间接非均匀张拉圆板屈曲行为的有限元模拟与实验研究
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摘要
采用有限元模拟结合实验的方法,通过张拉仅允许中央圆板发生面外位移的矩形板,分析圆板受间接非均匀张拉的屈曲行为.基于均匀受压圆板屈曲的结论,假定非均匀张拉圆板的临界屈曲荷载正比于杨氏模量,且正比于板厚(h)和圆板直径(d)之比的平方,采用一系列有限元分析拟合比例系数(临界屈曲系数).设计进行相关实验以验证模拟的可靠性.结果表明,临界屈曲系数的取值随结构长宽比(L/B)、泊松比和径宽比(d/B)的变化存在一定的规律.该工作可以为结构稳定性分析提供新的方法 .
Based on the finite element simulation and experimental method, the buckling behavior of circular plate subjected to indirect nonuniform tension is analyzed by stretching the rectangular plate where only a circular region at the center of a rectangular plate is allowed to buckle out of plane. On the basis of the analytical solution about the critical buckling load of a circular plate under uniform pressure, an assumption that the critical buckling load of the nonuniform stretched circular plate applied to structural boundary is proportional to the value of elastic modulus, as well as the ratio of plate thickness(h) and circular diameter(d) is made; finite element method is used to fit the proportionality coefficient(critical buckling coefficient) of a specific geometric scale structure. Some relevant experiments are designed and carried out to verify the reliability of the simulation.The results show that the value of the critical buckling coefficient varies with the structure length-width ratio(L/B), Poisson's ratio and diameter-width ratio(d/B). This research work can provide a new method for the analysis of structural stability.
Based on the finite element simulation and experimental method, the buckling behavior of circular plate subjected to indirect nonuniform tension is analyzed by stretching the rectangular plate where only a circular region at the center of a rectangular plate is allowed to buckle out of plane. On the basis of the analytical solution about the critical buckling load of a circular plate under uniform pressure, an assumption that the critical buckling load of the nonuniform stretched circular plate applied to structural boundary is proportional to the value of elastic modulus, as well as the ratio of plate thickness(h) and circular diameter(d) is made; finite element method is used to fit the proportionality coefficient(critical buckling coefficient) of a specific geometric scale structure. Some relevant experiments are designed and carried out to verify the reliability of the simulation.The results show that the value of the critical buckling coefficient varies with the structure length-width ratio(L/B), Poisson's ratio and diameter-width ratio(d/B). This research work can provide a new method for the analysis of structural stability.
引文
[1] Qiu Zhicheng. Modal analysis and model reduction for flexible cantilever plate system of spacecraft[J].Aerospace Control, 2006, 24(3):89-96.
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[3] Panda S K, Ramachandra L S. Buckling of rectangular plates with various boundary conditions loaded by uniform inplane loads[J]. International Journal of Mechanical Sciences, 2010, 52(6):819-828.
[4] Stollenwerk K, Wagner A. Optimality conditions for the buckling of a clamped plate[J]. Journal of Mathematical Analysis&Applications, 2015, 432(1):254-273.
[5] Bui T Q, Nguyen M N, Zhang C. Buckling analysis of Reissner-Mindlin plates subjected to in-plane edge loads using a shear-locking-free and meshfree method[J]. Engineering Analysis with Boundary Elements,2011, 35(9):1038-1053.
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[7] Bodaghi M, Saidi A R. Levy-type solution for buckling analysis of thick functionally graded rectangular plates based on the higher-order shear deformation plate theory[J]. Applied Mathematical Modelling, 2010, 34(11):3659-3673.
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[15] Brighenti R. Influence of a central straight crack on the buckling behaviour of thin plates under tension,compression or shear loading[J]. International Journal of Mechanics&Materials in Design, 2010, 6(1):73-87.
[16] Rad A A, Panahandeh-Shahraki D. Buckling of cracked functionally graded plates under tension[J]. ThinWalled Structures, 2014, 84:26-33.
[17] Kilardj M, Ikhenazen G, Messager T, et al. Linear and nonlinear buckling analysis of a locally stretched plate[J]. Journal of Mechanical Science&Technology,2016, 30(8):3607-3613.
[18] Friedl N, Rammerstorfer F G, Fischer F D. Buckling of stretched strips[J]. Computers&Structures, 2000,78(1):185-190.
[19] Taylor M, Bertoldi K, Steigmann D J. Spatial resolution of wrinkle patterns in thin elastic sheets at finite strain[J]. Journal of the Mechanics&Physics of Solids, 2014, 62(1):163-180.
[20] Puntel E, Deseri L, Fried E. Erratum to:wrinkling of a stretched thin sheet[J]. Journal of Elasticity, 2011, 105(1-2):171-172.
[21] Davidovitch B, Cerda E A. Prototypical model for tensional wrinkling in thin sheets[J]. Proceedings of the National Academy of Sciences of the United States of America, 2011, 108(45):18227-18232.
[22] Adams G G. Elastic wrinkling of a tensioned circular plate using von Kármán plate theory[J]. Journal of Applied Mechanics, 1993, 60(2):520-525.
[23] Coman C D. Asymmetric bifurcations in a pressurised circular thin plate under initial tension[J]. Mechanics Research Communications, 2013, 47(3):11-17.
[24] Timoshenko S P. Theory of Elastic Stability[M]. New York:McGraw-Hill, 1961:220.
[25]庄茁,由小川,廖剑晖.基于ABAQUS的有限元分析和应用[M].北京：清华大学出版社, 2009.Zhuang Zhuo, You Xiaochuan, Liao Jianhui. Finite element analysis and application based on ABAQUS[M].Beijing:Tsinghua University Press, 2009.
[26]杨鸣波,唐志玉.中国材料工程大典高分子材料工程[M].北京：化学工业出版社, 2006.Yang Mingbo, Tang Zhiyu. China Material Engineering:Polymer Materials Engineering[M]. Beijing:Chemical Industry Press, 2006.
[27] Zhang Y, Zhang J, Lu Y, et al. Glass transition temperaturedeterminationofpoly(ethylene terephthalate)thin films using reflection-absorption FTIR[J]. Macromolecules, 2004, 37(7):2532-2537.
[28]何平笙.高聚物的力学性能[M].合肥：中国科学技术大学出版社,1997.He Pingsheng. Mechanical properties of polymer[M].Hefei:University of Science and Technology of China Press, 1997.
[29]国家塑料制品质量监督检测中心. GB/T 1040-2006塑料拉伸性能的测定[S].北京：中国标准出版社，2006.National Quality Supervision and Testing Center for Plastic Products. GB/T 1040-2006 Determination of Tensile Properties of Plastics[S]. Beijing:Standards Press of China, 2006.
[2] Berger M S. On Von Kármán's equations and the buckling of a thin elastic plate, I the clamped plate[J].Communications on Pure&Applied Mathematics,1967, 20(4):687-719.
[3] Panda S K, Ramachandra L S. Buckling of rectangular plates with various boundary conditions loaded by uniform inplane loads[J]. International Journal of Mechanical Sciences, 2010, 52(6):819-828.
[4] Stollenwerk K, Wagner A. Optimality conditions for the buckling of a clamped plate[J]. Journal of Mathematical Analysis&Applications, 2015, 432(1):254-273.
[5] Bui T Q, Nguyen M N, Zhang C. Buckling analysis of Reissner-Mindlin plates subjected to in-plane edge loads using a shear-locking-free and meshfree method[J]. Engineering Analysis with Boundary Elements,2011, 35(9):1038-1053.
[6] El-Sawy K M, Nazmy A S. Effect of aspect ratio on the elastic buckling of uniaxially loaded plates with eccentric holes[J]. Thin-Walled Structures, 2001, 39(12):983-998.
[7] Bodaghi M, Saidi A R. Levy-type solution for buckling analysis of thick functionally graded rectangular plates based on the higher-order shear deformation plate theory[J]. Applied Mathematical Modelling, 2010, 34(11):3659-3673.
[8] Kumar D, Singh S B. Effects of boundary conditions on buckling and postbuckling responses of composite laminate with various shaped cutouts[J]. Composite Structures, 2010, 92(3):769-779.
[9] Brighenti R, Carpinteri A. Buckling and fracture behaviour of cracked thin plates under shear loading[J].Materials&Design, 2011, 32(3):1347-1355.
[10] Najafizadeh M M, Eslami M R. Buckling analysis of circular plates of functionally graded materials under uniform radial compression[J]. International Journal of Mechanical Sciences, 2002, 44(12):2479-2493.
[11] Ma L, Wang T. Nonlinear bending and post-buckling of a functionally graded circular plate under mechanical and thermal loadings[J]. International Journal of Solids&Structures, 2003, 40(13):3311-3330.
[12] Shariat S, Eslami M R. Buckling of thick functionally graded plates under mechanical and thermal loads[J].Composite Structures, 2007, 78(3):433-439.
[13] Feldman E, Aboudi J. Buckling analysis of functionally graded plates subjected to uniaxial loading[J].Composite Structures, 1997, 38(1-4):29-36.
[14] Gilabert A, Sibillot P, Sornette D, et al. Buckling instability and pattern around holes or cracks in thin plates under a tensile load[J]. European Journal of Mechanics A, 1992, 11(1):65-89.
[15] Brighenti R. Influence of a central straight crack on the buckling behaviour of thin plates under tension,compression or shear loading[J]. International Journal of Mechanics&Materials in Design, 2010, 6(1):73-87.
[16] Rad A A, Panahandeh-Shahraki D. Buckling of cracked functionally graded plates under tension[J]. ThinWalled Structures, 2014, 84:26-33.
[17] Kilardj M, Ikhenazen G, Messager T, et al. Linear and nonlinear buckling analysis of a locally stretched plate[J]. Journal of Mechanical Science&Technology,2016, 30(8):3607-3613.
[18] Friedl N, Rammerstorfer F G, Fischer F D. Buckling of stretched strips[J]. Computers&Structures, 2000,78(1):185-190.
[19] Taylor M, Bertoldi K, Steigmann D J. Spatial resolution of wrinkle patterns in thin elastic sheets at finite strain[J]. Journal of the Mechanics&Physics of Solids, 2014, 62(1):163-180.
[20] Puntel E, Deseri L, Fried E. Erratum to:wrinkling of a stretched thin sheet[J]. Journal of Elasticity, 2011, 105(1-2):171-172.
[21] Davidovitch B, Cerda E A. Prototypical model for tensional wrinkling in thin sheets[J]. Proceedings of the National Academy of Sciences of the United States of America, 2011, 108(45):18227-18232.
[22] Adams G G. Elastic wrinkling of a tensioned circular plate using von Kármán plate theory[J]. Journal of Applied Mechanics, 1993, 60(2):520-525.
[23] Coman C D. Asymmetric bifurcations in a pressurised circular thin plate under initial tension[J]. Mechanics Research Communications, 2013, 47(3):11-17.
[24] Timoshenko S P. Theory of Elastic Stability[M]. New York:McGraw-Hill, 1961:220.
[25]庄茁,由小川,廖剑晖.基于ABAQUS的有限元分析和应用[M].北京：清华大学出版社, 2009.Zhuang Zhuo, You Xiaochuan, Liao Jianhui. Finite element analysis and application based on ABAQUS[M].Beijing:Tsinghua University Press, 2009.
[26]杨鸣波,唐志玉.中国材料工程大典高分子材料工程[M].北京：化学工业出版社, 2006.Yang Mingbo, Tang Zhiyu. China Material Engineering:Polymer Materials Engineering[M]. Beijing:Chemical Industry Press, 2006.
[27] Zhang Y, Zhang J, Lu Y, et al. Glass transition temperaturedeterminationofpoly(ethylene terephthalate)thin films using reflection-absorption FTIR[J]. Macromolecules, 2004, 37(7):2532-2537.
[28]何平笙.高聚物的力学性能[M].合肥：中国科学技术大学出版社,1997.He Pingsheng. Mechanical properties of polymer[M].Hefei:University of Science and Technology of China Press, 1997.
[29]国家塑料制品质量监督检测中心. GB/T 1040-2006塑料拉伸性能的测定[S].北京：中国标准出版社，2006.National Quality Supervision and Testing Center for Plastic Products. GB/T 1040-2006 Determination of Tensile Properties of Plastics[S]. Beijing:Standards Press of China, 2006.
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