تحليلﺧﻤﺶ ﺗﯿﺮ ﺳﺎﻧﺪوﯾﭽﯽ اﻧﺤﻨﺎدار ﺑﺎ روﯾﻪ ﻫﺎي ﺗﻘﻮﯾﺖ ﺷﺪه ﺑﺎ ﻧﺎﻧﻮ ﻟﻮﻟﻪ ﮐﺮﺑﻨﯽ ﻣﺪرج و ﻫﺴﺘﻪ اﻧﻌﻄﺎف ﭘﺬﯾﺮ

Bending analysis of the curved sandwich beam with FG-CNT reinforced faces and flexible core

در اﯾﻦ ﻣﻘﺎﻟﻪ ﺑﻪ ﺑﺮرﺳﯽ رﻓﺘﺎر ﺧﻤﺸﯽ ﯾﮏ ﺗﯿﺮ ﺳﺎﻧﺪوﯾﭽﯽ اﻧﺤﻨﺎدار ﺑﺎ ﻫﺴﺘﻪ اﻧﻌﻄﺎف ﭘﺬﯾﺮ و روﯾﻪ ﻫﺎي ﮐﺎﻣﭙﻮزﯾﺘﯽ ﺗﻘﻮﯾﺖ ﺷﺪه ﺑﺎ ﻧﺎﻧﻮ ﻟﻮﻟﻪ ﮐﺮﺑﻨﯽ ﭘﺮداﺧﺘﻪ ﺷﺪه اﺳﺖ. ﻧﺎﻧﻮ ﻟﻮﻟﻪ ﻫﺎي ﮐﺮﺑﻨﯽ ﺑﻪ ﺻﻮرت ﻣﻮاد ﺗﺎﺑﻌﯽ ﻣﺪرج در ﺿﺨﺎﻣﺖ روﯾﻪ در ﻧﻈﺮ ﮔﺮﻓﺘﻪ ﺷﺪه اﺳﺖ و ﺧﻮاص آﻧﻬﺎ در راﺳﺘﺎي ﺿﺨﺎﻣﺖ روﯾﻪ ﻫﺎ ﺗﻐﯿﯿﺮ ﻣﯽ ﮐﻨﺪ. ﺑﺮاي ﻣﺪل ﺳﺎزي رﻓﺘﺎر ﺗﯿﺮ ﺳﺎﻧﺪوﯾﭽﯽ از ﺗﺌﻮري اوﯾﻠﺮ-ﺑﺮﻧﻮﻟﯽ ﺑﺮاي روﯾﻪ ﻫﺎ و اﻻﺳﺘﯿﺴﯿﺘﻪ ﺷﺒﻪ ﺳﻪ ﺑﻌﺪي ﺑﺮاي ﻫﺴﺘﻪ اﺳﺘﻔﺎده ﺷﺪه ﮐﻪ اﯾﻦ اﻣﺮ اﻣﮑﺎن ﺑﺮرﺳﯽ اﻧﻌﻄﺎف ﭘﺬﯾﺮي ﻫﺴﺘﻪ را ﻓﺮاﻫﻢ ﻣﯽﮐﻨﺪ. در اﯾﻦ ﺣﯿﻦ ﻫﻤﭽﻨﯿﻦ از اﻋﻤﺎل ﺷﺮاﯾﻂ ﺳﺎزﮔﺎري ﺑﯿﻦ روﯾﻪ ﻫﺎ و ﻫﺴﺘﻪ اﺳﺘﻔﺎده ﻣﯽ ﺷﻮد. ﻣﻌﺎدﻻت دﯾﻔﺮاﻧﺴﯿﻞ ﺣﺎﮐﻢ ﺑﺎ اﺳﺘﻔﺎده از اﺻﻞ ﺟﺎﺑﻪ ﺟﺎﯾﯽ ﻣﺠﺎزي اﺳﺘﺨﺮاج ﺷﺪهاﻧﺪ. ﺟﻬﺖ اﻋﺘﺒﺎر ﺳﻨﺠﯽ دﻗﺖ روش ﺣﺎﺿﺮ، ﻧﺘﺎﯾﺞ ﺑﺪﺳﺖ آﻣﺪه ﺑﺎ ﻧﺘﺎﯾﺞ ﻣﺸﺎﺑﻪ ﻣﻮﺟﻮد در ﺣﯿﻄﻪ ي اﯾﻦ ﻣﻮﺿﻮع ﻣﻘﺎﯾﺴﻪ و از ﺻﺤﺖ ﻣﻌﺎدﻻت اﺳﺘﺨﺮاج ﺷﺪه و ﺣﻞ آن ﻫﺎ اﻃﻤﯿﻨﺎن ﺣﺎﺻﻞ ﮔﺮدﯾﺪه اﺳﺖ. ﺑﺪﯾﻦ ﺗﺮﺗﯿﺐ ﺗﺎﺛﯿﺮ اﻟﮕﻮﻫﺎي ﻣﺨﺘﻠﻒ ﺗﻮزﯾﻊ ﻧﺎﻧﻮ ﻟﻮﻟﻪ ﻫﺎي ﮐﺮﺑﻨﯽ ﺑﺮ روي ﻣﻘﺪار ﺧﯿﺰ، ﺗﻐﯿﯿﺮ ﻣﮑﺎن ﻣﻤﺎﺳﯽ، ﻧﯿﺮوي ﻣﺤﻮري و ﻣﻤﺎن ﺧﻤﺸﯽ در روﯾﻪ ﻫﺎ و ﻫﻤﭽﻨﯿﻦ ﻣﻘﺪار ﺗﻨﺶ ﺷﻌﺎﻋﯽ و ﺑﺮﺷﯽ در ﻫﺴﺘﻪ ﻣﻮرد ﺑﺮرﺳﯽ و ﻣﻘﺎﯾﺴﻪ ﻗﺮار ﮔﺮﻓﺘﻪ اﻧﺪ. ﻫﻤﭽﻨﯿﻦ ﺗﺎﺛﯿﺮ ﻣﻘﺪار ﮐﺴﺮ ﺣﺠﻤﯽ ﻧﺎﻧﻮﻟﻮﻟﻪ ﻫﺎي ﮐﺮﺑﻨﯽ، ﻧﺴﺒﺖ ﺿﺨﺎﻣﺖ ﻫﺴﺘﻪ ﺑﻪ روﯾﻪ ﻫﺎ و ﻣﻘﺪار ﺷﻌﺎع و زاوﯾﻪ اﻧﺤﻨﺎي ﺗﯿﺮ ﺑﺮ ﻧﺘﺎﯾﺞ ﺑﺮرﺳﯽ ﺷﺪه اﻧﺪ. ﻧﺘﺎﯾﺞ ﻧﺸﺎن ﻣﯽ دﻫﺪ ﮐﻪ ﺑﯿﺸﺘﺮﯾﻦ ﻣﻘﺪار ﺗﻐﯿﯿﺮ ﻣﮑﺎن ﺷﻌﺎﻋﯽ و ﻣﻤﺎﺳﯽ در روﯾﻪ ﻫﺎ و ﻫﺴﺘﻪ و ﻫﻤﭽﻨﯿﻦ ﺑﯿﺸﺘﺮﯾﻦ ﻣﻘﺪار ﺗﻨﺶ ﺑﺮﺷﯽ و ﺷﻌﺎﻋﯽ در ﻫﺴﺘﻪ ﻣﺮﺑﻮط ﺑﻪ ﺗﻮزﯾﻊ A و ﮐﻤﺘﺮﯾﻦ آنﻫﺎ ﻣﺮﺑﻮط ﺑﻪ ﺗﻮزﯾﻊ V ﻣﯽ ﺑﺎﺷﺪ.

The present study investigated the bending behavior of a curved sandwich beam with flexible core and carbon nanotube reinforced face sheets. Carbon nanotubes are considered as functional graded material in the thickness of the face sheets and their properties change along the thickness of the face sheets. In order to model the behavior of the sandwich beam, the Euler-Bernoulli theory was applied for the face sheets and the quasi 3D elasticity was applied for the core, which allowed us to investigate the flexibility of the core. In this regard also, the compatibility condition between the face sheets and the core is used. The governing differential equations were extracted by using the principle of virtual displacement. In order to verify the accuracy of the formulation and present method, the results were compared with the existing results in this domain and was verified the validity of the extracted and solved equations. Therefore, the effect of different patterns of carbon nanotubes distribution have been investigated and compared on the radial deflection, the tangent displacement, the axial force, and the bending moment in the faces and the radial and shear stresses in the core. Also, the effect of the volume fraction of the carbon nanotubes, the ratio of the core thickness to the faces, and the beam curvature radius and angle have been investigated on results.