The four-dimensional(4D) printing technology, as a combination of additive manufacturing and smart materials, has attracted increasing research interest in recent years. The bilayer structures printed with smart mater...The four-dimensional(4D) printing technology, as a combination of additive manufacturing and smart materials, has attracted increasing research interest in recent years. The bilayer structures printed with smart materials using this technology can realize complicated deformation under some special stimuli due to the material properties.The deformation prediction of bilayer structures can make the design process more rapid and thus is of great importance. However, the previous works on deformation prediction of bilayer structures rarely study the complicated deformations or the influence of the printing process on deformation. Thus, this paper proposes a new method to predict the complicated deformations of temperature-sensitive 4D printed bilayer structures,in particular to the bilayer structures based on temperature-driven shape-memory polymers(SMPs) and fabricated using the fused deposition modeling(FDM) technology. The programming process to the material during printing is revealed and considered in the simulation model. Simulation results are compared with experiments to verify the validity of the method. The advantages of this method are stable convergence and high efficiency,as the three-dimensional(3D) problem is converted to a two-dimensional(2D) problem.The simulation parameters in the model can be further associated with the printing parameters, which shows good application prospect in 4D printed bilayer structure design.展开更多
A method of equivalent simplification,using equivalent-plate models(EPMs),is developed.It is to achieve goals of rapid modeling and effective analysis in structural dynamics and flutter analysis of complex wing struct...A method of equivalent simplification,using equivalent-plate models(EPMs),is developed.It is to achieve goals of rapid modeling and effective analysis in structural dynamics and flutter analysis of complex wing structures.It is on the assumption that the wing structures discussed are composed of skin,beams and ribs,and the different plate units(such as skin,beam web,rib web)are not distinguished in modeling,which is to avoid the complex pre-processing and make it more generalized.Taking the effect of transverse shear deformation into consideration,the equivalence is based on the first-order shear deformation theory,and it can import the model files of MSC/NASTRAN and process the information to accomplish the equivalent modeling.The Ritz method is applied with the Legendre polynomials,which is used to define the geometry,structure and displacements of the wing.Particularly,the selection of Legendre polynomials as trial functions brings good accuracy to the modeling and can avoid the ill-conditions.This is in contrast to the EPM method based on the classical plate theory.Through vibration and flutter analysis,the results obtained by using EPM agree well with those obtained by the finite element method,which indicates the accuracy and effectiveness in vibration and flutter analysis of the EPM method.展开更多
The influence of sand dust on discharge of external insulation has caused widespread concern.At present,the research results show wind-sand electricity has a remarkable effect on the discharge characteristics of insul...The influence of sand dust on discharge of external insulation has caused widespread concern.At present,the research results show wind-sand electricity has a remarkable effect on the discharge characteristics of insulator and has little influence on the discharge characteristics of air gap.The flashover of insulator strings occurs along the insulator surface and air gaps,and the sand dust deposited on the insulator surface may affect the flashover characteristics of insulator strings.This paper studies the flashover characteristics of flat plate model under DC voltage in wind-sand condition.The experimental results show that under positive polarity voltage,the flashover voltage of the flat plate model has a maximum value,while under negative polarity voltage,the flashover voltage of the flat plate model has a minimum value with a certain degree of sand dust deposition.The wind or sand in sand-dust weather has an important effect on the flashover characteristics of the flat plate model.In certain variation range of electric charge,electric charge of sand dust has little effect on the flashover voltage of flat plate model under DC voltage.The deposition of sand has significant influence on the flashover process of flat plate model,which is related to the deposition density and moisture content of sand particle.展开更多
Continuum plate model in the form of a cantilever anisotropic plate developed in the framework of the bimoment theory of plates describing seismic oscillations of buildings is proposed in this paper as a dynamic model...Continuum plate model in the form of a cantilever anisotropic plate developed in the framework of the bimoment theory of plates describing seismic oscillations of buildings is proposed in this paper as a dynamic model of a building. Formulas for the reduced moduli of elasticity, shear and density of the plate model of a building are given. Longitudinal oscillations of a building are studied using the continuum plate and box-like models of the building with Finite Element Model. Numerical results are obtained in the form of graphs, followed by their analysis.展开更多
In the paper a linear combination of both the standard mixed formulation and the displacement one of the Reissner-Mindlin plate theory is used to enhance stability of the former and to remove ''locking'...In the paper a linear combination of both the standard mixed formulation and the displacement one of the Reissner-Mindlin plate theory is used to enhance stability of the former and to remove ''locking'' of the later. For this new stabilized formulation, a unified approach to convergence analysis is presented for a wide spectrum of finite element spaces. As long as the rotation space is appropriately enriched, the formulation is convergent for the finite element spaces of sufficiently high order. Optimal-order error estimates with constants independent of the plate thickness are proved for the various lower order methods of this kind.展开更多
To study the bending deformation of the lithosphere, the simplification of replacing a spherical shell by a plate model is usually made. Based on the differential equations for the bending of plates and shallow spheri...To study the bending deformation of the lithosphere, the simplification of replacing a spherical shell by a plate model is usually made. Based on the differential equations for the bending of plates and shallow spherical shells, an expression for the error caused by such a simplification is derived in this paper. The effect of model sizes on the error is discussed. It is proved that if we replace the shallow spherical shell by a plate model to solve the bending deformation of lithospheric plate, a large error will be caused. In contrast, if we use a plate on an elastic foundation instead, an approximate solution closer to that of spherical shell can be obtained. In such a way, the error can be reduced effectively and the actual geological condition can be modeled more closely.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
Inclusion of dissipation and memory mechanisms, non-classical elasticity and thermal effects in the currently used plate/shell mathematical models require that we establish if these mathematical models can be derived ...Inclusion of dissipation and memory mechanisms, non-classical elasticity and thermal effects in the currently used plate/shell mathematical models require that we establish if these mathematical models can be derived using the conservation and balance laws of continuum mechanics in conjunction with the corresponding kinematic assumptions. This is referred to as thermodynamic consistency of the mathematical models. Thermodynamic consistency ensures thermodynamic equilibrium during the evolution of the deformation. When the mathematical models are thermodynamically consistent, the second law of thermodynamics facilitates consistent derivations of constitutive theories in the presence of dissipation and memory mechanisms. This is the main motivation for the work presented in this paper. In the currently used mathematical models for plates/shells based on the assumed kinematic relations, energy functional is constructed over the volume consisting of kinetic energy, strain energy and the potential energy of the loads. The Euler’s equations derived from the first variation of the energy functional for arbitrary length when set to zero yield the mathematical model(s) for the deforming plates/shells. Alternatively, principle of virtual work can also be used to derive the same mathematical model(s). For linear elastic reversible deformation physics with small deformation and small strain, these two approaches, based on energy functional and the principle of virtual work, yield the same mathematical models. These mathematical models hold for reversible mechanical deformation. In this paper, we examine whether the currently used plate/shell mathematical models with the corresponding kinematic assumptions can be derived using the conservation and balance laws of classical or non-classical continuum mechanics. The mathematical models based on Kirchhoff hypothesis (classical plate theory, CPT) and first order shear deformation theory (FSDT) that are representative of most mathematical models for plates/shells are investigated in this paper for their thermodynamic consistency. This is followed by the details of a general and higher order thermodynamically consistent plate/shell thermoelastic mathematical model that is free of a priori consideration of kinematic assumptions and remains valid for very thin as well as thick plates/shells with comprehensive nonlinear constitutive theories based on integrity. Model problem studies are presented for small deformation behavior of linear elastic plates in the absence of thermal effects and the results are compared with CPT and FSDT mathematical models.展开更多
The plate flexure and normal faulting characteristics along the Tonga, Japan, Izu-Bonin and Mariana Trenches are investigated by combining observations and modeling of elastoplastic deformation of the subducting plate...The plate flexure and normal faulting characteristics along the Tonga, Japan, Izu-Bonin and Mariana Trenches are investigated by combining observations and modeling of elastoplastic deformation of the subducting plate. The observed average trench relief is found to be the smallest at the Japan Trench(3 km) and the largest at the Mariana Trench(4.9 km), and the average fault throw is the smallest at the Japan Trench(113 m) and the largest at the Tonga Trench(284 m). A subducting plate is modeled to bend and generate normal faults subjected to three types of tectonic loading at the trench axis: vertical loading, bending moment, and horizontal tensional force. It is inverted for the solutions of tectonic loading that best fit the observed plate flexure and normal faulting characteristics of the four trenches. The results reveal that a horizontal tensional force(HTF) for the Japan Trench is 33%, 50% and 60% smaller than those of the Mariana, Tonga and Izu-Bonin Trenches, respectively. The normal faults are modeled to penetrate to a maximum depth of 29, 23, 32 and 32 km below the sea floor for the Tonga,Japan, Izu-Bonin and Mariana Trenches, respectively, which is consistent with the depths of relocated normal faulting earthquakes in the Japan and Izu-Bonin Trenches. Moreover, it is argued that the calculated horizontal tensional force is generally positively correlated with the observed mean fault throw, while the integrated area of the reduction in the effective elastic thickness is correlated with the trench relief. These results imply that the HTF plays a key role in controlling the normal faulting pattern and that plate weakening can lead to significant increase in the trench relief.展开更多
The internal balance technique is effective for model reduction in flexible structures, especially those with dense frequencies. However, due to the difficulty in extracting the internal balance modal coordinates from...The internal balance technique is effective for model reduction in flexible structures, especially those with dense frequencies. However, due to the difficulty in extracting the internal balance modal coordinates from the physical sensor readings, research so far on this topic has been mostly theoretic and little on experiment or engineering applications. This paper, by working on a DSP TMS320F2812-based experiment system with a flexible plate and bringing forward an approximating approach to accessing the internal balance modal coordinates, studies the internal balance method theoretically as well as experimentally, and further designs an active controller based on the reduced model. Simulation and test results have proven the proposed approximating approach feasible and effective, and the designed controller successful in restraining the plate vibration.展开更多
A mathematic model of the solid fraction during rheo-casting by the cooling sloping plate process was established, and the effects of the process parameters on the solid fraction were analyzed. The calculation results...A mathematic model of the solid fraction during rheo-casting by the cooling sloping plate process was established, and the effects of the process parameters on the solid fraction were analyzed. The calculation results show that the experimental result is approximately agreed with the calculation value. The effect of the casting temperature on the change rate of the solid fraction is not obvious. But the beginning solidification length is greatly influenced by the casting temperature. The beginning solidification length increases with the increment of the casting temperature. The effect of the sloping angle on the solid fraction becomes obvious with the increment of the sloping plate length. The solid fraction increases sharply with the decrease of the initial thickness of the melt. The melt initial thickness between 15 and 20 mm is suggested.展开更多
On the assumption that a plate is elastically deformable and may rotate as a whole, we found that Eurasian area may be divided into an Eurasian plate and three blocks of the Xiyu, the North China and the Southeast Asi...On the assumption that a plate is elastically deformable and may rotate as a whole, we found that Eurasian area may be divided into an Eurasian plate and three blocks of the Xiyu, the North China and the Southeast Asia according to tectonic frame of the East and Southeast Asia and the ITRF2008 velocity field in Eurasian area. F tests show that the accuracy of this elastic-plate/block model is significantly higher than the corresponding rigid-plate models; the area covered is notably larger also.展开更多
A metal plate cooling model for 400~ single concentrator solar cells was established. The effects of the thickness and the radius of the metal plate, and the air environment on the temperature of the solar cells were ...A metal plate cooling model for 400~ single concentrator solar cells was established. The effects of the thickness and the radius of the metal plate, and the air environment on the temperature of the solar cells were analyzed in detail. It is shown that the temperature of the solar cells decreased sharply at the beginning, with the increase in the thickness of the metal plate, and then changed more smoothly. When the radius of the metal plate was 4 cm and the thickness increased to 2 mm or thicker, the temperature of the solar cell basically stabilized at about 53℃. Increasing the radius of the metal plate and the convective transfer coefficient made the temperature of the solar cell decrease remarkably. The effects of A1 and Cu as the metal plate material on cooling were analyzed contrastively, and demonstrated the superiority of A1 material for the cooling system. Furthermore, considering cost reduction, space holding and the stress of the system, we optimized the structural design of the metal plate. The simulated results can be referred to the design of the structure for the metal plate. Finally, a method to devise the structure of the metal plate for single concentrator solar cells was given.展开更多
Waves occurring in cold-rolled plates or sheets can be divided into longitudinal and transverse waves. Classical leveling theories merely solve the problem of longitudinal waves, while no well accepted method can be e...Waves occurring in cold-rolled plates or sheets can be divided into longitudinal and transverse waves. Classical leveling theories merely solve the problem of longitudinal waves, while no well accepted method can be employed for transverse waves. In order to investigate the essential deformation law of leveling for plates with transverse waves, a 2.5-dimensional （2.5- D） analytical approach was proposed. In this model, the plate was transversely divided into some strips with equal width; the strips are considered to be in the state of plane strain and each group of adjacent strips are assumed to be deformation compatible under stress. After calculation, the bending deformation of each strip and the leveling effect of overall plate were obtained by comprehensNe consideration of various strips along with the width. Bending of roller is a main approach to eliminate the transverse waves, which is widely accepted by the industry, but the essential effect of bending of roller on the deformation of plates and the calculation of bending of roller are unknown. According to the 2.5-D analytical model, it can be found that, for plates, it is neutral plane offsetting and middle plane elongation or contraction under inner stress that can effectively improve plate shape. Taking double side waves as an example, the appropriate values of bending of roller were obtained by the 2.5-D analytical model related to different initial unevenness, which was applicable to the current on-line adjusting of bending of roller in rolling industry.展开更多
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
Multi- pass spray deposition shows apparent advantages in preparing large scale plates with rapid solidification. Shape model is promoted to obtain excellent shape. Three dimensional mathematical models considering mo...Multi- pass spray deposition shows apparent advantages in preparing large scale plates with rapid solidification. Shape model is promoted to obtain excellent shape. Three dimensional mathematical models considering motion of atomization cone and substrate, deposition distance and atomization parameters were used to predict deposited plate’s shape. The results can be used to optimize the process parameters.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
In order to design the scale model in a wide frequency range,a method based on the reflective loss is proposed according to the high-frequency approximation algorithm,and an example of designing the scale model of a p...In order to design the scale model in a wide frequency range,a method based on the reflective loss is proposed according to the high-frequency approximation algorithm,and an example of designing the scale model of a plate-shaped absorber is given in this paper.In the example,the frequency of the full-size measurement ranges from 2.0 GHz to 2.4 GHz,the thickness of the full-size absorber is 1 mm and the scale ratio is 1/5.A two-layer scale absorber is obtained by the proposed method.The thickness values of the bottom and top layer are 0.4 mm and 0.5 mm,respectively.Furthermore,the scattering properties of a plate model and an SLICY model are studied by FEKO to verify the effectiveness of the designed scale absorber.Compared with the corresponding values from the theoretical scale model,the average values of the absolute deviations in 10 GHz～12 GHz are 0.53 d Bm^2,0.65 d Bm^2,0.76 d Bm^2 for the plate model and 0.20 d Bm^2,0.95 d Bm^2,0.77 d Bm^2 for the SLICY model while the incident angles are 0°,30°,and 60°,respectively.These deviations fall within the Radar cross section（RCS） measurement tolerance.Thus,the work in this paper has important theoretical and practical significance.展开更多
In this paper, the generalized Oldroyd-B with fractional calculus approach is used. An exact solution in terms of Fox-H function for flow past an accelerated horizontal plate in a rotating fluid is obtained by using d...In this paper, the generalized Oldroyd-B with fractional calculus approach is used. An exact solution in terms of Fox-H function for flow past an accelerated horizontal plate in a rotating fluid is obtained by using discrete Laplace transform method. A comparison among the influence of various parameters in the Oldroyd-B model and the angular velocity of the fluid on the velocity profiles is made through numerical method in graphic form.展开更多
基金the National Natural Science Foundation of China(Nos.52130501 and 52075479)the National Key R&D Program of China(No.2018YFB1700804)。
文摘The four-dimensional(4D) printing technology, as a combination of additive manufacturing and smart materials, has attracted increasing research interest in recent years. The bilayer structures printed with smart materials using this technology can realize complicated deformation under some special stimuli due to the material properties.The deformation prediction of bilayer structures can make the design process more rapid and thus is of great importance. However, the previous works on deformation prediction of bilayer structures rarely study the complicated deformations or the influence of the printing process on deformation. Thus, this paper proposes a new method to predict the complicated deformations of temperature-sensitive 4D printed bilayer structures,in particular to the bilayer structures based on temperature-driven shape-memory polymers(SMPs) and fabricated using the fused deposition modeling(FDM) technology. The programming process to the material during printing is revealed and considered in the simulation model. Simulation results are compared with experiments to verify the validity of the method. The advantages of this method are stable convergence and high efficiency,as the three-dimensional(3D) problem is converted to a two-dimensional(2D) problem.The simulation parameters in the model can be further associated with the printing parameters, which shows good application prospect in 4D printed bilayer structure design.
文摘A method of equivalent simplification,using equivalent-plate models(EPMs),is developed.It is to achieve goals of rapid modeling and effective analysis in structural dynamics and flutter analysis of complex wing structures.It is on the assumption that the wing structures discussed are composed of skin,beams and ribs,and the different plate units(such as skin,beam web,rib web)are not distinguished in modeling,which is to avoid the complex pre-processing and make it more generalized.Taking the effect of transverse shear deformation into consideration,the equivalence is based on the first-order shear deformation theory,and it can import the model files of MSC/NASTRAN and process the information to accomplish the equivalent modeling.The Ritz method is applied with the Legendre polynomials,which is used to define the geometry,structure and displacements of the wing.Particularly,the selection of Legendre polynomials as trial functions brings good accuracy to the modeling and can avoid the ill-conditions.This is in contrast to the EPM method based on the classical plate theory.Through vibration and flutter analysis,the results obtained by using EPM agree well with those obtained by the finite element method,which indicates the accuracy and effectiveness in vibration and flutter analysis of the EPM method.
基金Project Supported by National Natural Science Foundation of China（90510014 ）.
文摘The influence of sand dust on discharge of external insulation has caused widespread concern.At present,the research results show wind-sand electricity has a remarkable effect on the discharge characteristics of insulator and has little influence on the discharge characteristics of air gap.The flashover of insulator strings occurs along the insulator surface and air gaps,and the sand dust deposited on the insulator surface may affect the flashover characteristics of insulator strings.This paper studies the flashover characteristics of flat plate model under DC voltage in wind-sand condition.The experimental results show that under positive polarity voltage,the flashover voltage of the flat plate model has a maximum value,while under negative polarity voltage,the flashover voltage of the flat plate model has a minimum value with a certain degree of sand dust deposition.The wind or sand in sand-dust weather has an important effect on the flashover characteristics of the flat plate model.In certain variation range of electric charge,electric charge of sand dust has little effect on the flashover voltage of flat plate model under DC voltage.The deposition of sand has significant influence on the flashover process of flat plate model,which is related to the deposition density and moisture content of sand particle.
文摘Continuum plate model in the form of a cantilever anisotropic plate developed in the framework of the bimoment theory of plates describing seismic oscillations of buildings is proposed in this paper as a dynamic model of a building. Formulas for the reduced moduli of elasticity, shear and density of the plate model of a building are given. Longitudinal oscillations of a building are studied using the continuum plate and box-like models of the building with Finite Element Model. Numerical results are obtained in the form of graphs, followed by their analysis.
文摘In the paper a linear combination of both the standard mixed formulation and the displacement one of the Reissner-Mindlin plate theory is used to enhance stability of the former and to remove ''locking'' of the later. For this new stabilized formulation, a unified approach to convergence analysis is presented for a wide spectrum of finite element spaces. As long as the rotation space is appropriately enriched, the formulation is convergent for the finite element spaces of sufficiently high order. Optimal-order error estimates with constants independent of the plate thickness are proved for the various lower order methods of this kind.
文摘To study the bending deformation of the lithosphere, the simplification of replacing a spherical shell by a plate model is usually made. Based on the differential equations for the bending of plates and shallow spherical shells, an expression for the error caused by such a simplification is derived in this paper. The effect of model sizes on the error is discussed. It is proved that if we replace the shallow spherical shell by a plate model to solve the bending deformation of lithospheric plate, a large error will be caused. In contrast, if we use a plate on an elastic foundation instead, an approximate solution closer to that of spherical shell can be obtained. In such a way, the error can be reduced effectively and the actual geological condition can be modeled more closely.
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.
文摘Inclusion of dissipation and memory mechanisms, non-classical elasticity and thermal effects in the currently used plate/shell mathematical models require that we establish if these mathematical models can be derived using the conservation and balance laws of continuum mechanics in conjunction with the corresponding kinematic assumptions. This is referred to as thermodynamic consistency of the mathematical models. Thermodynamic consistency ensures thermodynamic equilibrium during the evolution of the deformation. When the mathematical models are thermodynamically consistent, the second law of thermodynamics facilitates consistent derivations of constitutive theories in the presence of dissipation and memory mechanisms. This is the main motivation for the work presented in this paper. In the currently used mathematical models for plates/shells based on the assumed kinematic relations, energy functional is constructed over the volume consisting of kinetic energy, strain energy and the potential energy of the loads. The Euler’s equations derived from the first variation of the energy functional for arbitrary length when set to zero yield the mathematical model(s) for the deforming plates/shells. Alternatively, principle of virtual work can also be used to derive the same mathematical model(s). For linear elastic reversible deformation physics with small deformation and small strain, these two approaches, based on energy functional and the principle of virtual work, yield the same mathematical models. These mathematical models hold for reversible mechanical deformation. In this paper, we examine whether the currently used plate/shell mathematical models with the corresponding kinematic assumptions can be derived using the conservation and balance laws of classical or non-classical continuum mechanics. The mathematical models based on Kirchhoff hypothesis (classical plate theory, CPT) and first order shear deformation theory (FSDT) that are representative of most mathematical models for plates/shells are investigated in this paper for their thermodynamic consistency. This is followed by the details of a general and higher order thermodynamically consistent plate/shell thermoelastic mathematical model that is free of a priori consideration of kinematic assumptions and remains valid for very thin as well as thick plates/shells with comprehensive nonlinear constitutive theories based on integrity. Model problem studies are presented for small deformation behavior of linear elastic plates in the absence of thermal effects and the results are compared with CPT and FSDT mathematical models.
基金The National Natural Science Foundation of China under contract Nos 41706056,91628301 and U1606401the Program of Chinese Academy of Sciences under contract Nos Y4SL021001,QYZDY-SSW-DQC005,YZ201325 and YZ201534+1 种基金the Natural Science Foundation of Guangdong Province of China under contract No.2017A030310066the China Ocean Mineral Resources R&D Association under contract No.DY135-S2-1-04
文摘The plate flexure and normal faulting characteristics along the Tonga, Japan, Izu-Bonin and Mariana Trenches are investigated by combining observations and modeling of elastoplastic deformation of the subducting plate. The observed average trench relief is found to be the smallest at the Japan Trench(3 km) and the largest at the Mariana Trench(4.9 km), and the average fault throw is the smallest at the Japan Trench(113 m) and the largest at the Tonga Trench(284 m). A subducting plate is modeled to bend and generate normal faults subjected to three types of tectonic loading at the trench axis: vertical loading, bending moment, and horizontal tensional force. It is inverted for the solutions of tectonic loading that best fit the observed plate flexure and normal faulting characteristics of the four trenches. The results reveal that a horizontal tensional force(HTF) for the Japan Trench is 33%, 50% and 60% smaller than those of the Mariana, Tonga and Izu-Bonin Trenches, respectively. The normal faults are modeled to penetrate to a maximum depth of 29, 23, 32 and 32 km below the sea floor for the Tonga,Japan, Izu-Bonin and Mariana Trenches, respectively, which is consistent with the depths of relocated normal faulting earthquakes in the Japan and Izu-Bonin Trenches. Moreover, it is argued that the calculated horizontal tensional force is generally positively correlated with the observed mean fault throw, while the integrated area of the reduction in the effective elastic thickness is correlated with the trench relief. These results imply that the HTF plays a key role in controlling the normal faulting pattern and that plate weakening can lead to significant increase in the trench relief.
基金supported by the Key Project (No. 11132001)the General Projects (Nos. 11072146 and 11002087) of the National Natural Science Foundation of China
文摘The internal balance technique is effective for model reduction in flexible structures, especially those with dense frequencies. However, due to the difficulty in extracting the internal balance modal coordinates from the physical sensor readings, research so far on this topic has been mostly theoretic and little on experiment or engineering applications. This paper, by working on a DSP TMS320F2812-based experiment system with a flexible plate and bringing forward an approximating approach to accessing the internal balance modal coordinates, studies the internal balance method theoretically as well as experimentally, and further designs an active controller based on the reduced model. Simulation and test results have proven the proposed approximating approach feasible and effective, and the designed controller successful in restraining the plate vibration.
基金Supported by National High Technology Research and Development Program of China （863 Program） （2008AA04Z129） National Natural Science Foundation of China （60504010 60864004 60774015）+1 种基金 Disbursal Budget Program of Shanghai Municipal Education Commission of China （2008093） Innovation Program of Shanghai Municipal Education Commission of China （09YZ241）
基金supported by the National Natural Science Foundation of China (Nos.51034002 and 50974038)National Program for Fundamental Research and Development of China (No.2011CB610405)
文摘A mathematic model of the solid fraction during rheo-casting by the cooling sloping plate process was established, and the effects of the process parameters on the solid fraction were analyzed. The calculation results show that the experimental result is approximately agreed with the calculation value. The effect of the casting temperature on the change rate of the solid fraction is not obvious. But the beginning solidification length is greatly influenced by the casting temperature. The beginning solidification length increases with the increment of the casting temperature. The effect of the sloping angle on the solid fraction becomes obvious with the increment of the sloping plate length. The solid fraction increases sharply with the decrease of the initial thickness of the melt. The melt initial thickness between 15 and 20 mm is suggested.
基金supported by the China National Key Basic Research Program (2007CB411702)the National Natural Science Fundation of China(40474036,40474039)+1 种基金Earthquake Industry Research Special MajorProjects China Comprehensive Geophysical Fied Observation( 200908029)the Old Expert Research Foundation of China Earth-quake Administration
文摘On the assumption that a plate is elastically deformable and may rotate as a whole, we found that Eurasian area may be divided into an Eurasian plate and three blocks of the Xiyu, the North China and the Southeast Asia according to tectonic frame of the East and Southeast Asia and the ITRF2008 velocity field in Eurasian area. F tests show that the accuracy of this elastic-plate/block model is significantly higher than the corresponding rigid-plate models; the area covered is notably larger also.
基金Project supported by the Doctoral Initial Fund of Beijing University of Technology,China (Grant No. X0006015201101)the National Natural Science Foundation of China (Grant No. 10804005)
文摘A metal plate cooling model for 400~ single concentrator solar cells was established. The effects of the thickness and the radius of the metal plate, and the air environment on the temperature of the solar cells were analyzed in detail. It is shown that the temperature of the solar cells decreased sharply at the beginning, with the increase in the thickness of the metal plate, and then changed more smoothly. When the radius of the metal plate was 4 cm and the thickness increased to 2 mm or thicker, the temperature of the solar cell basically stabilized at about 53℃. Increasing the radius of the metal plate and the convective transfer coefficient made the temperature of the solar cell decrease remarkably. The effects of A1 and Cu as the metal plate material on cooling were analyzed contrastively, and demonstrated the superiority of A1 material for the cooling system. Furthermore, considering cost reduction, space holding and the stress of the system, we optimized the structural design of the metal plate. The simulated results can be referred to the design of the structure for the metal plate. Finally, a method to devise the structure of the metal plate for single concentrator solar cells was given.
基金Sponsored by National Science and Technology Major Project of China(2012ZX04012011)National Natural Science Foundation of China(51375306)
文摘Waves occurring in cold-rolled plates or sheets can be divided into longitudinal and transverse waves. Classical leveling theories merely solve the problem of longitudinal waves, while no well accepted method can be employed for transverse waves. In order to investigate the essential deformation law of leveling for plates with transverse waves, a 2.5-dimensional （2.5- D） analytical approach was proposed. In this model, the plate was transversely divided into some strips with equal width; the strips are considered to be in the state of plane strain and each group of adjacent strips are assumed to be deformation compatible under stress. After calculation, the bending deformation of each strip and the leveling effect of overall plate were obtained by comprehensNe consideration of various strips along with the width. Bending of roller is a main approach to eliminate the transverse waves, which is widely accepted by the industry, but the essential effect of bending of roller on the deformation of plates and the calculation of bending of roller are unknown. According to the 2.5-D analytical model, it can be found that, for plates, it is neutral plane offsetting and middle plane elongation or contraction under inner stress that can effectively improve plate shape. Taking double side waves as an example, the appropriate values of bending of roller were obtained by the 2.5-D analytical model related to different initial unevenness, which was applicable to the current on-line adjusting of bending of roller in rolling industry.
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.
文摘Multi- pass spray deposition shows apparent advantages in preparing large scale plates with rapid solidification. Shape model is promoted to obtain excellent shape. Three dimensional mathematical models considering motion of atomization cone and substrate, deposition distance and atomization parameters were used to predict deposited plate’s shape. The results can be used to optimize the process parameters.
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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61601299 and 11404213)the Shanghai Municipal Science and Technology Commission,China(Grant Nos.17210730900 and 15ZR1439600)the Defense Industrial Technology,China(Grant No.B2120132001)
文摘In order to design the scale model in a wide frequency range,a method based on the reflective loss is proposed according to the high-frequency approximation algorithm,and an example of designing the scale model of a plate-shaped absorber is given in this paper.In the example,the frequency of the full-size measurement ranges from 2.0 GHz to 2.4 GHz,the thickness of the full-size absorber is 1 mm and the scale ratio is 1/5.A two-layer scale absorber is obtained by the proposed method.The thickness values of the bottom and top layer are 0.4 mm and 0.5 mm,respectively.Furthermore,the scattering properties of a plate model and an SLICY model are studied by FEKO to verify the effectiveness of the designed scale absorber.Compared with the corresponding values from the theoretical scale model,the average values of the absolute deviations in 10 GHz～12 GHz are 0.53 d Bm^2,0.65 d Bm^2,0.76 d Bm^2 for the plate model and 0.20 d Bm^2,0.95 d Bm^2,0.77 d Bm^2 for the SLICY model while the incident angles are 0°,30°,and 60°,respectively.These deviations fall within the Radar cross section（RCS） measurement tolerance.Thus,the work in this paper has important theoretical and practical significance.
基金supported by The project supported by the Natural Science Foundation of Shandong Province of China (Y2007A06)
文摘In this paper, the generalized Oldroyd-B with fractional calculus approach is used. An exact solution in terms of Fox-H function for flow past an accelerated horizontal plate in a rotating fluid is obtained by using discrete Laplace transform method. A comparison among the influence of various parameters in the Oldroyd-B model and the angular velocity of the fluid on the velocity profiles is made through numerical method in graphic form.
