ﺗﺤﻠﻴﻞ ﭘﺎﻳﺪاري ﺣﺮارﺗﻲ ﭘﻮﺳﺘﻪ اﺳﺘﻮاﻧﻪاي ﺗﻘﻮﻳﺖ ﺷﺪه ﺑﺎ ورقﻫﺎي ﮔﺮاﻓﻦ GPL ﺑﺎ اﺳﺘﻔﺎده از روش ﻣﺮﺑﻌﺎت ﺗﻔﺎﺿﻠﻲ

Thermal stability analysis of cylindrical shell reinforced with GPL graphene sheets using differential squares method

ﻣﻘﺎﻟﻪ ﺣﺎﺿﺮ ﺑﻪ ﺗﺤﻠﻴﻞ ﻛﻤﺎﻧﺶ ﺣﺮارﺗﻲ ﭘﻮﺳﺘﻪ اﺳﺘﻮاﻧﻪ ﺗﺤﺖ اﻓﺰاﻳﺶ دﻣﺎي ﻳﻜﻨﻮاﺧﺖ ﻣﻲﭘﺮدازد. ﭘﻮﺳﺘﻪ ﻧﺎﻧﻮﻛﺎﻣﭙﻮزﻳﺘﻲ از ﻻﻳﻪﻫﺎي ﺗﻘﻮﻳﺖ ﺷﺪه ﺑﺎ ورقﻫﺎي ﮔﺮاﻓﻦ Graphene Platelets ﺗﺸﻜﻴﻞ ﺷﺪه اﺳﺖ. ﻧﺎﻧﻮورقﻫﺎ ﺑﻪ ﺻﻮرت ﺗﺼﺎدﻓﻲ و ﻳﻜﻨﻮاﺧﺖ در ﻫﺮ ﻻﻳﻪ ﺗﻮزﻳﻊ ﺷﺪهاﻧﺪ. ﻣﻘﺪار ﻛﺴﺮ ﺣﺠﻤﻲ ﮔﺮاﻓﻦﻫﺎ ﺑﻪ ﺻﻮرت ﺗﺎﺑﻌﻲ ﻣﺪرج FG در ﺟﻬﺖ ﺿﺨﺎﻣﺖ ﭘﻮﺳﺘﻪ ﺗﻐﻴﻴﺮ ﻣﻲﻛﻨﺪ. ﺧﻮاص ﻣﺆﺛﺮ اﻻﺳﺘﻴﻚ ﭘﻮﺳﺘﻪ ﺑﺎ اﺳﺘﻔﺎده از ﻗﺎﻧﻮن ﻫﺎﻟﭙﻴﻦ-ﺳﺎي ﺑﻪ دﺳﺖ آﻣﺪه اﺳﺖ. ﻣﻴﺪان ﺟﺎﺑﺠﺎﻳﻲ ﺑﺮ اﺳﺎس ﺗﺌﻮري ﻣﺮﺗﺒﻪ اول ﺗﻐﻴﻴﺮ ﺷﻜﻞ ﺑﺮﺷﻲ و ﻣﻌﺎدﻻت ﺳﻴﻨﻤﺎﺗﻴﻜﻲ ﭘﻮﺳﺘﻪ اﺳﺘﻮاﻧﻪاي ﺑﺎ اﺳﺘﻔﺎده از ﺗﺌﻮري ﻏﻴﺮﺧﻄﻲ ﻫﻨﺪﺳﻲ ون-ﻛﺎرﻣﻦ و داﻧﻞ اﺳﺘﺨﺮاج ﺷﺪهاﻧﺪ. ﻣﻌﺎدﻻت ﺗﻌﺎدل ﭘﺲ از ﺗﺤﻠﻴﻞ ﭘﻴﺶﻛﻤﺎﻧﺶ ﺗﻮﺳﻂ روش ﻣﺮﺑﻌﺎت ﺗﻔﺎﺿﻠﻲ ﺗﻌﻤﻴﻢﻳﺎﻓﺘﻪ GDQ ﺟﺪاﺳﺎزي ﺷﺪه و در ﻧﻬﺎﻳﺖ ﻣﺴﺌﻠﻪ ﻣﻘﺪار وﻳﮋه ﺣﻞ ﺷﺪه ﺗﺎ دﻣﺎي ﺑﺤﺮاﻧﻲ ﭘﻮﺳﺘﻪ اﺳﺘﻮاﻧﻪ ﻣﺤﺎﺳﺒﻪ ﺷﻮد. ﭘﺲ از ﺻﺤﻪﮔﺬاري ﺑﺮ ﻣﻌﺎدﻻت و روش ﺣﻞ اﺳﺘﻔﺎده ﺷﺪه، ﻧﺘﺎﻳﺞ ﺟﺪﻳﺪ ﺑﺮاي ﻧﺸﺎن دادن اﺛﺮ ﭘﺎراﻣﺘﺮﻫﺎي ﻣﺨﺘﻠﻒ ﻣﺎﻧﻨﺪ ﻫﻨﺪﺳﻪ، ﺷﺮاﻳﻂ ﻣﺮزي ﻛﺴﺮ ﺟﺮﻣﻲ ﻧﺎﻧﻮورقﻫﺎي ﮔﺮاﻓﻦ، اﻟﮕﻮي ﺗﻘﻮﻳﺖ ﺷﺪﮔﻲ ﺑﻪ دﺳﺖ آﻣﺪه اﺳﺖ.

In the current paper thermal buckling of cylindrical shells reinforced with GPL graphene sheets subjected to uniform temperature rise is investigated. Nanocomposite shell reinforced by graphene platelets (GPLs). It is assumed that the GPLs are randomly oriented and uniformly distributed along in each layer. Variation of volume fraction from each layer to other is based on the several functionally graded types. The effective material properties are obtained using the Halpin-Tsai rule. The equilibrium equations are obtained considering the first order shear deformation shell theory, Donnell assumption, and Von-karman type of geometrical nonlinearity. The linear obtained stability equations are discrete utilizing the generalized differential quadrature procedure along the shell domain. Then the eigenvalue problem is solved and critical buckling temperature is calculated. In the section of numerical results, after validation, the effects of geometric parameter, boundary conditions, mass fraction of GPL, and also type of functionally graded on the stability of structure are studied.