As an essential model of magnetoelastic interaction between magnetic field and mechanical deformation, the study on magnetoelastic buckling phenomenon of soft ferromagnetic plates in a magnetic environment has been co...As an essential model of magnetoelastic interaction between magnetic field and mechanical deformation, the study on magnetoelastic buckling phenomenon of soft ferromagnetic plates in a magnetic environment has been conducted. One of the key steps for the theoretical prediction of the critical magnetic field is how to formulate magnetic force exerted on the magnetized medium. Till today, the theoretical predictions, from theoretical models in publications, of the magnetoelastic buckling of ferromagnetic cantilevered beam-plate in transverse magnetic field are all higher than their experimental data. Sometimes, the discrepancy between them is as high as 100%. In this paper, the macroscope formulation of the magnetic forces is strictly obtained from the microscope Amperion current model. After that, a new theoretical model is established to describe the magnetoelastic buckling phenomenon of ferromagnetic thin plates with geometrically nonlinear deformation in a nonuniform transverse magnetic field. The numerical method for quantitative analysis is employed by combining the finite elemental method for magnetic fields and the finite difference method for deformation of plates. The numerical results obtained from this new theoretical model show that the theoretical predictions of critical values of the buckling magnetic field for the ferromagnetic cantilevered beam-plate are in excellent agreement with their experimental data. By the way, the region of applicability to the Moon-Pao's model, or the couple model, is checked by quantitative results.展开更多
In this paper, to investigate the influence of soil inhomogeneity on the bending of circular thinplates on elastic foundations, the static problem of circular thin plates on Gibson elasticfoundation is solved using an...In this paper, to investigate the influence of soil inhomogeneity on the bending of circular thinplates on elastic foundations, the static problem of circular thin plates on Gibson elasticfoundation is solved using an iterative method based on the modified Vlasov model. On the basisof the principle of minimum potential energy, the governing differential equations and boundaryconditions for circular thin plates on modified Vlasov foundation considering the characteristics ofGibson soil are derived. The equations for the attenuation parameter in bending problem are alsoobtained, and the issue of unknown parameters being difficult to determine is solved using theiterative method. Numerical examples are analyzed and the results are in good agreement withthose form other literatures. It proves that the method is practical and accurate. Theinhomogeneity of modified Vlasov foundations has some influence on the deformation andinternal force behavior of circular thin plates. The effects of various parameters on the bending ofcircular plates and characteristic parameters of the foundation are discussed. The modified modelfurther enriches and develops the elastic foundations. Relevant conclusions that are meaningful toengineering practice are drawn.展开更多
On foe basis of the Kirchoff-Karman hypothses for the nonlinear bending of thin plates, the three kinds of boundary value problems of nonlinear analysis for perforated fhin plates are presented under the differenr in...On foe basis of the Kirchoff-Karman hypothses for the nonlinear bending of thin plates, the three kinds of boundary value problems of nonlinear analysis for perforated fhin plates are presented under the differenr in-plane boundary conditions and the corresponding generalized varialional principles are established. One can see that all mathematical models presented in this paper are completely new ones and differ from the ordinary von Karman theory. These mathematical models can be applied to the nonlinear analysis and the Stability analysis of perforaled thin plates in arbitraryplane boundary conditions.展开更多
Understanding the mechanical response of coal mine roofs under combined vertical overburden loads and horizontal lateral stresses is critical for assessing roof stability in longwall mining.In this study,the periodica...Understanding the mechanical response of coal mine roofs under combined vertical overburden loads and horizontal lateral stresses is critical for assessing roof stability in longwall mining.In this study,the periodically weighting roof is idealized as a rectangular thin plate model with two adjacent sides clamped and the other two simply supported(CCSS),and a composite deflection function is constructed by coupling polynomial terms with trigonometric series.The Galerkin method is applied to convert the governing partial differential equation for the deflection function into an algebraic system,deriving an analytical solution that enables modal analysis of roof deflection and stress.Results show that the deformation is predominantly controlled by the superposition of the mode with one modal number in the x direction and one in the y direction,and the mode with one modal number in the x-direction and two in the y-direction,together contributing 96.67%of the global strain energy,with the latter mode alone contributing 61.5%.High tensile stress regions are found to spatially coincide with large deflection zones.The theoretical results show high consistency with the concentration of high energy microseismic events and the peak hydraulic support resistance observed at the 14321 longwall working face in the Gubei Mine,Huainan.This study establishes a new theoretical framework for analyzing the mechanical response of mine roofs and provides a reliable approach for accurate prediction of periodic weighting.展开更多
Through changing the axial load on backfilling material compaction test to reflect different overlying strata pressure on backfilling material, the stress-strain relations in the compaction process of backfilling mate...Through changing the axial load on backfilling material compaction test to reflect different overlying strata pressure on backfilling material, the stress-strain relations in the compaction process of backfilling material under the geological condition can be obtained. Based on the characteristic of overlying strata movement in backfill mining, a model of roof thin plate is established. By introducing the stress-strain relation in compaction process into the model and using RIZT method to analyze the bending deformation of roof, the bending deflection and stress distribution can be obtained. The results show that the maximum roof subsidence and maximum tensile stress occurring at the center are 255 mm and5 MPa, respectively. Tensile fracture of roof under the geological condition of Dongping Mine did not occur. The dynamic measurement results of roof in Dongping Mine verify the theoretical result from the aforementioned model, thereby suggesting the roof mechanical model is reliable. The roof thin plate model based on the compaction characteristic of backfilling material in this study is of importance to research on backfill mining theories and application of backfilling material characteristics.展开更多
The present paper is concerned with the steady thin film flow of the Sisko fluid on a horizontal moving plate, where the surface tension gradient is a driving mechanism. The analytic solution for the resulting nonline...The present paper is concerned with the steady thin film flow of the Sisko fluid on a horizontal moving plate, where the surface tension gradient is a driving mechanism. The analytic solution for the resulting nonlinear ordinary differential equation is obtained by the Adomian decomposition method （ADM）. The physical quantities are derived including the pressure profile, the velocity profile, the maximum residue time, the stationary points, the volume flow rate, the average film velocity, the uniform film thickness, the shear stress, the surface tension profile~ and the vorticity vector. It is found that the velocity of the Sisko fluid film decreases when the fluid behavior index and the Sisko fluid parameter increase, whereas it increases with an increase in the inverse capillary number. An increase in the inverse capillary number results in an increase in the surface tension which in turn results in an increase in the surface tension gradient on the Sisko fluid film. The locations of the stationary points are shifted towards the moving plate with the increase in the inverse capillary number, and vice versa locations for the stationary points are found with the increasing Sisko fluid parameter. Furthermore, shear thinning and shear thickening characteristics of the Sisko fluid are discussed. A comparison is made between the Sisko fluid film and the Newtonian fluid film.展开更多
基金This project was supported in part by the National Natural Science Foundation of ChinaFoundation of the SEdC of China for Returned Chinese Scholars from Abroad
文摘As an essential model of magnetoelastic interaction between magnetic field and mechanical deformation, the study on magnetoelastic buckling phenomenon of soft ferromagnetic plates in a magnetic environment has been conducted. One of the key steps for the theoretical prediction of the critical magnetic field is how to formulate magnetic force exerted on the magnetized medium. Till today, the theoretical predictions, from theoretical models in publications, of the magnetoelastic buckling of ferromagnetic cantilevered beam-plate in transverse magnetic field are all higher than their experimental data. Sometimes, the discrepancy between them is as high as 100%. In this paper, the macroscope formulation of the magnetic forces is strictly obtained from the microscope Amperion current model. After that, a new theoretical model is established to describe the magnetoelastic buckling phenomenon of ferromagnetic thin plates with geometrically nonlinear deformation in a nonuniform transverse magnetic field. The numerical method for quantitative analysis is employed by combining the finite elemental method for magnetic fields and the finite difference method for deformation of plates. The numerical results obtained from this new theoretical model show that the theoretical predictions of critical values of the buckling magnetic field for the ferromagnetic cantilevered beam-plate are in excellent agreement with their experimental data. By the way, the region of applicability to the Moon-Pao's model, or the couple model, is checked by quantitative results.
基金financially supported by the National Natural Science Foundation of China (Grant 51278420)the Natural Science Foundation of Shaanxi Province (Grant 2017JM5021)
文摘In this paper, to investigate the influence of soil inhomogeneity on the bending of circular thinplates on elastic foundations, the static problem of circular thin plates on Gibson elasticfoundation is solved using an iterative method based on the modified Vlasov model. On the basisof the principle of minimum potential energy, the governing differential equations and boundaryconditions for circular thin plates on modified Vlasov foundation considering the characteristics ofGibson soil are derived. The equations for the attenuation parameter in bending problem are alsoobtained, and the issue of unknown parameters being difficult to determine is solved using theiterative method. Numerical examples are analyzed and the results are in good agreement withthose form other literatures. It proves that the method is practical and accurate. Theinhomogeneity of modified Vlasov foundations has some influence on the deformation andinternal force behavior of circular thin plates. The effects of various parameters on the bending ofcircular plates and characteristic parameters of the foundation are discussed. The modified modelfurther enriches and develops the elastic foundations. Relevant conclusions that are meaningful toengineering practice are drawn.
文摘On foe basis of the Kirchoff-Karman hypothses for the nonlinear bending of thin plates, the three kinds of boundary value problems of nonlinear analysis for perforated fhin plates are presented under the differenr in-plane boundary conditions and the corresponding generalized varialional principles are established. One can see that all mathematical models presented in this paper are completely new ones and differ from the ordinary von Karman theory. These mathematical models can be applied to the nonlinear analysis and the Stability analysis of perforaled thin plates in arbitraryplane boundary conditions.
基金supported by the Natural Science Research Project of Colleges and Universities in Anhui Province(Grant No.2024AH050374)Anhui Provincial Natural Science Foundation(Grant No.2508085QE186)+1 种基金Research Foundation for Postdoctoral of Anhui Province(Grant No.2024B817)National Natural Science Foundation of China(Grant No.52074009).
文摘Understanding the mechanical response of coal mine roofs under combined vertical overburden loads and horizontal lateral stresses is critical for assessing roof stability in longwall mining.In this study,the periodically weighting roof is idealized as a rectangular thin plate model with two adjacent sides clamped and the other two simply supported(CCSS),and a composite deflection function is constructed by coupling polynomial terms with trigonometric series.The Galerkin method is applied to convert the governing partial differential equation for the deflection function into an algebraic system,deriving an analytical solution that enables modal analysis of roof deflection and stress.Results show that the deformation is predominantly controlled by the superposition of the mode with one modal number in the x direction and one in the y direction,and the mode with one modal number in the x-direction and two in the y-direction,together contributing 96.67%of the global strain energy,with the latter mode alone contributing 61.5%.High tensile stress regions are found to spatially coincide with large deflection zones.The theoretical results show high consistency with the concentration of high energy microseismic events and the peak hydraulic support resistance observed at the 14321 longwall working face in the Gubei Mine,Huainan.This study establishes a new theoretical framework for analyzing the mechanical response of mine roofs and provides a reliable approach for accurate prediction of periodic weighting.
基金financial assistance provided by the National Natural Science Foundation of China(No.51304206)China Postdoctoral Science Foundation funded project(No.2015M580492)
文摘Through changing the axial load on backfilling material compaction test to reflect different overlying strata pressure on backfilling material, the stress-strain relations in the compaction process of backfilling material under the geological condition can be obtained. Based on the characteristic of overlying strata movement in backfill mining, a model of roof thin plate is established. By introducing the stress-strain relation in compaction process into the model and using RIZT method to analyze the bending deformation of roof, the bending deflection and stress distribution can be obtained. The results show that the maximum roof subsidence and maximum tensile stress occurring at the center are 255 mm and5 MPa, respectively. Tensile fracture of roof under the geological condition of Dongping Mine did not occur. The dynamic measurement results of roof in Dongping Mine verify the theoretical result from the aforementioned model, thereby suggesting the roof mechanical model is reliable. The roof thin plate model based on the compaction characteristic of backfilling material in this study is of importance to research on backfill mining theories and application of backfilling material characteristics.
文摘The present paper is concerned with the steady thin film flow of the Sisko fluid on a horizontal moving plate, where the surface tension gradient is a driving mechanism. The analytic solution for the resulting nonlinear ordinary differential equation is obtained by the Adomian decomposition method （ADM）. The physical quantities are derived including the pressure profile, the velocity profile, the maximum residue time, the stationary points, the volume flow rate, the average film velocity, the uniform film thickness, the shear stress, the surface tension profile~ and the vorticity vector. It is found that the velocity of the Sisko fluid film decreases when the fluid behavior index and the Sisko fluid parameter increase, whereas it increases with an increase in the inverse capillary number. An increase in the inverse capillary number results in an increase in the surface tension which in turn results in an increase in the surface tension gradient on the Sisko fluid film. The locations of the stationary points are shifted towards the moving plate with the increase in the inverse capillary number, and vice versa locations for the stationary points are found with the increasing Sisko fluid parameter. Furthermore, shear thinning and shear thickening characteristics of the Sisko fluid are discussed. A comparison is made between the Sisko fluid film and the Newtonian fluid film.
