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
Background: The shape of the capitellum has been traditionally described in anatomy books as part of a sphere. Alteration in the capitellar morphology following pathologies such as fractures, osteochondrosis, and dege...Background: The shape of the capitellum has been traditionally described in anatomy books as part of a sphere. Alteration in the capitellar morphology following pathologies such as fractures, osteochondrosis, and degenerative arthritis has been associated with less optimum functional results. Aim: To define the relationship between the sphericity of the capitellar morphology as measured on trauma series plain radiographs and the elbow range of motion. Methods: 40 patients were included in the study. All patients recruited from the upper limb clinics presented with non-elbow joint-related complaints. The elbow range of motion was measured using a standardized technique. Digital anteroposterior and lateral radiographs of patients’ elbows were used to measure capitellar circularity using the ImageJ processing program and circularity calculation equation. Correlation analyses were conducted between the degree of capitellar sphericity and elbow range of motion. Results: The results of measurements from the anteroposterior radiographs showed a positive correlation between increased circularity and an increase in the range of flexion, pronation, and supination. The range of extension decreased with the increased circularity of the capitellum. This trend was repeated with measures of lateral radiographs but was statistically not significant. Conclusion: Native capitellar circularity has an impact on the elbow range of motion. This should be put into consideration when dealing with pathologies that affect capitellar morphology.展开更多
Using hybrid perturbatin_Galerkin technique,a crcular cross_section tube model with sinusoidal wall is studied.This technique can remove the limitation of small parameters for perturbation and the difficulty of select...Using hybrid perturbatin_Galerkin technique,a crcular cross_section tube model with sinusoidal wall is studied.This technique can remove the limitation of small parameters for perturbation and the difficulty of selecting good coordinate functions about Galerkin technique.The effects caused by the boundary conditions and the Reynolds number on the flow were discussed.The position of the separate and reattachment points was obtained.The tendency of the variation about the shear stress on the wall and friction factor along the axis direction were also analyzed.The results at a small parameter have good agreements with the perturbation ones.展开更多
For any study ofa suspension entering a pore, the knowledge of the force and moment exerted on a solute particle in an arbitrary position outside the pore is essential, 'This paper for the first lime presents appr...For any study ofa suspension entering a pore, the knowledge of the force and moment exerted on a solute particle in an arbitrary position outside the pore is essential, 'This paper for the first lime presents approximate analytical expressions (in closed form) of all the twelve force and moment coefficienis for a sphere outsied a circular orifice, on the basis of a number of discrete data computed by Yan et al(1987).These coefficients are then applied to calculate the trajectory and angular velocity of a spherical particle approaching the pore at zero Reynolds number. The trajectory is in excellent agreement with the available experimental results. An analysis of the relative importance of the coefficients shows that the rotation effect cannot be neglected near the pore opening or near the wall, and that the lateral force effect must be taken into account in the neighborhood of the edge of the pore opening. It is due to neglecting these factors that previous theoretical results deviate from the experimental ones near the pore opening. The effects of the ratio of the particle to pore radii as well as the influences of the graritytbuoyance on the particle trajectory, velocity distribution and rotation are discnssed in detail. It is pointed out that in the experiments of neutrally-buoyant suspensions, the restriction on the density of the particle is most demanding for a large particle size.The expressions of forces and moments presenled herein are complete, relatively accurate and convenient, thus providing a good prerequisite for further studies of any problems involving the entrance of particles to a pare.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.
文摘Background: The shape of the capitellum has been traditionally described in anatomy books as part of a sphere. Alteration in the capitellar morphology following pathologies such as fractures, osteochondrosis, and degenerative arthritis has been associated with less optimum functional results. Aim: To define the relationship between the sphericity of the capitellar morphology as measured on trauma series plain radiographs and the elbow range of motion. Methods: 40 patients were included in the study. All patients recruited from the upper limb clinics presented with non-elbow joint-related complaints. The elbow range of motion was measured using a standardized technique. Digital anteroposterior and lateral radiographs of patients’ elbows were used to measure capitellar circularity using the ImageJ processing program and circularity calculation equation. Correlation analyses were conducted between the degree of capitellar sphericity and elbow range of motion. Results: The results of measurements from the anteroposterior radiographs showed a positive correlation between increased circularity and an increase in the range of flexion, pronation, and supination. The range of extension decreased with the increased circularity of the capitellum. This trend was repeated with measures of lateral radiographs but was statistically not significant. Conclusion: Native capitellar circularity has an impact on the elbow range of motion. This should be put into consideration when dealing with pathologies that affect capitellar morphology.
文摘Using hybrid perturbatin_Galerkin technique,a crcular cross_section tube model with sinusoidal wall is studied.This technique can remove the limitation of small parameters for perturbation and the difficulty of selecting good coordinate functions about Galerkin technique.The effects caused by the boundary conditions and the Reynolds number on the flow were discussed.The position of the separate and reattachment points was obtained.The tendency of the variation about the shear stress on the wall and friction factor along the axis direction were also analyzed.The results at a small parameter have good agreements with the perturbation ones.
基金Project supported by the National Natural Science Foundation of China
文摘For any study ofa suspension entering a pore, the knowledge of the force and moment exerted on a solute particle in an arbitrary position outside the pore is essential, 'This paper for the first lime presents approximate analytical expressions (in closed form) of all the twelve force and moment coefficienis for a sphere outsied a circular orifice, on the basis of a number of discrete data computed by Yan et al(1987).These coefficients are then applied to calculate the trajectory and angular velocity of a spherical particle approaching the pore at zero Reynolds number. The trajectory is in excellent agreement with the available experimental results. An analysis of the relative importance of the coefficients shows that the rotation effect cannot be neglected near the pore opening or near the wall, and that the lateral force effect must be taken into account in the neighborhood of the edge of the pore opening. It is due to neglecting these factors that previous theoretical results deviate from the experimental ones near the pore opening. The effects of the ratio of the particle to pore radii as well as the influences of the graritytbuoyance on the particle trajectory, velocity distribution and rotation are discnssed in detail. It is pointed out that in the experiments of neutrally-buoyant suspensions, the restriction on the density of the particle is most demanding for a large particle size.The expressions of forces and moments presenled herein are complete, relatively accurate and convenient, thus providing a good prerequisite for further studies of any problems involving the entrance of particles to a pare.
