The bending and free vibrational behaviors of functionally graded(FG)cylindrical beams with radially and axially varying material inhomogeneities are investigated.Based on a high-order cylindrical beam model,where the...The bending and free vibrational behaviors of functionally graded(FG)cylindrical beams with radially and axially varying material inhomogeneities are investigated.Based on a high-order cylindrical beam model,where the shear deformation and rotary inertia are both considered,the two coupled governing differential motion equations for the deflection and rotation are established.The analytical bending solutions for various boundary conditions are derived.In the vibrational analysis of FG cylindrical beams,the two governing equations are firstly changed to a single equation by means of an auxiliary function,and then the vibration mode is expanded into shifted Chebyshev polynomials.Numerical examples are given to investigate the effects of the material gradient indices on the deflections,the stress distributions,and the eigenfrequencies of the cylindrical beams,respectively.By comparing the obtained numerical results with those obtained by the three-dimensional(3D)elasticity theory and the Timoshenko beam theory,the effectiveness of the present approach is verified.展开更多
A systematic numerical integration method is applied to the absolute nodal coordinate formulation(ANCF)fully parameterized beam element with smooth varying and continuous cross section.Moreover,the formulation for the...A systematic numerical integration method is applied to the absolute nodal coordinate formulation(ANCF)fully parameterized beam element with smooth varying and continuous cross section.Moreover,the formulation for the integration points and weight coefficients are given in the method which is used to model the multilayer beam with a circular cross section.To negate the effect of the bending stiffness for the element used to model the high-voltage electrical wire,the general continuum mechanical approach is adjusted.Additionally,the insulation cover for some particular types of the wire is described by the nearly incompressible Mooney-Rivlin material model.Finally,a static problem is presented to prove the accuracy and convergence properties of the element,and a dynamic problem of a flexible pendulum is simulated whereby the balance of the energy can be ensured.An experiment is carried out in which a wire is released as a pendulum and falls on a steel rod.The configurations of the wire are captured by a high-speed camera and compared with the simulation results.The feasibility of the wire model can therefore be demonstrated.展开更多
基金Project supported by the Natural Science Foundation of Guangdong Province of China(No.2018A030313258)。
文摘The bending and free vibrational behaviors of functionally graded(FG)cylindrical beams with radially and axially varying material inhomogeneities are investigated.Based on a high-order cylindrical beam model,where the shear deformation and rotary inertia are both considered,the two coupled governing differential motion equations for the deflection and rotation are established.The analytical bending solutions for various boundary conditions are derived.In the vibrational analysis of FG cylindrical beams,the two governing equations are firstly changed to a single equation by means of an auxiliary function,and then the vibration mode is expanded into shifted Chebyshev polynomials.Numerical examples are given to investigate the effects of the material gradient indices on the deflections,the stress distributions,and the eigenfrequencies of the cylindrical beams,respectively.By comparing the obtained numerical results with those obtained by the three-dimensional(3D)elasticity theory and the Timoshenko beam theory,the effectiveness of the present approach is verified.
基金the National Natural Science Foundation of China(Grant 11802072)the Fundamental Research Funds for the Central Universities(Grant HIT.NSRIF 2018032).
文摘A systematic numerical integration method is applied to the absolute nodal coordinate formulation(ANCF)fully parameterized beam element with smooth varying and continuous cross section.Moreover,the formulation for the integration points and weight coefficients are given in the method which is used to model the multilayer beam with a circular cross section.To negate the effect of the bending stiffness for the element used to model the high-voltage electrical wire,the general continuum mechanical approach is adjusted.Additionally,the insulation cover for some particular types of the wire is described by the nearly incompressible Mooney-Rivlin material model.Finally,a static problem is presented to prove the accuracy and convergence properties of the element,and a dynamic problem of a flexible pendulum is simulated whereby the balance of the energy can be ensured.An experiment is carried out in which a wire is released as a pendulum and falls on a steel rod.The configurations of the wire are captured by a high-speed camera and compared with the simulation results.The feasibility of the wire model can therefore be demonstrated.
