Position Monitor Based on Clustering by Fast Search and Find of Density Peaks [J]. J Shanghai Jiaotong Univ Sci, 2024, 29(3): 457-462.
[8]	GUO Xiaoliang1, ZHANG Xiaodong2, ZHANG Mingming2, TANG Yong2, CUI Wentao1, CHEN Chong1. The Design and Application of Step-by-step Retractable Beam System in Monopile Installation [J]. Ocean Engineering Equipment and Technology, 2024, 11(3): 63-68.
[9]	Xiaoyang Xu, Jia Zhang, Zihao Zhang, Guandan Lu, Wei Cao, Ning Wang, Yunmeng Xia, Qingliang Feng, Shanlin Qiao. All-Covalent Organic Framework Nanofilms Assembled Lithium-Ion Capacitor to Solve the Imbalanced Charge Storage Kinetics [J]. Nano-Micro Letters, 2024, 16(1): 116-.
[10]	Fan He, Yingnan Liu, Xiaoxuan Yang, Yaqi Chen, Cheng-Chieh Yang, Chung-Li Dong, Qinggang He, Bin Yang, Zhongjian Li, Yongbo Kuang, Lecheng Lei, Liming Dai, Yang Hou. Accelerating Oxygen Electrocatalysis Kinetics on Metal-Organic Frameworks via Bond Length Optimization [J]. Nano-Micro Letters, 2024, 16(1): 175-.
[11]	Yayu Dong, Jian Zhang, Hongyu Zhang, Wei Wang, Boyuan Hu, Debin Xia, Kaifeng Lin, Lin Geng, Yulin Yang. Multifunctional MOF@COF Nanoparticles Mediated Perovskite Films Management Toward Sustainable Perovskite Solar Cells [J]. Nano-Micro Letters, 2024, 16(1): 171-.
[12]	Tian Mai, Lei Chen, Pei-Lin Wang, Qi Liu, Ming-Guo Ma. Hollow Metal-Organic Framework/MXene/Nanocellulose Composite Films for Giga/Terahertz Electromagnetic Shielding and Photothermal Conversion [J]. Nano-Micro Letters, 2024, 16(1): 169-.
[13]	Ximeng Liu, Dan Zhao, John Wang. Challenges and Opportunities in Preserving Key Structural Features of 3D-Printed Metal/Covalent Organic Framework [J]. Nano-Micro Letters, 2024, 16(1): 157-.
[14]	Xi Zhou, Quan Zhou, Zhaozhi He, Yi Xiao, Yan Liu, Zhuohang Huang, Yaoji Sun, Jiawei Wang, Zhengdong Zhao, Xiaozhou Liu, Bin Zhou, Lei Ren, Yu Sun, Zhiwei Chen, Xingcai Zhang. ROS Balance Autoregulating Core-Shell CeO₂@ZIF-8/Au Nanoplatform for Wound Repair [J]. Nano-Micro Letters, 2024, 16(1): 156-.
[15]	Zerui Chen, Wei Zhao, Qian Liu, Yifei Xu, Qinghe Wang, Jinmin Lin, Hao Bin Wu. Janus Quasi-Solid Electrolyte Membranes with Asymmetric Porous Structure for High-Performance Lithium-Metal Batteries [J]. Nano-Micro Letters, 2024, 16(1): 114-.