This paper studies the vibration responses of porous functionally graded(FG)thin plates with four various types of porous distribution based on the physical neutral plane by employing the peridynamic differential oper...This paper studies the vibration responses of porous functionally graded(FG)thin plates with four various types of porous distribution based on the physical neutral plane by employing the peridynamic differential operator(PDDO).It is assumed that density and elastic modulus continuously vary along the transverse direction following the power law distribution for porous FG plates.The governing differential equation of free vibration for a porous rectangular FG plate and its associated boundary conditions are expressed by a Lévy-type solution based on nonlinear von Karman plate theory.Dimensionless frequencies and mode shapes are obtained after solving the characteristic equations established by PDDO.The results of the current method are validated through comparison with existing literature.The effects of geometric parameters,material properties,elastic foundation,porosity distribution,and boundary conditions on the frequency are investigated and discussed in detail.The highest fundamental dimensionless frequency occurs under SCSC boundary conditions,while the lowest is under SFSF boundary conditions.The porous FG plate with the fourth pore type,featuring high density of porosity at the top and low at the bottom,exhibits the highest fundamental frequency under SSSS,SFSF,and SCSC boundary conditions.The dimensionless frequency increases with an increase in the elastic foundation stiffness coefficient.展开更多
Isogeometric analysis (IGA) is known to showadvanced features compared to traditional finite element approaches.Using IGA one may accurately obtain the geometrically nonlinear bending behavior of plates with functiona...Isogeometric analysis (IGA) is known to showadvanced features compared to traditional finite element approaches.Using IGA one may accurately obtain the geometrically nonlinear bending behavior of plates with functionalgrading (FG). However, the procedure is usually complex and often is time-consuming. We thus put forward adeep learning method to model the geometrically nonlinear bending behavior of FG plates, bypassing the complexIGA simulation process. A long bidirectional short-term memory (BLSTM) recurrent neural network is trainedusing the load and gradient index as inputs and the displacement responses as outputs. The nonlinear relationshipbetween the outputs and the inputs is constructed usingmachine learning so that the displacements can be directlyestimated by the deep learning network. To provide enough training data, we use S-FSDT Von-Karman IGA andobtain the displacement responses for different loads and gradient indexes. Results show that the recognition erroris low, and demonstrate the feasibility of deep learning technique as a fast and accurate alternative to IGA formodeling the geometrically nonlinear bending behavior of FG plates.展开更多
基金supported by the Research Start-Up Fund for Introducing Talents from Anhui Polytechnic University(S022023032)the Program for Synergy Innovation in the Anhui Higher Education Institutions of China(GXXT-2021-044 and GXXT-2022-082)+2 种基金the Scientific Research Foundation of Education Department of Anhui Province,China(2022AH040361)the National Natural Science Foundation of China(12172114)the Natural Science Funds for Distinguished Young Scholar of Anhui Province of China(2208085J25).
文摘This paper studies the vibration responses of porous functionally graded(FG)thin plates with four various types of porous distribution based on the physical neutral plane by employing the peridynamic differential operator(PDDO).It is assumed that density and elastic modulus continuously vary along the transverse direction following the power law distribution for porous FG plates.The governing differential equation of free vibration for a porous rectangular FG plate and its associated boundary conditions are expressed by a Lévy-type solution based on nonlinear von Karman plate theory.Dimensionless frequencies and mode shapes are obtained after solving the characteristic equations established by PDDO.The results of the current method are validated through comparison with existing literature.The effects of geometric parameters,material properties,elastic foundation,porosity distribution,and boundary conditions on the frequency are investigated and discussed in detail.The highest fundamental dimensionless frequency occurs under SCSC boundary conditions,while the lowest is under SFSF boundary conditions.The porous FG plate with the fourth pore type,featuring high density of porosity at the top and low at the bottom,exhibits the highest fundamental frequency under SSSS,SFSF,and SCSC boundary conditions.The dimensionless frequency increases with an increase in the elastic foundation stiffness coefficient.
基金the National Natural Science Foundation of China(NSFC)under Grant Nos.12272124 and 11972146.
文摘Isogeometric analysis (IGA) is known to showadvanced features compared to traditional finite element approaches.Using IGA one may accurately obtain the geometrically nonlinear bending behavior of plates with functionalgrading (FG). However, the procedure is usually complex and often is time-consuming. We thus put forward adeep learning method to model the geometrically nonlinear bending behavior of FG plates, bypassing the complexIGA simulation process. A long bidirectional short-term memory (BLSTM) recurrent neural network is trainedusing the load and gradient index as inputs and the displacement responses as outputs. The nonlinear relationshipbetween the outputs and the inputs is constructed usingmachine learning so that the displacements can be directlyestimated by the deep learning network. To provide enough training data, we use S-FSDT Von-Karman IGA andobtain the displacement responses for different loads and gradient indexes. Results show that the recognition erroris low, and demonstrate the feasibility of deep learning technique as a fast and accurate alternative to IGA formodeling the geometrically nonlinear bending behavior of FG plates.
