含孔隙变厚度FG圆板的湿热力学响应
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摘要
功能梯度材料(functionally graded materials,FGM)是组份含量按特定方向连续变化的非均匀复合材料,可有效解决传统复合材料组份之间结合能力弱和不同组份性能难以协调等问题,达到诸如缓和应力集中和优化应力分布等效果,使整体材料在保持细观结构完整性的同时充分发挥各组份材料的性能优势.由于制备技术等原因或出于特殊功能的需要,微孔或孔隙是各类型FGM中的常见缺陷.从细观结构上看,多孔FGM中的孔隙包含了单一组份内的材料孔隙和组份微粒间的结构间隙,这些孔隙将对FGM的力学性能,尤其是在湿热环境下的力学行为产生影响.本文考虑FGM中的两类细观孔隙(材料孔隙和结构孔隙),提出了令各类孔隙依赖于各自组份变化,再线性叠加得到的整体孔隙计算式.考虑组份材料和孔隙填充物(液相水和水蒸气)性质的温度相关性,建立了湿热相关FGM材料模型.针对厚度沿径向变化的旋转圆板结构,应用该FGM材料模型,推导了圆板的非线性稳态湿热控制方程及考虑湿热弹性本构的位移控制方程,采用微分求积法(differential quadrature method,DQM),获得了圆板的湿热场、位移场和应力分布.在数值算例中,利用退化模型的解析解对本文的数值计算方法进行了验证,继而通过改变各关键参数,讨论了两类孔隙率、梯度指数和圆板厚度变化对含孔隙FGM变厚度旋转圆板湿热力学响应的影响规律.
Functionally graded materials(FGMs) are composed of two or more discrete constituent phases with continuous and smoothly varying components. Due to the distinctive merit comparing with usual composite materials that they can reduce the stress concentration and optimize the stress distribution to make good use of each component, utilizing of FGMs helps to resolve some problems in composite materials such as low bond strength and inharmonious of properties effectively. Because of the preparation technology or for the need of special structures, micropores or pores are commonly found in various types of FGM and play an important role in the influence factors on mechanical properties of FGMs.In addition, the application conditions of FGMs are usually complex or extreme with multiple physical fields, and the mechanical responses of various FGMs under coupling multi-fields will be more complex. On micro scale, the pores in porous FGM include material pores of each components and structural gaps between different particles. These pores will affect the properties of FGM, especially under hygrothermal environments. In this paper, two kinds of micro pores(material pores and structural gaps) in FGM are both considered. An expression to characterize porosity of the whole FGM is proposed, where the porosity of each component is related to its volume fraction and the global porosity is a linear superposition. Considering temperature dependency of the component properties as well as the material properties of pore fillers(liquid water or vapor), a prediction model of the porous FGM is established. Focusing on a rotating circular plate with its thickness varying along the radial direction, and applying the current porous FGM model, governing equations of the nonlinear steady-state temperature and moisture fields as well as displacement field are derived. Solving the governing equations by the differential quadrature method(DQM), distributions of temperature, moisture, displacement and stress of the FG circular plate are obtained. In the numerical examples, analytic solution of a simplified mechanical model is carried out to verify the numerical calculation process of the current study. By changing the key parameters, influences of each porosity, gradient index and thickness change rule on the hygrothermal mechanical responses of the porous FG circular plate with variable thickness are discussed in detail.
Functionally graded materials(FGMs) are composed of two or more discrete constituent phases with continuous and smoothly varying components. Due to the distinctive merit comparing with usual composite materials that they can reduce the stress concentration and optimize the stress distribution to make good use of each component, utilizing of FGMs helps to resolve some problems in composite materials such as low bond strength and inharmonious of properties effectively. Because of the preparation technology or for the need of special structures, micropores or pores are commonly found in various types of FGM and play an important role in the influence factors on mechanical properties of FGMs.In addition, the application conditions of FGMs are usually complex or extreme with multiple physical fields, and the mechanical responses of various FGMs under coupling multi-fields will be more complex. On micro scale, the pores in porous FGM include material pores of each components and structural gaps between different particles. These pores will affect the properties of FGM, especially under hygrothermal environments. In this paper, two kinds of micro pores(material pores and structural gaps) in FGM are both considered. An expression to characterize porosity of the whole FGM is proposed, where the porosity of each component is related to its volume fraction and the global porosity is a linear superposition. Considering temperature dependency of the component properties as well as the material properties of pore fillers(liquid water or vapor), a prediction model of the porous FGM is established. Focusing on a rotating circular plate with its thickness varying along the radial direction, and applying the current porous FGM model, governing equations of the nonlinear steady-state temperature and moisture fields as well as displacement field are derived. Solving the governing equations by the differential quadrature method(DQM), distributions of temperature, moisture, displacement and stress of the FG circular plate are obtained. In the numerical examples, analytic solution of a simplified mechanical model is carried out to verify the numerical calculation process of the current study. By changing the key parameters, influences of each porosity, gradient index and thickness change rule on the hygrothermal mechanical responses of the porous FG circular plate with variable thickness are discussed in detail.
引文
1 Heydari A,Jalali A,Nemati A.Buckling analysis of circular functionally graded plate under uniform radial compression including shear deformation with linear and quadratic thickness variation on the Pasternak elastic foundation.Applied Mathematical Modelling,2017,41:494-507
2 Moita JS,Ara′ujo AL,Correia VF,et al.Buckling and nonlinear response of functionally graded plates under thermo-mechanical loading.Composite Structures,2018,https://doi.org/10.1016/j.compstruct.2018.03.082
3 Yu TT,Yin SH,Bui TQ,et al.Buckling isogeometric analysis of functionally graded plates under combined thermal and mechanical loads.Composite Structures,2017,162:54-69
4 Nguyen TN,Thai CH,Nguyen-Xuan H,et al.Geometrically nonlinear analysis of functionally graded material plates using an improved moving Kriging meshfree method based on a refined plate theory.Composite Structures,2018,193:268-280
5 Ashoori AR,Sadough Vanini SA.Nonlinear bending,postbuckling and snap-through of circular sizedependent functionally graded piezoelectric plates.Thin-Walled Structures,2017,111:19-28
6 Yin SH,Yu TT,Bui TQ,et al.Rotation-free isogeometric analysis of functionally graded thin plates considering in-plane material inhomogeneity.Thin-Walled Structures,2017,119:385-395
7 Thai S,Thai HT,Vo TP,et al.Size-dependant behaviour of functionally graded microplates based on the modified strain gradient elasticity theory and isogeometric analysis.Computers and Structures,2017,190:219-241
8张靖华,潘双超,李世荣.热冲击下功能梯度圆板的动力屈曲.应用力学学报,2015,32(6):901-906(Zhang Jinghua,Pan Shuangchao,Li Shirong.Dynamic buckling of functionally graded circular plate under thermal shock.Chinese Journal of Applied Mechanics,2015,32(6):901-906(in Chinese))
9 Dai HL,Yan X,Yang L.Nonlinear dynamic analysis for FGM circular plates.Journal of Mechanics,2013,29(2):287-296
10 Dai HL,Guo ZY,Yang L.Nonlinear dynamic response of functionally graded materials circular plates subject to low-velocity impact.Journal of Composite Materials,2012,47(22):2797-280711 Lal R,Ahlawat N.Buckling and vibrations of two-directional functionally graded circular plates subjected to hydrostatic inplane force.Journal of Vibration and Control,2017,23(13):2111-2127
12 Yousefzadeh SH,Jafari AA,Mohammadzadeh A.Effect of hydrostatic pressure on vibrating functionally graded circular plate coupled with bounded fluid.Applied Mathematical Modelling,2018,60:435-446
13 Mahinzare M,Ranjbarpur H,Ghadiri M.Free vibration analysis of a rotary smart two directional functionally graded piezoelectric material in axial symmetry circular nanoplate.Mechanical Systems and Signal Processing,2018,100:188-207
14夏巍,冯浩成.热过屈曲功能梯度壁板的气动弹性颤振.力学学报,2016,48(3):609-614(Xia Wei,Feng Haocheng.Aeroelastic flutter of post-buckled functionally graded panels.Chinese Journal of Theoretical and Applied Mechanics,2016,48(3):609-614(in Chinese))
15许新,李世荣.功能梯度材料微梁的热弹性阻尼研究.力学学报,2017,49(2):308-316(Xu Xin,Li Shirong.Analysis of thermoelastic damping for functionally graded material micro-beam.Chinese Journal of Theoretical and Applied Mechanics,2017,49(2):308-316(in Chinese))
16高晨彤,黎亮,章定国等.考虑剪切效应的旋转FGM楔形梁刚柔耦合动力学建模与仿真.力学学报,2018,50(3):654-666(Gao Chentong,Li Liang,Zhang Dingguo,et al.Dynamic modeling and simulation of rotating FGM tapered beams with shear effect.Chinese Journal of Theoretical and Applied Mechanics,2018,50(3):654-666(in Chinese))
17许良,赵昺,马少华等.湿热环境下复合材料板拉-压性能.材料工程,2018,46(3):124-130(Xu Liang,Zhao Bing,Ma Shaohua,et al.Tensile and compress property of composite laminate in hygrothermal environment.Journal of Materials Engineering,2018,46(3):124-130(in Chinese))
18赵天,杨智春,田玮等.湿热环境下复合材料层合板振动与声辐射特性分析.航空学报,2017,38(10):221038(1-
10)(Zhao Tian,Yang Zhichun,Tian Wei,et al.Vibration and acoustic radiation characteristics analysis of composite laminated plate in hygrothermal environment.Acta Aeronutica et Astronautica Sinica,2017,38(10):221038(1-10)(in Chinese))
19苏伯阳,李书欣,刘立胜等.湿热环境下复合材料冲击损伤的近场动力学模拟.科学技术与工程,2018,18(1):201-206(Su Boyang,Li Shuxin,Liu Lisheng,et al.Peridynamic simulation of impact damage of composite material under hygrothermal environment.Science Technology and Engineering,2018,18(1):201-206(in Chinese))
20吴振,刘子茗.湿热力载荷下复合材料层合板力学行为.工程力学,2016,33(11):11-19(Wu Zhen,Liu Ziming.Mechanical behaviors of laminated composite plate subject to hygro-thermomechanical loading.Engineering Mechanics,2016,33(11):11-19(in Chinese))
21王柏臣,刘永娜,李伟等.湿热环境对PMMA混杂纳米复合材料性能的影响.装备环境工程,2018,15(2):36-40(Wang Baichen,Liu Yongna,Li Wei,et al.Effects of hygrothermal environment on properties of PMMA hybrid nanocomposites.Equipment Environmental Engineering,2018,15(2):36-40(in Chinese))
22曹志远,程红梅.空隙、杂质及组分突变对功能梯度构件动力特性的影响.复合材料学报,2007,24(5):136-141(Cao Zhiyuan,Cheng Hongmei.Influence of gap,impurities and component mutation on dynamic character of functionally graded structures.Acta Materiae Compositae Sinica,2007,24(5):136-141(in Chinese))
23 Zenkour AM.A quasi-3D refined theory for functionally graded single-layered and sandwich plates with porosities.Composite Structures,2018,201:38-48
24 Boutahar L,Bikri KE,Benamar R.A homogenization procedure for geometrically non-linear free vibration analysis of functionally graded annular plates with porosities,resting on elastic foundations.Ain Shams Engineering Journal,2016,7:313-333
25 Kiran MC,Kattimani SC.Assessment of porosity influence on vibration and static behaviour of functionally graded magnetoelectro-elastic plate:A finite element study.European Journal of Mechanics/A Solids,2018,71:258-277
26 Rezaei AS,Saidi AR,Abrishamdari M,et al.Natural frequencies of functionally graded plates with porosities via a simple four variable plate theory:An analytical approach.Thin-Walled Structures,2017,120:366-377
27 Kiran MC,Kattimani SC,Vinyas M.Porosity influence on structural behaviour of skew functionally graded magneto-electroelastic plate.Composite Structures,2018,191:36-77
28 Wang YQ,Zu JW.Vibration behaviors of functionally graded rectangular plates with porosities and moving in thermal environment.Aerospace Science and Technology,2017,69:550-562
29郑保敬,梁钰,高效伟等.功能梯度材料动力学问题的POD模型降阶分析.力学学报,2018,50(4):787-797(Zheng Baojing,Liang Yu,Gao Xiaowei,et al.Analysis for dynamic response of functionally graded materials using POD based reduced order model.Chinese Journal of Theoretical and Applied Mechanics,2018,50(4):787-797(in Chinese))
30 Damircheli M,Azadi M.Temperature and thickness effects on thermal and mechanical stresses of rotating FG-disks.Journal of Mechanical Science and Technology,2011,25(3):827
31 Fung T.Solving initial value problems by differential quadrature method-part 1:First-order equations.International Journal for Numerical Methods in Engineering,2001,50(6):1411-1427
32叶天贵,靳国永,刘志刚.多层复合壳体三维振动分析的谱-微分求积混合法.力学学报,2018,50(4):847-852(Ye Tiangui,Jin Guoyong,Liu Zhigang.A spectral-differential quadrature method for 3-D vibration analysis of multilayered shells.Chinese Journal of Theoretical and Applied Mechanics,2018,50(4):847-852(in Chinese))
33 Reddy J,Chin C.Thermomechanical analysis of functionally graded cylinders and plates.Journal of thermal Stresses,1998,21(6):593-626
2 Moita JS,Ara′ujo AL,Correia VF,et al.Buckling and nonlinear response of functionally graded plates under thermo-mechanical loading.Composite Structures,2018,https://doi.org/10.1016/j.compstruct.2018.03.082
3 Yu TT,Yin SH,Bui TQ,et al.Buckling isogeometric analysis of functionally graded plates under combined thermal and mechanical loads.Composite Structures,2017,162:54-69
4 Nguyen TN,Thai CH,Nguyen-Xuan H,et al.Geometrically nonlinear analysis of functionally graded material plates using an improved moving Kriging meshfree method based on a refined plate theory.Composite Structures,2018,193:268-280
5 Ashoori AR,Sadough Vanini SA.Nonlinear bending,postbuckling and snap-through of circular sizedependent functionally graded piezoelectric plates.Thin-Walled Structures,2017,111:19-28
6 Yin SH,Yu TT,Bui TQ,et al.Rotation-free isogeometric analysis of functionally graded thin plates considering in-plane material inhomogeneity.Thin-Walled Structures,2017,119:385-395
7 Thai S,Thai HT,Vo TP,et al.Size-dependant behaviour of functionally graded microplates based on the modified strain gradient elasticity theory and isogeometric analysis.Computers and Structures,2017,190:219-241
8张靖华,潘双超,李世荣.热冲击下功能梯度圆板的动力屈曲.应用力学学报,2015,32(6):901-906(Zhang Jinghua,Pan Shuangchao,Li Shirong.Dynamic buckling of functionally graded circular plate under thermal shock.Chinese Journal of Applied Mechanics,2015,32(6):901-906(in Chinese))
9 Dai HL,Yan X,Yang L.Nonlinear dynamic analysis for FGM circular plates.Journal of Mechanics,2013,29(2):287-296
10 Dai HL,Guo ZY,Yang L.Nonlinear dynamic response of functionally graded materials circular plates subject to low-velocity impact.Journal of Composite Materials,2012,47(22):2797-280711 Lal R,Ahlawat N.Buckling and vibrations of two-directional functionally graded circular plates subjected to hydrostatic inplane force.Journal of Vibration and Control,2017,23(13):2111-2127
12 Yousefzadeh SH,Jafari AA,Mohammadzadeh A.Effect of hydrostatic pressure on vibrating functionally graded circular plate coupled with bounded fluid.Applied Mathematical Modelling,2018,60:435-446
13 Mahinzare M,Ranjbarpur H,Ghadiri M.Free vibration analysis of a rotary smart two directional functionally graded piezoelectric material in axial symmetry circular nanoplate.Mechanical Systems and Signal Processing,2018,100:188-207
14夏巍,冯浩成.热过屈曲功能梯度壁板的气动弹性颤振.力学学报,2016,48(3):609-614(Xia Wei,Feng Haocheng.Aeroelastic flutter of post-buckled functionally graded panels.Chinese Journal of Theoretical and Applied Mechanics,2016,48(3):609-614(in Chinese))
15许新,李世荣.功能梯度材料微梁的热弹性阻尼研究.力学学报,2017,49(2):308-316(Xu Xin,Li Shirong.Analysis of thermoelastic damping for functionally graded material micro-beam.Chinese Journal of Theoretical and Applied Mechanics,2017,49(2):308-316(in Chinese))
16高晨彤,黎亮,章定国等.考虑剪切效应的旋转FGM楔形梁刚柔耦合动力学建模与仿真.力学学报,2018,50(3):654-666(Gao Chentong,Li Liang,Zhang Dingguo,et al.Dynamic modeling and simulation of rotating FGM tapered beams with shear effect.Chinese Journal of Theoretical and Applied Mechanics,2018,50(3):654-666(in Chinese))
17许良,赵昺,马少华等.湿热环境下复合材料板拉-压性能.材料工程,2018,46(3):124-130(Xu Liang,Zhao Bing,Ma Shaohua,et al.Tensile and compress property of composite laminate in hygrothermal environment.Journal of Materials Engineering,2018,46(3):124-130(in Chinese))
18赵天,杨智春,田玮等.湿热环境下复合材料层合板振动与声辐射特性分析.航空学报,2017,38(10):221038(1-
10)(Zhao Tian,Yang Zhichun,Tian Wei,et al.Vibration and acoustic radiation characteristics analysis of composite laminated plate in hygrothermal environment.Acta Aeronutica et Astronautica Sinica,2017,38(10):221038(1-10)(in Chinese))
19苏伯阳,李书欣,刘立胜等.湿热环境下复合材料冲击损伤的近场动力学模拟.科学技术与工程,2018,18(1):201-206(Su Boyang,Li Shuxin,Liu Lisheng,et al.Peridynamic simulation of impact damage of composite material under hygrothermal environment.Science Technology and Engineering,2018,18(1):201-206(in Chinese))
20吴振,刘子茗.湿热力载荷下复合材料层合板力学行为.工程力学,2016,33(11):11-19(Wu Zhen,Liu Ziming.Mechanical behaviors of laminated composite plate subject to hygro-thermomechanical loading.Engineering Mechanics,2016,33(11):11-19(in Chinese))
21王柏臣,刘永娜,李伟等.湿热环境对PMMA混杂纳米复合材料性能的影响.装备环境工程,2018,15(2):36-40(Wang Baichen,Liu Yongna,Li Wei,et al.Effects of hygrothermal environment on properties of PMMA hybrid nanocomposites.Equipment Environmental Engineering,2018,15(2):36-40(in Chinese))
22曹志远,程红梅.空隙、杂质及组分突变对功能梯度构件动力特性的影响.复合材料学报,2007,24(5):136-141(Cao Zhiyuan,Cheng Hongmei.Influence of gap,impurities and component mutation on dynamic character of functionally graded structures.Acta Materiae Compositae Sinica,2007,24(5):136-141(in Chinese))
23 Zenkour AM.A quasi-3D refined theory for functionally graded single-layered and sandwich plates with porosities.Composite Structures,2018,201:38-48
24 Boutahar L,Bikri KE,Benamar R.A homogenization procedure for geometrically non-linear free vibration analysis of functionally graded annular plates with porosities,resting on elastic foundations.Ain Shams Engineering Journal,2016,7:313-333
25 Kiran MC,Kattimani SC.Assessment of porosity influence on vibration and static behaviour of functionally graded magnetoelectro-elastic plate:A finite element study.European Journal of Mechanics/A Solids,2018,71:258-277
26 Rezaei AS,Saidi AR,Abrishamdari M,et al.Natural frequencies of functionally graded plates with porosities via a simple four variable plate theory:An analytical approach.Thin-Walled Structures,2017,120:366-377
27 Kiran MC,Kattimani SC,Vinyas M.Porosity influence on structural behaviour of skew functionally graded magneto-electroelastic plate.Composite Structures,2018,191:36-77
28 Wang YQ,Zu JW.Vibration behaviors of functionally graded rectangular plates with porosities and moving in thermal environment.Aerospace Science and Technology,2017,69:550-562
29郑保敬,梁钰,高效伟等.功能梯度材料动力学问题的POD模型降阶分析.力学学报,2018,50(4):787-797(Zheng Baojing,Liang Yu,Gao Xiaowei,et al.Analysis for dynamic response of functionally graded materials using POD based reduced order model.Chinese Journal of Theoretical and Applied Mechanics,2018,50(4):787-797(in Chinese))
30 Damircheli M,Azadi M.Temperature and thickness effects on thermal and mechanical stresses of rotating FG-disks.Journal of Mechanical Science and Technology,2011,25(3):827
31 Fung T.Solving initial value problems by differential quadrature method-part 1:First-order equations.International Journal for Numerical Methods in Engineering,2001,50(6):1411-1427
32叶天贵,靳国永,刘志刚.多层复合壳体三维振动分析的谱-微分求积混合法.力学学报,2018,50(4):847-852(Ye Tiangui,Jin Guoyong,Liu Zhigang.A spectral-differential quadrature method for 3-D vibration analysis of multilayered shells.Chinese Journal of Theoretical and Applied Mechanics,2018,50(4):847-852(in Chinese))
33 Reddy J,Chin C.Thermomechanical analysis of functionally graded cylinders and plates.Journal of thermal Stresses,1998,21(6):593-626