Scale effects on nonlocal buckling analysis of bilayer composite plates under non-uniform uniaxial loads

doi:10.1007/s10483-015-1900-7

Applied Mathematics and Mechanics (English Edition) ›› 2015, Vol. 36 ›› Issue (1): 1-10.doi: https://doi.org/10.1007/s10483-015-1900-7

• 论文 • 下一篇

Scale effects on nonlocal buckling analysis of bilayer composite plates under non-uniform uniaxial loads

Xiang-wu PENG, Xing-ming GUO, Liang LIU, Bing-jie WU

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, P. R. China

收稿日期:2014-06-13 修回日期:2014-10-31 出版日期:2015-01-01 发布日期:2015-01-01
通讯作者: Xing-ming GUO, xmguo@shu.edu.cn E-mail:xmguo@shu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 10632040 and 11472163), the National Key Basic Research Project of China (No. 2014CB04623), and the Shanghai Municipal Commission of Eduction (No. 13ZZ067)

Scale effects on nonlocal buckling analysis of bilayer composite plates under non-uniform uniaxial loads

Xiang-wu PENG, Xing-ming GUO, Liang LIU, Bing-jie WU

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, P. R. China

Received:2014-06-13 Revised:2014-10-31 Online:2015-01-01 Published:2015-01-01
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 10632040 and 11472163), the National Key Basic Research Project of China (No. 2014CB04623), and the Shanghai Municipal Commission of Eduction (No. 13ZZ067)

摘要/Abstract

摘要：

Scale effects are studied on the buckling behavior of bilayer composite plates under non-uniform uniaxial compression via the nonlocal theory. Each isotropic plate is composed of a material that is different from others, and the adhesive between the plates is modeled as the Winkler elastic medium. According to the symmetry, effects of the Winkler non-dimensional parameter, the thickness ratio, the ratio of Young's moduli, and the aspect ratio are also considered on the buckling problem of bilayer plates, where only the top plate is under the uniaxial compression. Numerical examples show that the Winkler elastic coefficient, the thickness ratio, and the ratio of Young's moduli play decisive roles in the buckling behavior. Nonlocal effect is significant when the high-order buckling mode occurs or the aspect ratio is small.

关键词: buckling, bilayer composite plates, Winkler elastic medium, nonlocal scale effect

Abstract:

Key words: Winkler elastic medium, buckling, nonlocal scale effect, bilayer composite plates

中图分类号:

O346

Xiang-wu PENG;Xing-ming GUO;Liang LIU;Bing-jie WU. Scale effects on nonlocal buckling analysis of bilayer composite plates under non-uniform uniaxial loads[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(1): 1-10.

参考文献

[1] Iijima, S. Helical microtubules of graphitic carbon. nature, 354, 56-58 (1991)
[2] Lu, P., Lee, H. P., Lu, C., and Zhang, P. Q. Dynamic properties of flexural beams using a nonlocal elasticity model. Journal of Applied Physics, 99, 073510 (2006)
[3] Wang, C. M. and Duan, W. H. Free vibration of nanorings/arches based on nonlocal elasticity. Journal of Applied Physics, 104, 014303 (2008)
[4] Duan, W. H. and Wang, C. M. Exact solutions for axisymmetric bending of micro/nanoscale circular plates based on nonlocal plate theory. Nanotechnology, 18(38), 385704 (2007)
[5] Gupta, A., Akin, D., and Bashir, R. Detection of bacterial cells and antibodies using surface micromachined thin silicon cantilever resonators. Journal of Vacuum Science & Technology B, 22(6), 2785-2791 (2004)
[6] Li, C., Thostenson, E. T., and Chou, T. W. Sensors and actuators based on carbon nanotubes and their composites: a review. Composites Science and Technology, 68(6), 1227-1249 (2008)
[7] Timoshenko, S. P. and Goodier, J. N. Theory of Elasticity, McGraw-Hill Publishing Company, New York (1970)
[8] Yakobson, B. I., Brabec, C. J., and Bernholc, J. Nanomechanics of carbon tubes: instabilities beyond linear response. Physcial Review Letters, 76, 2511-2514 (1996)
[9] Ru, C. Q. Axially compressed buckling of a double-walled carbon nanotube embedded in an elastic medium. Journal of the Mechanics and Physics of Solids, 49, 1265-1279 (2001)
[10] Ru, C. Q. Effect of van de Waals forces on axial buckling of a double-walled carbon nanotube. Journal of Applied Physics, 87, 7227-7231 (2000)
[11] Ansari, R., Rajabiehfard, R., and Arash, B. Nonlocal finite element model for vibrations of em-bedded multilayered graphene sheets. Computational Materials Science, 49, 831-838 (2010)
[12] Arash, B. and Wang, Q. A review on the application of nonlocal elastic models in modeling of carbon nanotubes and graphenes. Computational Materials Science, 51, 303-313 (2012)
[13] Wang, C. M., Zhang, Y. Y., Ramesh, S. S., and Kitipornchai, S. Buckling analysis of micro-and nano-rods/tubes based on nonlocal Timoshenko beam theory. Journal of Physics D: Applied Physics, 39(17), 3904-3909 (2006)
[14] Erigen, A. C. Nonlocal Continuum Field Theories, Springer, New York (2001)
[15] Pradhan, S. C. andMurmu, T. Small scale effect on the buckling analysis of single-layered graphene sheet embedded in an elastic medium based on nonlocal plate theory. Physica E, 42, 1293-1301 (2010)
[16] Assadi, A. and Farshi, B. Stability analysis of graphene based laminated composite sheets under non-uniform inplane loading by nonlocal elasticity. Applied Mathematical Modelling, 35, 4541-4549 (2011)
[17] Murmu, T., Sienz, J., Adhikari, S., and Arnold, C. Nonlocal buckling of double nanoplate systems under biaxial compression. Composites Part B: Engineering, 44, 84-94 (2013)
[18] Erigen, A. C. Nonlocal polar elastic continua. International Journal of Engineering Science, 10, 1-16 (1972)
[19] Eringen, A. C. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. Journal of Applied Physics, 54, 4703-4710 (1983)
[20] Wu, L. Y. Stability Theory of Plates and Shells (in Chinese), Huazhong University of Science & Technology Press, Wuhan (1996)
[21] Huang, Y. and He, F. S. Beams, Plates and Shells on Elastic Foundation (in Chinese), Science Press, Beijing (2005)
[22] Reddy, J. N. Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates. International Journal of Engineering Science, 48, 1507-1518 (2010)

Scale effects on nonlocal buckling analysis of bilayer composite plates under non-uniform uniaxial loads

Scale effects on nonlocal buckling analysis of bilayer composite plates under non-uniform uniaxial loads

PDF

可视化

被引次数

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	H. M. FEIZABAD, M. H. YAS. Free vibration and buckling analysis of polymeric composite beams reinforced by functionally graded bamboo fibers[J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(3): 543-562.
[2]	Lei WANG, Yingge LIU, Juxi HU, Weimin CHEN, Bing HAN. A non-probabilistic reliability topology optimization method based on aggregation function and matrix multiplication considering buckling response constraints[J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(2): 321-336.
[3]	Qiao ZHANG, Yuxin SUN. Statics, vibration, and buckling of sandwich plates with metamaterial cores characterized by negative thermal expansion and negative Poisson's ratio[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(9): 1457-1486.
[4]	Shan XIA, Linghui HE. Buckling morphology of glassy nematic films with staggered director field[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(11): 1841-1852.
[5]	Andi LAI, Bing ZHAO, Xulong PENG, Chengyun LONG. Effects of local thickness defects on the buckling of micro-beam[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(5): 729-742.
[6]	Chi XU, Yang LI, Mingyue LU, Zhendong DAI. Buckling analysis of functionally graded nanobeams under non-uniform temperature using stress-driven nonlocal elasticity[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(3): 355-370.
[7]	Shuai WANG, Jiajia MAO, Wei ZHANG, Haoming LU. Nonlocal thermal buckling and postbuckling of functionally graded graphene nanoplatelet reinforced piezoelectric micro-plate[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(3): 341-354.
[8]	Xinlei LI, Jianfei WANG. Effects of layer number and initial pressure on continuum-based buckling analysis of multi-walled carbon nanotubes accounting for van der Waals interaction[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(12): 1857-1872.
[9]	Cheng LI, Chengxiu ZHU, C. W. LIM, Shuang LI. Nonlinear in-plane thermal buckling of rotationally restrained functionally graded carbon nanotube reinforced composite shallow arches under uniform radial loading[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(12): 1821-1840.
[10]	Tuoya SUN, Junhong GUO, E. PAN. Nonlocal vibration and buckling of two-dimensional layered quasicrystal nanoplates embedded in an elastic medium[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(8): 1077-1094.
[11]	Zixuan LU, Liang GUO, Hongyu ZHAO. Mechanics of nonbuckling interconnects with prestrain for stretchable electronics[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(5): 689-702.
[12]	Zhiwei LI, Guohua NIE. A procedure of the method of reverberation ray matrix for the buckling analysis of a thin multi-span plate[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(7): 1055-1068.
[13]	A. AMIRI, M. MOHAMMADIMEHR, M. ANVARI. Stress and buckling analysis of a thick-walled micro sandwich panel with a flexible foam core and carbon nanotube reinforced composite (CNTRC) face sheets[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(7): 1027-1038.
[14]	A. H. SOFIYEV, I. T. PIRMAMEDOV, N. KURUOGLU. Influence of elastic foundations and carbon nanotube reinforcement on the hydrostatic buckling pressure of truncated conical shells[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(7): 1011-1026.
[15]	S. AFSHIN, M. H. YAS. Dynamic and buckling analysis of polymer hybrid composite beam with variable thickness[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(5): 785-804.