Coal wall stability is a critical factor influencing coal mining efficiency and threatens the safety of working faces,where irregular coal wall surfaces significantly affect the contact and support effectiveness of th...Coal wall stability is a critical factor influencing coal mining efficiency and threatens the safety of working faces,where irregular coal wall surfaces significantly affect the contact and support effectiveness of the support plate,thereby impacting stability.Through a combination of theoretical analysis,mechanical testing,and numerical simulations,this study establishes a mechanical model of irregular coal wall surfaces to investigate the effects of the undulation period and undulation height on coal wall failure characteristics.This research reveals the mechanical response mechanisms of irregular coal wall surfaces and proposes an innovative method to enhance coal wall stability by improving the supporting cushion material of the support plate,which was validated through numerical simulations.The results show that the undulation height and undulation period significantly influence the macroscopic mechanical parameters of the samples,with the undulation height exerting a more pronounced effect.The strength of the samples with undulating surfaces is approximately 50%-60% that of the samples with flat surfaces.The failure mode under uniaxial compression is predominantly tensile,resulting in long and slender block fragments with a characteristic“Ⅲ”-shaped tensile fracture pattern.During the loading process,samples with undu-lating surfaces dissipate energy at all stages,with a greater proportion of energy dissipation occurring during the early loading stage because of structural damage and the formation of internal cracks.The surface compressive and tensile stresses are correlated with the curvature radius of the convex surface and the elastic modulus of the supporting plate.Reducing the elastic modulus of the supporting plate material can effectively alleviate the stress concentration at convex locations and increase the peak strength.This study provides theoretical foundations and technical references for the prevention and control of coal wall spalling in deep thick coal seam mining.展开更多
This paper considers the pure bending problem of simply supported transversely isotropic circular plates with elastic compliance coefficients being arbitrary functions of the thickness coordinate. First, the partial d...This paper considers the pure bending problem of simply supported transversely isotropic circular plates with elastic compliance coefficients being arbitrary functions of the thickness coordinate. First, the partial differential equation, which is satisfied by the stress functions for the axisymmetric deformation problem is derived. Then, stress functions are obtained by proper manipulation. The analytical expressions of axial force, bending moment and displacements are then deduced through integration. And then, stress functions are employed to solve problems of transversely isotropic functionally graded circular plate, with the integral constants completely determined from boundary conditions. An elasticity solution for pure bending problem, which coincides with the available solution when degenerated into the elasticity solutions for homogenous circular plate, is thus obtained. A numerical example is finally presented to show the effect of material inhomogeneity on the elastic field in a simply supported circular plate of transversely isotropic functionally graded material (FGM).展开更多
Mechanical analysis of cylinders being upset between spherical concave platen and concave supporting plate is conducted. Rigid-plastic mechanical models for cylinders are presented. When the ratio of height to diamete...Mechanical analysis of cylinders being upset between spherical concave platen and concave supporting plate is conducted. Rigid-plastic mechanical models for cylinders are presented. When the ratio of height to diameter, is larger than 1, there exists two-dimensional tensile stress in the deformed body, when the ratio is smaller than 1, there exists shear stress in static hydraulic zone. The former breaks through the theory that there is three-dimensional compressive stress irrespective of any ratio of height to diameter. The latter satisfactorily explains the mechanism of layer-like cracks in disk-shaped forgings and the flanges of forged gear axles. The representation of the two models makes the upsetting, theory into correct and perfect stage.展开更多
A theoretical analysis is presented for the dynamic plastic behavior of a simply supported rigid, perfectly plastic circular plate in damping medium with finite-deflections subjected to a rectangular pressure pulse. A...A theoretical analysis is presented for the dynamic plastic behavior of a simply supported rigid, perfectly plastic circular plate in damping medium with finite-deflections subjected to a rectangular pressure pulse. Analytical solutions of every moving stage under both medium and high loads are developed.展开更多
A closed series solution is proposed for the bending of point-supported orthotropic rectangular thin plates. The positions of support points and the distribution of transverse loadare arbitrary. If the number of simpl...A closed series solution is proposed for the bending of point-supported orthotropic rectangular thin plates. The positions of support points and the distribution of transverse loadare arbitrary. If the number of simply supported points gradually increases the solution can infinitely approach to Navier's solution. For the square plate simply supported on the middle of each edge and free at each corner, the results are very close to the numerical solutions in the past.展开更多
This paper discusses by energy theorem the methodof approximate computation for the lowest eigenfrequencies of rechmguhir plates,on which there are symmetrical concentrated masses,supported at corner points,In the cas...This paper discusses by energy theorem the methodof approximate computation for the lowest eigenfrequencies of rechmguhir plates,on which there are symmetrical concentrated masses,supported at corner points,In the case of seseral concentrated masses,by using the prineiple of superposition we mayfiml the reduneed coefficients of masses comveniently.llence we can louain the lowest eigenfrequencies of thin plates.In the paper a good mamy mmerical caleuhting eximples are inustrated展开更多
This paper studies transverse vibration of rectangular plates with two opposite edges simply supperted other two edges arbitrarily supported and free edges elaslically supported at points,A highly accurate solution is...This paper studies transverse vibration of rectangular plates with two opposite edges simply supperted other two edges arbitrarily supported and free edges elaslically supported at points,A highly accurate solution is presented for calculating inherent frequencies and mode shape of rectangular platen elaslically supported at points. The number and location of these points on free edges may be completely arbitrary. This paper uses impulse function to represent reaction and moment at points. Fourter series is used to expand the impulse function along the edges. Characteristic equations satisfying all boundary conditions are given.Inherent frequencies and mode shape with any accutacy can be gained.展开更多
In this paper, the nonlinear bandings for the orthotropic rectangular thin plates under various supports are studied.The uniformly valid asymptotic solutions of the displacement ? and stress function φ are derived by...In this paper, the nonlinear bandings for the orthotropic rectangular thin plates under various supports are studied.The uniformly valid asymptotic solutions of the displacement ? and stress function φ are derived by the perturbation offered in [1].展开更多
In this paper, an exact solution for an uniformly loaded rectangular plate with two adjacent edges clamped, one edge simply supported and the other edge free, was given by using the concept of generalized simply suppo...In this paper, an exact solution for an uniformly loaded rectangular plate with two adjacent edges clamped, one edge simply supported and the other edge free, was given by using the concept of generalized simply supported edges and superposition method. The numerical results were given for the deflections along the free edge and bending moments along the clamped edges of a square plate.展开更多
In this study, integral operational methods are used to investigate the thermally induced transverse vibration of a thin elliptic annulus plate with elastic supports at both radial boundaries.The axisymmetric temperat...In this study, integral operational methods are used to investigate the thermally induced transverse vibration of a thin elliptic annulus plate with elastic supports at both radial boundaries.The axisymmetric temperature distribution is determined by the heat conduction differential equation and its corresponding boundary conditions by employing a unified integral transform technique by use of Mathieu functions and modified Mathieu functions. The solution of thermally induced vibration of the plate with both ends encased with elastic supports is obtained by employing an integral transform for double Laplace differential equation. The thermal moment is derived on the basis of temperature distribution, and its stresses are obtained based on resultant bending moments per unit width. The numerical calculations of the distributions of the transient temperature and its associated stress distributions are shown in the figures.展开更多
The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton＇s principle for t...The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton＇s principle for the elastic dynamics system,the dimensionless equations of motion of rectangular plates with finite interior elastic point supports and the edge elastically restrained are established using the element-free Galerkin method.Through numerical calculation,curves of the natural frequency of thin plates with three edges simply supported and one edge elastically restrained,and three edges clamped and the other edge elastically restrained versus the spring constant,locations of elastic point support and the elastic stiffness of edge elastically restrained are obtained.Effects of elastic point supports and edge elastically restrained on the free vibration characteristics of the thin plates are analyzed.展开更多
This paper presents presents a new analytical solution of transverse vibration ofrectangular plaies simply supported at two opposite edges with arbitrary number ofelastic line supports in one way. The reaction forces ...This paper presents presents a new analytical solution of transverse vibration ofrectangular plaies simply supported at two opposite edges with arbitrary number ofelastic line supports in one way. The reaction forces of the elastic line supports areregarded as foe unknown external forces acted on the plate. The analytical solution ofthe differential equation of motion of the rectangular plate, which includes theunknown reaction forces. is gained. The frequency' equation is derived by using thelinear relationships between the reaction forces of the elastic line supports and thetransverse displacements of the plale along the elastic line supports. Therepresentations of foe frequency equation and the mode shape functions are differentfrom those obtained by other methods.展开更多
In this paper, the method of relaxed boundary conditions is applied to rectangular plates with edges which are a sort of the mixture of simply supported portions and clamped portions, so that the lower limit of fundam...In this paper, the method of relaxed boundary conditions is applied to rectangular plates with edges which are a sort of the mixture of simply supported portions and clamped portions, so that the lower limit of fundamental frequency of such plates is evaluated. A kind of polynomial satisfying the displacement boundary conditions is designed, os that it is enabled to evaluate the upper limit of fundamental frequency by Ritz' method. The practical calculation examples solved by these methods have given satisfactory results. At the end of this paper, it is pointed out that the socalled exact solution of such plates usually evaluated by the force superposition method is essentially a kind of lower limit of solution, if the truncated error of series which occurs in actual calculation is considered.展开更多
The hydroelastic response of very large floating structures (VLFS) under the action of ocean waves is analysed considering the small amplitude wave theory. The very large floating structure is modelled as a floating t...The hydroelastic response of very large floating structures (VLFS) under the action of ocean waves is analysed considering the small amplitude wave theory. The very large floating structure is modelled as a floating thick elastic plate based on Timoshenko- Mindlin plate theory, and the analysis for the hydroelastic response is performed considering different edge boundary conditions. The numerical study is performed to analyse the wave reflection and transmission characteristics of the floating plate under the influence of different support conditions using eigenfunction expansion method along with the orthogonal mode-coupling relation in the case of finite water depth. Further, the analysis is extended for shallow water depth, and the continuity of energy and mass flux is applied along the edges of the plate to obtain the solution for the problem. The hydroelastic behaviour in terms of reflection and transmission coefficients, plate deflection, strain, bending moment and shear force of the floating thick elastic plate with support conditions is analysed and compared for finite and shallow water depth. The study reveals an interesting aspect in the analysis of thick floating elastic plate with support condition due to the presence of the rotary inertia and transverse shear deformation. The present study will be helpful for the design and analysis of the VLFS in the case of finite and shallow water depth.展开更多
The thermal behavior of a thick transversely isotropic FGM rectangular plate was investigated within the scope of three-dimensional elasticity. Noticing many FGMs may have temperature-dependent properties, the materia...The thermal behavior of a thick transversely isotropic FGM rectangular plate was investigated within the scope of three-dimensional elasticity. Noticing many FGMs may have temperature-dependent properties, the material constants were further considered as functions of temperature. A solution method based on state-space formulations with a laminate approximate model was proposed. For a thin plate, the method was clarified by comparison with the thin plate theory. The influences of material inhomogeneity and temperature-dependent characteristics were finally discussed through numerical examples.展开更多
The present work was focused on the preparation of palladium alloy membranes and the effect of properties of ceramic support on the composited membrane morphology. Palladium-base membrane is known to have high selecti...The present work was focused on the preparation of palladium alloy membranes and the effect of properties of ceramic support on the composited membrane morphology. Palladium-base membrane is known to have high selectivity and stability for hydrogen separation. In order to increase hydrogen permeation and separation factor, the membrane must be thinner and defect-free. Palladium membrane supported on a porous alumina prepared by electroless plating is the promising method to provide good hydrogen permeability. The alumina tube substrate was pre-seeded by immersing in the palladium acetate solution and followed by reduction in the alkaline hydrazine solution. After that, the deposition of palladium membrane could be achieved from the plating bath containing ethylenediamine tetraacetic acid （EDTA） stabilized palladium complex and hydrazine. The morphology of palladium film was observed to progress as a function of plating time and a dense layer membrane was available after plating for 3 h. The porosity of ceramic support exhibited an effect on the microstructure of deposited film such that the support with low porosity tended to achieve a defect free palladium membrane.展开更多
3D and 2D closed form plate models are here applied to static analysis of simply supported square isotropic plates. 2D theories are hierarchically classified on the basis of the accuracy of the displacements and stres...3D and 2D closed form plate models are here applied to static analysis of simply supported square isotropic plates. 2D theories are hierarchically classified on the basis of the accuracy of the displacements and stresses obtained by comparison to the 3D exact results that could be assumed by the reader as benchmark for further analyses. Attention is mainly paid on localized loading conditions, that is, piecewise constant load. Also bi-sinusoidal and uniformly distributed loadings are taken into account. All of those configurations are considered in order to investigate the behavior of the 2D models in the case of continu- ous/uncontinuous, centric or off-centric loading conditions. The ratio between the side length a and the plate thickness h has been assumed as analysis parameter. Higher order 2D models yield accurate results for any considered load condition in the case of moderately thick plates, a/h=10. In the case of thick plates, a/h=5, and continuous/uncontinuous centric loading conditions high accuracy is also obtained. For the considered off-centric load condition and thick plates good results are provided for some output quantities. A better solution could be achieved by simply increasing the polynomial approximation order of the axiomatic 2D displacement field.展开更多
基金the National Key Research and Development Program of China(Nos.2023YFC2907501 and 2023YFC2907503)the National Natural Science Foundation of China(Nos.52374106 and 52274154)the Fundamental Research Funds for the Central Universities(No.2023YQTD02).
文摘Coal wall stability is a critical factor influencing coal mining efficiency and threatens the safety of working faces,where irregular coal wall surfaces significantly affect the contact and support effectiveness of the support plate,thereby impacting stability.Through a combination of theoretical analysis,mechanical testing,and numerical simulations,this study establishes a mechanical model of irregular coal wall surfaces to investigate the effects of the undulation period and undulation height on coal wall failure characteristics.This research reveals the mechanical response mechanisms of irregular coal wall surfaces and proposes an innovative method to enhance coal wall stability by improving the supporting cushion material of the support plate,which was validated through numerical simulations.The results show that the undulation height and undulation period significantly influence the macroscopic mechanical parameters of the samples,with the undulation height exerting a more pronounced effect.The strength of the samples with undulating surfaces is approximately 50%-60% that of the samples with flat surfaces.The failure mode under uniaxial compression is predominantly tensile,resulting in long and slender block fragments with a characteristic“Ⅲ”-shaped tensile fracture pattern.During the loading process,samples with undu-lating surfaces dissipate energy at all stages,with a greater proportion of energy dissipation occurring during the early loading stage because of structural damage and the formation of internal cracks.The surface compressive and tensile stresses are correlated with the curvature radius of the convex surface and the elastic modulus of the supporting plate.Reducing the elastic modulus of the supporting plate material can effectively alleviate the stress concentration at convex locations and increase the peak strength.This study provides theoretical foundations and technical references for the prevention and control of coal wall spalling in deep thick coal seam mining.
基金Project (Nos. 10472102 and 10432030) supported by the NationalNatural Science Foundation of China
文摘This paper considers the pure bending problem of simply supported transversely isotropic circular plates with elastic compliance coefficients being arbitrary functions of the thickness coordinate. First, the partial differential equation, which is satisfied by the stress functions for the axisymmetric deformation problem is derived. Then, stress functions are obtained by proper manipulation. The analytical expressions of axial force, bending moment and displacements are then deduced through integration. And then, stress functions are employed to solve problems of transversely isotropic functionally graded circular plate, with the integral constants completely determined from boundary conditions. An elasticity solution for pure bending problem, which coincides with the available solution when degenerated into the elasticity solutions for homogenous circular plate, is thus obtained. A numerical example is finally presented to show the effect of material inhomogeneity on the elastic field in a simply supported circular plate of transversely isotropic functionally graded material (FGM).
基金National Natural Science Foundation of China(No.59235101)
文摘Mechanical analysis of cylinders being upset between spherical concave platen and concave supporting plate is conducted. Rigid-plastic mechanical models for cylinders are presented. When the ratio of height to diameter, is larger than 1, there exists two-dimensional tensile stress in the deformed body, when the ratio is smaller than 1, there exists shear stress in static hydraulic zone. The former breaks through the theory that there is three-dimensional compressive stress irrespective of any ratio of height to diameter. The latter satisfactorily explains the mechanism of layer-like cracks in disk-shaped forgings and the flanges of forged gear axles. The representation of the two models makes the upsetting, theory into correct and perfect stage.
文摘A theoretical analysis is presented for the dynamic plastic behavior of a simply supported rigid, perfectly plastic circular plate in damping medium with finite-deflections subjected to a rectangular pressure pulse. Analytical solutions of every moving stage under both medium and high loads are developed.
文摘A closed series solution is proposed for the bending of point-supported orthotropic rectangular thin plates. The positions of support points and the distribution of transverse loadare arbitrary. If the number of simply supported points gradually increases the solution can infinitely approach to Navier's solution. For the square plate simply supported on the middle of each edge and free at each corner, the results are very close to the numerical solutions in the past.
文摘This paper discusses by energy theorem the methodof approximate computation for the lowest eigenfrequencies of rechmguhir plates,on which there are symmetrical concentrated masses,supported at corner points,In the case of seseral concentrated masses,by using the prineiple of superposition we mayfiml the reduneed coefficients of masses comveniently.llence we can louain the lowest eigenfrequencies of thin plates.In the paper a good mamy mmerical caleuhting eximples are inustrated
文摘This paper studies transverse vibration of rectangular plates with two opposite edges simply supperted other two edges arbitrarily supported and free edges elaslically supported at points,A highly accurate solution is presented for calculating inherent frequencies and mode shape of rectangular platen elaslically supported at points. The number and location of these points on free edges may be completely arbitrary. This paper uses impulse function to represent reaction and moment at points. Fourter series is used to expand the impulse function along the edges. Characteristic equations satisfying all boundary conditions are given.Inherent frequencies and mode shape with any accutacy can be gained.
文摘In this paper, the nonlinear bandings for the orthotropic rectangular thin plates under various supports are studied.The uniformly valid asymptotic solutions of the displacement ? and stress function φ are derived by the perturbation offered in [1].
文摘In this paper, an exact solution for an uniformly loaded rectangular plate with two adjacent edges clamped, one edge simply supported and the other edge free, was given by using the concept of generalized simply supported edges and superposition method. The numerical results were given for the deflections along the free edge and bending moments along the clamped edges of a square plate.
文摘In this study, integral operational methods are used to investigate the thermally induced transverse vibration of a thin elliptic annulus plate with elastic supports at both radial boundaries.The axisymmetric temperature distribution is determined by the heat conduction differential equation and its corresponding boundary conditions by employing a unified integral transform technique by use of Mathieu functions and modified Mathieu functions. The solution of thermally induced vibration of the plate with both ends encased with elastic supports is obtained by employing an integral transform for double Laplace differential equation. The thermal moment is derived on the basis of temperature distribution, and its stresses are obtained based on resultant bending moments per unit width. The numerical calculations of the distributions of the transient temperature and its associated stress distributions are shown in the figures.
基金Project supported by the National Natural Science Foundation of China (Grant No.10872163)the Natural Science Foundation of Education Department of Shaanxi Province (Grant No.08JK394)
文摘The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton＇s principle for the elastic dynamics system,the dimensionless equations of motion of rectangular plates with finite interior elastic point supports and the edge elastically restrained are established using the element-free Galerkin method.Through numerical calculation,curves of the natural frequency of thin plates with three edges simply supported and one edge elastically restrained,and three edges clamped and the other edge elastically restrained versus the spring constant,locations of elastic point support and the elastic stiffness of edge elastically restrained are obtained.Effects of elastic point supports and edge elastically restrained on the free vibration characteristics of the thin plates are analyzed.
文摘This paper presents presents a new analytical solution of transverse vibration ofrectangular plaies simply supported at two opposite edges with arbitrary number ofelastic line supports in one way. The reaction forces of the elastic line supports areregarded as foe unknown external forces acted on the plate. The analytical solution ofthe differential equation of motion of the rectangular plate, which includes theunknown reaction forces. is gained. The frequency' equation is derived by using thelinear relationships between the reaction forces of the elastic line supports and thetransverse displacements of the plale along the elastic line supports. Therepresentations of foe frequency equation and the mode shape functions are differentfrom those obtained by other methods.
文摘In this paper, the method of relaxed boundary conditions is applied to rectangular plates with edges which are a sort of the mixture of simply supported portions and clamped portions, so that the lower limit of fundamental frequency of such plates is evaluated. A kind of polynomial satisfying the displacement boundary conditions is designed, os that it is enabled to evaluate the upper limit of fundamental frequency by Ritz' method. The practical calculation examples solved by these methods have given satisfactory results. At the end of this paper, it is pointed out that the socalled exact solution of such plates usually evaluated by the force superposition method is essentially a kind of lower limit of solution, if the truncated error of series which occurs in actual calculation is considered.
基金NITK SurathkalMHRD+2 种基金the Science and Engineering Research Board(SERB)Department of Science&Technology(DST)Government of India,for supporting financially under the Young Scientist research grant No.YSS/2014/000812
文摘The hydroelastic response of very large floating structures (VLFS) under the action of ocean waves is analysed considering the small amplitude wave theory. The very large floating structure is modelled as a floating thick elastic plate based on Timoshenko- Mindlin plate theory, and the analysis for the hydroelastic response is performed considering different edge boundary conditions. The numerical study is performed to analyse the wave reflection and transmission characteristics of the floating plate under the influence of different support conditions using eigenfunction expansion method along with the orthogonal mode-coupling relation in the case of finite water depth. Further, the analysis is extended for shallow water depth, and the continuity of energy and mass flux is applied along the edges of the plate to obtain the solution for the problem. The hydroelastic behaviour in terms of reflection and transmission coefficients, plate deflection, strain, bending moment and shear force of the floating thick elastic plate with support conditions is analysed and compared for finite and shallow water depth. The study reveals an interesting aspect in the analysis of thick floating elastic plate with support condition due to the presence of the rotary inertia and transverse shear deformation. The present study will be helpful for the design and analysis of the VLFS in the case of finite and shallow water depth.
文摘The thermal behavior of a thick transversely isotropic FGM rectangular plate was investigated within the scope of three-dimensional elasticity. Noticing many FGMs may have temperature-dependent properties, the material constants were further considered as functions of temperature. A solution method based on state-space formulations with a laminate approximate model was proposed. For a thin plate, the method was clarified by comparison with the thin plate theory. The influences of material inhomogeneity and temperature-dependent characteristics were finally discussed through numerical examples.
基金supported by the National Metal and Materials Center,Thailand under Grant No.MT-B-51-END-07-057-I
文摘The present work was focused on the preparation of palladium alloy membranes and the effect of properties of ceramic support on the composited membrane morphology. Palladium-base membrane is known to have high selectivity and stability for hydrogen separation. In order to increase hydrogen permeation and separation factor, the membrane must be thinner and defect-free. Palladium membrane supported on a porous alumina prepared by electroless plating is the promising method to provide good hydrogen permeability. The alumina tube substrate was pre-seeded by immersing in the palladium acetate solution and followed by reduction in the alkaline hydrazine solution. After that, the deposition of palladium membrane could be achieved from the plating bath containing ethylenediamine tetraacetic acid （EDTA） stabilized palladium complex and hydrazine. The morphology of palladium film was observed to progress as a function of plating time and a dense layer membrane was available after plating for 3 h. The porosity of ceramic support exhibited an effect on the microstructure of deposited film such that the support with low porosity tended to achieve a defect free palladium membrane.
文摘3D and 2D closed form plate models are here applied to static analysis of simply supported square isotropic plates. 2D theories are hierarchically classified on the basis of the accuracy of the displacements and stresses obtained by comparison to the 3D exact results that could be assumed by the reader as benchmark for further analyses. Attention is mainly paid on localized loading conditions, that is, piecewise constant load. Also bi-sinusoidal and uniformly distributed loadings are taken into account. All of those configurations are considered in order to investigate the behavior of the 2D models in the case of continu- ous/uncontinuous, centric or off-centric loading conditions. The ratio between the side length a and the plate thickness h has been assumed as analysis parameter. Higher order 2D models yield accurate results for any considered load condition in the case of moderately thick plates, a/h=10. In the case of thick plates, a/h=5, and continuous/uncontinuous centric loading conditions high accuracy is also obtained. For the considered off-centric load condition and thick plates good results are provided for some output quantities. A better solution could be achieved by simply increasing the polynomial approximation order of the axiomatic 2D displacement field.
