Recent advancements in additive manufacturing(AM)have revolutionized the design and production of complex engineering microstructures.Despite these advancements,their mathematical modeling and computational analysis r...Recent advancements in additive manufacturing(AM)have revolutionized the design and production of complex engineering microstructures.Despite these advancements,their mathematical modeling and computational analysis remain significant challenges.This research aims to develop an effective computational method for analyzing the free vibration of functionally graded(FG)microplates under high temperatures while resting on a Pasternak foundation(PF).This formulation leverages a new thirdorder shear deformation theory(new TSDT)for improved accuracy without requiring shear correction factors.Additionally,the modified couple stress theory(MCST)is incorporated to account for sizedependent effects in microplates.The PF is characterized by two parameters including spring stiffness(k_(w))and shear layer stiffness(k_(s)).To validate the proposed method,the results obtained are compared with those of the existing literature.Furthermore,numerical examples explore the influence of various factors on the high-temperature free vibration of FG microplates.These factors include the length scale parameter(l),geometric dimensions,material properties,and the presence of the elastic foundation.The findings significantly enhance our comprehension of the free vibration of FG microplates in high thermal environments.In addition,the findings significantly enhance our comprehension of the free vibration of FG microplates in high thermal environments.In addition,the results of this research will have great potential in military and defense applications such as components of submarines,fighter aircraft,and missiles.展开更多
This study proposes an alternative calculation mode for stresses on the slip surface(SS).The calculation of the normal stress(NS)on the SS involves examining its composition and expanding its unknown using the Taylor ...This study proposes an alternative calculation mode for stresses on the slip surface(SS).The calculation of the normal stress(NS)on the SS involves examining its composition and expanding its unknown using the Taylor series.This expansion enables the reasonable construction of a function describing the NS on the SS.Additionally,by directly incorporating the nonlinear Generalized Hoke-Brown(GHB)strength criterion and utilizing the slope factor of safety(FOS)definition,a function of the shear stress on the SS is derived.This function considers the mutual feedback mechanism between the NS and strength parameters of the SS.The stress constraints conditions are then introduced at both ends of the SS based on the spatial stress relation of one point.Determining the slope FOS and stress solution for the SS involves considering the mechanical equilibrium conditions and the stress constraint conditions satisfied by the sliding body.The proposed approach successfully simulates the tension-shear stress zone near the slope top and provides an intuitive description of the concentration effect of compression-shear stress of the SS near the slope toe.Furthermore,compared to other methods,the present method demonstrates superior processing capabilities for the embedded nonlinear GHB strength criterion.展开更多
The finite element method (FEM) and the boundary element method (BEM) are often adopted. However, they are not convenient to spatially vary thermal properties of functionally graded material (FGM). Therefore, the meth...The finite element method (FEM) and the boundary element method (BEM) are often adopted. However, they are not convenient to spatially vary thermal properties of functionally graded material (FGM). Therefore, the method of lines (MOL) is introduced to solve the temperature field of FGM. The basic idea of the method is to semi-discretize the governing equation into a system of ordinary differential equations (ODEs) defined on discrete lines by means of the finite difference method. The temperature field of FGM can be obtained by solving the ODEs. The functions of thermal properties are directly embodied in these equations and these properties are not discretized in the domain. Thus, difficulty of FEM and BEM is overcome by the method. As a numerical example, the temperature field of a plane problem is analyzed for FGMs through varying thermal conductivity coefficient by the MOL.展开更多
Water function classification is to divide the waters in a basin or a region into different water function regions according to the natural features such as water resources condition, physical geographical location, e...Water function classification is to divide the waters in a basin or a region into different water function regions according to the natural features such as water resources condition, physical geographical location, environmental condition, etc. and social features such as the status quo of development and utilization, the requirement of social and economic development on water quantity and quality etc. Water function division has not ever been carried out in China and no ready-made theory and method can be complied with, in the meantime, it is a fundamental work with strong practical function. Therefore, the basic concept and theory foundation and research method are put forward on the base of summary of water resources management and developed and will be perfected in practice process of water function division. The Yangtze function zone covers the Yangtze river basin, the Lancang river basin and the rivers in the western area of the Lancang river in Southwest China. According to the technical outline of national water function division and combined with division practice of the Yangtze function zone, this paper presents the scope determination, procedure and method of water function division.展开更多
In the finite element method,the numerical simulation of three-dimensional crack propagation is relatively rare,and it is often realized by commercial programs.In addition to the geometric complexity,the determination...In the finite element method,the numerical simulation of three-dimensional crack propagation is relatively rare,and it is often realized by commercial programs.In addition to the geometric complexity,the determination of the cracking direction constitutes a great challenge.In most cases,the local stress state provides the fundamental criterion to judge the presence of cracks and the direction of crack propagation.However,in the case of three-dimensional analysis,the coordination relationship between grid elements due to occurrence of cracks becomes a difficult problem for this method.In this paper,based on the extended finite element method,the stress-related function field is introduced into the calculation domain,and then the boundary value problem of the function is solved.Subsequently,the envelope surface of all propagation directions can be obtained at one time.At last,the possible surface can be selected as the direction of crack development.Based on the aforementioned procedure,such method greatly reduces the programming complexity of tracking the crack propagation.As a suitable method for simulating tension-induced failure,it can simulate multiple cracks simultaneously.展开更多
The main purpose of this paper is to present numerical results of static bending and free vibration of functionally graded porous(FGP) variable-thickness plates by using an edge-based smoothed finite element method(ES...The main purpose of this paper is to present numerical results of static bending and free vibration of functionally graded porous(FGP) variable-thickness plates by using an edge-based smoothed finite element method(ES-FEM) associate with the mixed interpolation of tensorial components technique for the three-node triangular element(MITC3), so-called ES-MITC3. This ES-MITC3 element is performed to eliminate the shear locking problem and to enhance the accuracy of the existing MITC3 element. In the ES-MITC3 element, the stiffness matrices are obtained by using the strain smoothing technique over the smoothing domains formed by two adjacent MITC3 triangular elements sharing an edge. Materials of the plate are FGP with a power-law index(k) and maximum porosity distributions(U) in the forms of cosine functions. The influences of some geometric parameters, material properties on static bending, and natural frequency of the FGP variable-thickness plates are examined in detail.展开更多
An analytical method for analyzing the thermal vibration of multi-directional functionally graded porous rectangular plates in fluid media with novel porosity patterns is developed in this study.Mechanical properties ...An analytical method for analyzing the thermal vibration of multi-directional functionally graded porous rectangular plates in fluid media with novel porosity patterns is developed in this study.Mechanical properties of MFG porous plates change according to the length,width,and thickness directions for various materials and the porosity distribution which can be widely applied in many fields of engineering and defence technology.Especially,new porous rules that depend on spatial coordinates and grading indexes are proposed in the present work.Applying Hamilton's principle and the refined higher-order shear deformation plate theory,the governing equation of motion of an MFG porous rectangular plate in a fluid medium(the fluid-plate system)is obtained.The fluid velocity potential is derived from the boundary conditions of the fluid-plate system and is used to compute the extra mass.The GalerkinVlasov solution is used to solve and give natural frequencies of MFG porous plates with various boundary conditions in a fluid medium.The validity and reliability of the suggested method are confirmed by comparing numerical results of the present work with those from available works in the literature.The effects of different parameters on the thermal vibration response of MFG porous rectangular plates are studied in detail.These findings demonstrate that the behavior of the structure within a liquid medium differs significantly from that within a vacuum medium.Thereby,they offer appropriate operational approaches for the structure when employed in various mediums.展开更多
The method of lines(MOL) for solving the problems of functionally gradient materials(FGMs) was studied. Navier’s equations for FGMs were derived, and were semi-discretized into a system of ordinary differential (equa...The method of lines(MOL) for solving the problems of functionally gradient materials(FGMs) was studied. Navier’s equations for FGMs were derived, and were semi-discretized into a system of ordinary differential (equations(ODEs)) defined on discrete lines with the finite difference. By solving the system of ODEs, the solutions to the problem can be obtained. An example of three-point bending was given to demonstrate the application of MOL for a crack problem in the FGM. The computational results show that the more accurate results can be obtained with less computational time and resources. The obvious difficulties of numerical method for crack problems in FGMs, such as the effect of material nonhomogeneity and the existence of high gradient stress and strain near a crack tip, can be overcome without additional consideration if this method is adopted.展开更多
文摘Recent advancements in additive manufacturing(AM)have revolutionized the design and production of complex engineering microstructures.Despite these advancements,their mathematical modeling and computational analysis remain significant challenges.This research aims to develop an effective computational method for analyzing the free vibration of functionally graded(FG)microplates under high temperatures while resting on a Pasternak foundation(PF).This formulation leverages a new thirdorder shear deformation theory(new TSDT)for improved accuracy without requiring shear correction factors.Additionally,the modified couple stress theory(MCST)is incorporated to account for sizedependent effects in microplates.The PF is characterized by two parameters including spring stiffness(k_(w))and shear layer stiffness(k_(s)).To validate the proposed method,the results obtained are compared with those of the existing literature.Furthermore,numerical examples explore the influence of various factors on the high-temperature free vibration of FG microplates.These factors include the length scale parameter(l),geometric dimensions,material properties,and the presence of the elastic foundation.The findings significantly enhance our comprehension of the free vibration of FG microplates in high thermal environments.In addition,the findings significantly enhance our comprehension of the free vibration of FG microplates in high thermal environments.In addition,the results of this research will have great potential in military and defense applications such as components of submarines,fighter aircraft,and missiles.
基金Project(52278380)supported by the National Natural Science Foundation of ChinaProject(2023JJ30670)supported by the National Science Foundation of and Technology Major Project of Hunan Province,China。
文摘This study proposes an alternative calculation mode for stresses on the slip surface(SS).The calculation of the normal stress(NS)on the SS involves examining its composition and expanding its unknown using the Taylor series.This expansion enables the reasonable construction of a function describing the NS on the SS.Additionally,by directly incorporating the nonlinear Generalized Hoke-Brown(GHB)strength criterion and utilizing the slope factor of safety(FOS)definition,a function of the shear stress on the SS is derived.This function considers the mutual feedback mechanism between the NS and strength parameters of the SS.The stress constraints conditions are then introduced at both ends of the SS based on the spatial stress relation of one point.Determining the slope FOS and stress solution for the SS involves considering the mechanical equilibrium conditions and the stress constraint conditions satisfied by the sliding body.The proposed approach successfully simulates the tension-shear stress zone near the slope top and provides an intuitive description of the concentration effect of compression-shear stress of the SS near the slope toe.Furthermore,compared to other methods,the present method demonstrates superior processing capabilities for the embedded nonlinear GHB strength criterion.
文摘The finite element method (FEM) and the boundary element method (BEM) are often adopted. However, they are not convenient to spatially vary thermal properties of functionally graded material (FGM). Therefore, the method of lines (MOL) is introduced to solve the temperature field of FGM. The basic idea of the method is to semi-discretize the governing equation into a system of ordinary differential equations (ODEs) defined on discrete lines by means of the finite difference method. The temperature field of FGM can be obtained by solving the ODEs. The functions of thermal properties are directly embodied in these equations and these properties are not discretized in the domain. Thus, difficulty of FEM and BEM is overcome by the method. As a numerical example, the temperature field of a plane problem is analyzed for FGMs through varying thermal conductivity coefficient by the MOL.
文摘Water function classification is to divide the waters in a basin or a region into different water function regions according to the natural features such as water resources condition, physical geographical location, environmental condition, etc. and social features such as the status quo of development and utilization, the requirement of social and economic development on water quantity and quality etc. Water function division has not ever been carried out in China and no ready-made theory and method can be complied with, in the meantime, it is a fundamental work with strong practical function. Therefore, the basic concept and theory foundation and research method are put forward on the base of summary of water resources management and developed and will be perfected in practice process of water function division. The Yangtze function zone covers the Yangtze river basin, the Lancang river basin and the rivers in the western area of the Lancang river in Southwest China. According to the technical outline of national water function division and combined with division practice of the Yangtze function zone, this paper presents the scope determination, procedure and method of water function division.
基金Project(2017YFC0404802)supported by the National Key R&D Program of ChinaProjects(U1965206,51979143)supported by the National Natural Science Foundation of China。
文摘In the finite element method,the numerical simulation of three-dimensional crack propagation is relatively rare,and it is often realized by commercial programs.In addition to the geometric complexity,the determination of the cracking direction constitutes a great challenge.In most cases,the local stress state provides the fundamental criterion to judge the presence of cracks and the direction of crack propagation.However,in the case of three-dimensional analysis,the coordination relationship between grid elements due to occurrence of cracks becomes a difficult problem for this method.In this paper,based on the extended finite element method,the stress-related function field is introduced into the calculation domain,and then the boundary value problem of the function is solved.Subsequently,the envelope surface of all propagation directions can be obtained at one time.At last,the possible surface can be selected as the direction of crack development.Based on the aforementioned procedure,such method greatly reduces the programming complexity of tracking the crack propagation.As a suitable method for simulating tension-induced failure,it can simulate multiple cracks simultaneously.
基金funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant number 107.02-2019.330。
文摘The main purpose of this paper is to present numerical results of static bending and free vibration of functionally graded porous(FGP) variable-thickness plates by using an edge-based smoothed finite element method(ES-FEM) associate with the mixed interpolation of tensorial components technique for the three-node triangular element(MITC3), so-called ES-MITC3. This ES-MITC3 element is performed to eliminate the shear locking problem and to enhance the accuracy of the existing MITC3 element. In the ES-MITC3 element, the stiffness matrices are obtained by using the strain smoothing technique over the smoothing domains formed by two adjacent MITC3 triangular elements sharing an edge. Materials of the plate are FGP with a power-law index(k) and maximum porosity distributions(U) in the forms of cosine functions. The influences of some geometric parameters, material properties on static bending, and natural frequency of the FGP variable-thickness plates are examined in detail.
文摘An analytical method for analyzing the thermal vibration of multi-directional functionally graded porous rectangular plates in fluid media with novel porosity patterns is developed in this study.Mechanical properties of MFG porous plates change according to the length,width,and thickness directions for various materials and the porosity distribution which can be widely applied in many fields of engineering and defence technology.Especially,new porous rules that depend on spatial coordinates and grading indexes are proposed in the present work.Applying Hamilton's principle and the refined higher-order shear deformation plate theory,the governing equation of motion of an MFG porous rectangular plate in a fluid medium(the fluid-plate system)is obtained.The fluid velocity potential is derived from the boundary conditions of the fluid-plate system and is used to compute the extra mass.The GalerkinVlasov solution is used to solve and give natural frequencies of MFG porous plates with various boundary conditions in a fluid medium.The validity and reliability of the suggested method are confirmed by comparing numerical results of the present work with those from available works in the literature.The effects of different parameters on the thermal vibration response of MFG porous rectangular plates are studied in detail.These findings demonstrate that the behavior of the structure within a liquid medium differs significantly from that within a vacuum medium.Thereby,they offer appropriate operational approaches for the structure when employed in various mediums.
基金Projects(90305023 59731020) supported by the National Natural Science Foundation of China
文摘The method of lines(MOL) for solving the problems of functionally gradient materials(FGMs) was studied. Navier’s equations for FGMs were derived, and were semi-discretized into a system of ordinary differential (equations(ODEs)) defined on discrete lines with the finite difference. By solving the system of ODEs, the solutions to the problem can be obtained. An example of three-point bending was given to demonstrate the application of MOL for a crack problem in the FGM. The computational results show that the more accurate results can be obtained with less computational time and resources. The obvious difficulties of numerical method for crack problems in FGMs, such as the effect of material nonhomogeneity and the existence of high gradient stress and strain near a crack tip, can be overcome without additional consideration if this method is adopted.
