柔性支撑上FGM矩形薄板热屈曲的封闭形式解
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摘要
针对典型的热防护组合结构建立物理模型,基于经典薄板理论(CPT),选取中性面为分析平面,推导出柔性支撑上FGM矩形薄板热屈曲方程。利用分离变量法得到了柔性支撑上FGM矩形薄板热屈曲问题的封闭形式解,该方法不仅适用于对边简支情况也适用于四边固支情况。分别对均匀升温、线性升温和非线性升温三种温度场的临界屈曲热载荷进行了计算,与已有文献结果对比验证了本文方法以及结果的正确性,同时进行了数值分析并给出结论。
This article presents closed form solutions for thermal buckling of FGM rectangular thin plates with flexible support. A neutral surface is employed to eliminate the stretching-bending coupling in functionally graded plates. Based on CPT, the equilibrium equations of FGM plate with flexible support in thermal environment are derived. The separation-of-variables method is adopted to obtain the exact solutions for thermal buckling problems of FGM rectangular thin plates with simply supported boundary condition and clamped boundary condition. The buckling of FGM plates under three types of thermal loads is analyzed. The present formulations and solutions are validated by comprehensive comparisons with results in literature.
This article presents closed form solutions for thermal buckling of FGM rectangular thin plates with flexible support. A neutral surface is employed to eliminate the stretching-bending coupling in functionally graded plates. Based on CPT, the equilibrium equations of FGM plate with flexible support in thermal environment are derived. The separation-of-variables method is adopted to obtain the exact solutions for thermal buckling problems of FGM rectangular thin plates with simply supported boundary condition and clamped boundary condition. The buckling of FGM plates under three types of thermal loads is analyzed. The present formulations and solutions are validated by comprehensive comparisons with results in literature.
引文
[1]Javaheri R,Eslami M R.Thermal buckling of functionally graded plates[J].AIAA journal,2002,40(1):162-169.
[2]Javaheri R,Eslami M R.Buckling of functionally graded plates under in-plane compressive loading[J].Zamm-journal of applied mathematics and mechanics/zeitschrift für angewandte mathematik und mechanik,2002,82(4):277-283.
[3]Kiani Y,Bagherizadeh E,Eslami M R.Thermal buckling of clamped thin rectangular FGM plates resting on pasternak elastic foundation(three approximate analytical solutions)[J].Zamm-journal of applied mathematics and mechanics/zeitschrift für angewandte mathematik und mechanik,2011,91(7):581-593.
[4]Ghannadpour S A M,Ovesy H R,Nassirnia M.Buckling analysis of functionally graded plates under thermal loadings using the finite strip method[J].Computers&structures,2012,108:93-99.
[5]Ghomshei M M,Abbasi V.Thermal buckling analysis of annular FGM plate having variable thickness under thermal load of arbitrary distribution by finite element method[J].Journal of mechanical science and technology,2013,27(4):1031-1039.
[6]Lanhe W.Thermal buckling of a simply supported moderately thick rectangular FGM plate[J].Composite structures,2004,64(2):211-218.
[7]Bouazza M,Tounsi A,Adda-Bedia E A,et al.Thermoelastic stability analysis of functionally graded plates:An analytical approach[J].Computational materials science,2010,49(4):865-870.
[8]Ganapathi M,Prakash T,Sundararajan N.Influence of functionally graded material on buckling of skew plates under mechanical loads[J].Journal of engineering mechanics,2006,132(8):902-905.
[9]Yaghoobi H,Yaghoobi P.Buckling analysis of sandwich plates with FGM face sheets resting on elastic foundation with various boundary conditions:an analytical approach[J].Meccanica,2013,48(8):2019-2035.
[10]Zhang L W,Zhu P,Liew K M.Thermal buckling of functionally graded plates using a local Kriging meshless method[J].Composite structures,2014,108:472-492.
[11]Lee Y H,Bae S I,Kim J H.Thermal buckling behavior of functionally graded plates based on neutral surface[J].Composite structures,2016,137:208-214.
[12]宫文然,吴振强,李海波,等.飞行器壁板结构热屈曲分析和试验研究进展[J].强度与环境,2016,43(4):9-16.
[13]吴振强,李海波,程昊,等.热环境下金属壁板噪声激励动响应试验研究[J].强度与环境,2016,43(2):25-33.
[14]Xu T F,Xing Y F.Closed-form solutions for free vibration of rectangular FGM thin plates resting on elastic foundation[J].Acta mechanica sinica,2016,32(6):1-16.
[15]陈蕾,胡祖明.芳纶1313纤维制备技术进展[J].高分子通报,2014,6:1-8.
[2]Javaheri R,Eslami M R.Buckling of functionally graded plates under in-plane compressive loading[J].Zamm-journal of applied mathematics and mechanics/zeitschrift für angewandte mathematik und mechanik,2002,82(4):277-283.
[3]Kiani Y,Bagherizadeh E,Eslami M R.Thermal buckling of clamped thin rectangular FGM plates resting on pasternak elastic foundation(three approximate analytical solutions)[J].Zamm-journal of applied mathematics and mechanics/zeitschrift für angewandte mathematik und mechanik,2011,91(7):581-593.
[4]Ghannadpour S A M,Ovesy H R,Nassirnia M.Buckling analysis of functionally graded plates under thermal loadings using the finite strip method[J].Computers&structures,2012,108:93-99.
[5]Ghomshei M M,Abbasi V.Thermal buckling analysis of annular FGM plate having variable thickness under thermal load of arbitrary distribution by finite element method[J].Journal of mechanical science and technology,2013,27(4):1031-1039.
[6]Lanhe W.Thermal buckling of a simply supported moderately thick rectangular FGM plate[J].Composite structures,2004,64(2):211-218.
[7]Bouazza M,Tounsi A,Adda-Bedia E A,et al.Thermoelastic stability analysis of functionally graded plates:An analytical approach[J].Computational materials science,2010,49(4):865-870.
[8]Ganapathi M,Prakash T,Sundararajan N.Influence of functionally graded material on buckling of skew plates under mechanical loads[J].Journal of engineering mechanics,2006,132(8):902-905.
[9]Yaghoobi H,Yaghoobi P.Buckling analysis of sandwich plates with FGM face sheets resting on elastic foundation with various boundary conditions:an analytical approach[J].Meccanica,2013,48(8):2019-2035.
[10]Zhang L W,Zhu P,Liew K M.Thermal buckling of functionally graded plates using a local Kriging meshless method[J].Composite structures,2014,108:472-492.
[11]Lee Y H,Bae S I,Kim J H.Thermal buckling behavior of functionally graded plates based on neutral surface[J].Composite structures,2016,137:208-214.
[12]宫文然,吴振强,李海波,等.飞行器壁板结构热屈曲分析和试验研究进展[J].强度与环境,2016,43(4):9-16.
[13]吴振强,李海波,程昊,等.热环境下金属壁板噪声激励动响应试验研究[J].强度与环境,2016,43(2):25-33.
[14]Xu T F,Xing Y F.Closed-form solutions for free vibration of rectangular FGM thin plates resting on elastic foundation[J].Acta mechanica sinica,2016,32(6):1-16.
[15]陈蕾,胡祖明.芳纶1313纤维制备技术进展[J].高分子通报,2014,6:1-8.