期刊
COMPOSITE STRUCTURES
卷 125, 期 -, 页码 41-50出版社
ELSEVIER SCI LTD
DOI: 10.1016/j.compstruct.2015.01.039
关键词
Weak form quadrature thin beam element; Functionally graded beam; Free vibration; Classical beam theory
资金
- Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures (Nanjing University of Aeronautics and Astronautics) [0214G02]
- Jiangsu Innovation Program for Graduate Education [KYLX_0219]
- Fundamental Research Funds for the Central Universities
- Priority Academic Program Development of Jiangsu Higher Education Institutions
Based on the classical beam theory (CBT) and differential quadrature (DQ) rule, an N-node novel weak form quadrature functionally graded (FG) beam element is established. Both Young's modulus and mass density of the beam materials vary exponentially through the thickness. The element node points can be different from the integration points. Either Gauss-Lobatto-Legendre (GLL) quadrature or Gauss quadrature can be used to obtain the element stiffness matrix and mass matrix. Detailed formulations are given. Convergence study is performed. For verification, results are compared with available solutions in literature. It is shown that the proposed thin beam element can yield very accurate frequencies with relatively small number of nodal points. New accurate results are presented for functionally graded beams with nine different boundary conditions. The tabulated results will be a reference with which other researchers can compare their results during developing new numerical method. (C) 2015 Elsevier Ltd. All rights reserved.
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