Marine thin plates are susceptible to welding deformation owing to their low structural stiffness.Therefore,the efficient and accurate prediction of welding deformation is essential for improving welding quality.The t...Marine thin plates are susceptible to welding deformation owing to their low structural stiffness.Therefore,the efficient and accurate prediction of welding deformation is essential for improving welding quality.The traditional thermal elastic-plastic finite element method(TEP-FEM)can accurately predict welding deformation.However,its efficiency is low because of the complex nonlinear transient computation,making it difficult to meet the needs of rapid engineering evaluation.To address this challenge,this study proposes an efficient prediction method for welding deformation in marine thin plate butt welds.This method is based on the coupled temperature gradient-thermal strain method(TG-TSM)that integrates inherent strain theory with a shell element finite element model.The proposed method first extracts the distribution pattern and characteristic value of welding-induced inherent strain through TEP-FEM analysis.This strain is then converted into the equivalent thermal load applied to the shell element model for rapid computation.The proposed method-particularly,the gradual temperature gradient-thermal strain method(GTG-TSM)-achieved improved computational efficiency and consistent precision.Furthermore,the proposed method required much less computation time than the traditional TEP-FEM.Thus,this study lays the foundation for future prediction of welding deformation in more complex marine thin plates.展开更多
The analysis of the dynamics of surface girders is of great importance in the design of engineering structures such as steel welded bridge plane girders or concrete plate-column structures.This work is an extension of...The analysis of the dynamics of surface girders is of great importance in the design of engineering structures such as steel welded bridge plane girders or concrete plate-column structures.This work is an extension of the classical deterministic problem of free vibrations of thin(Kirchhoff)plates.Themain aim of this work is the study of stochastic eigenvibrations of thin(Kirchhoff)elastic plates resting on internal continuous and column supports by the Boundary Element Method(BEM).This work is a continuation of previous research related to the random approach in plate analysis using the BEM.The static fundamental solution(Green’s function)is applied,coupled with a nonsingular formulation of the boundary and domain integral equations.These are derived using a modified and simplified formulation of the boundary conditions,inwhich there is no need to introduce theKirchhoff forces on a plate boundary.The role of the Kirchhoff corner forces is played by the boundary elements placed close to a single corner.Internal column or linear continuous supports are introduced using the Bezine technique,where the additional collocation points are introduced inside a plate domain.This allows for significant simplification of the BEM computational algorithm.An application of the polynomial approximations in the Least Squares Method(LSM)recovery of the structural response is done.The probabilistic analysis will employ three independent computational approaches:semi-analytical method(SAM),stochastic perturbation technique(SPT),and Monte-Carlo simulations.Numerical investigations include the fundamental eigenfrequencies of an elastic,thin,homogeneous,and isotropic plate.展开更多
The challenge of solving nonlinear problems in multi-connected domains with high accuracy has garnered significant interest.In this paper,we propose a unified wavelet solution method for accurately solving nonlinear b...The challenge of solving nonlinear problems in multi-connected domains with high accuracy has garnered significant interest.In this paper,we propose a unified wavelet solution method for accurately solving nonlinear boundary value problems on a two-dimensional(2D)arbitrary multi-connected domain.We apply this method to solve large deflection bending problems of complex plates with holes.Our solution method simplifies the treatment of the 2D multi-connected domain by utilizing a natural discretization approach that divides it into a series of one-dimensional(1D)intervals.This approach establishes a fundamental relationship between the highest-order derivative in the governing equation of the problem and the remaining lower-order derivatives.By combining a wavelet high accuracy integral approximation format on 1D intervals,where the convergence order remains constant regardless of the number of integration folds,with the collocation method,we obtain a system of algebraic equations that only includes discrete point values of the highest order derivative.In this process,the boundary conditions are automatically replaced using integration constants,eliminating the need for additional processing.Error estimation and numerical results demonstrate that the accuracy of this method is unaffected by the degree of nonlinearity of the equations.When solving the bending problem of multi-perforated complex-shaped plates under consideration,it is evident that directly using higher-order derivatives as unknown functions significantly improves the accuracy of stress calculation,even when the stress exhibits large gradient variations.Moreover,compared to the finite element method,the wavelet method requires significantly fewer nodes to achieve the same level of accuracy.Ultimately,the method achieves a sixth-order accuracy and resembles the treatment of one-dimensional problems during the solution process,effectively avoiding the need for the complex 2D meshing process typically required by conventional methods when solving problems with multi-connected domains.展开更多
A mesh-free method is presented to investigate the static bending properties of functionally graded carbon nanotube-reinforced composite(FG-CNTRC)plates.The curvature of the plate is directly interpolated with the nod...A mesh-free method is presented to investigate the static bending properties of functionally graded carbon nanotube-reinforced composite(FG-CNTRC)plates.The curvature of the plate is directly interpolated with the nodal deflections due to the higher-order continuity property of the moving leastsquares approximation,establishing a mesh-free computational scheme where the nodal deflections are the only unknowns.The convergence and efficiency of the proposed method are studied based on a homogeneous square plate.The FG-CNTRC plates are modeled with continuously varying Young’s moduli along the thickness direction according to the volume fraction of the carbon nanotubes(CNTs).Detailed studies have been conducted on the effects of different boundary conditions,CNT volume fractions,geometric shapes,and width-to-thickness ratios on bending behavior.CNT efficiency parameters are introduced to account for load transfer between the nanotubes and the matrix,treating the nanocomposites as orthotropic materials.However,in the actual structure,arranging the CNTs in the desired direction is more difficult compared to other fibers.Therefore,in the present study,CNTs in the composites are considered to be arranged randomly,resulting in the composite properties being treated as isotropic.The study includes second-order derivatives of deflections,and the finite element method typically requires C1 continuity for interpolation,which introduces challenges in building elements and constructing interpolation functions.The distinct advantage of the mesh-free method is that it requires only C0 weight functions.A mesh-free computational scheme based on moving leastsquares approximations for composite plates using Kirchhoffplate theory is established.Bending analyses of homogeneous and FG-CNTRC plates are conducted using the proposed method.Aspects such as boundary conditions,CNT volume fractions,geometric shapes,and width-to-thickness ratios are also discussed.Regular node arrangements and background meshes are adopted in the present study.Results are computed using different scalar parameters and numbers of nodes.Convergence properties for the central deflection of isotropic plates are analyzed in terms of the number of nodes and different scalar parameters.The normalized central deflection is defined and examined under various boundary conditions.展开更多
To investigate the residual stress distribution and its influence on machining deformation in 6061-T651 aluminum alloy plates,this paper uses the crack compliance method to study the residual stress characteristics of...To investigate the residual stress distribution and its influence on machining deformation in 6061-T651 aluminum alloy plates,this paper uses the crack compliance method to study the residual stress characteristics of 6061-T651 aluminum alloy plates with a thickness of 75 mm produced by two domestic manufacturers in China.The results indicate that both types of plates exhibit highly consistent and symmetrical M-shaped residual stress profile along the thickness direction,manifested as surface layer compression and core tension.The strain energy density across all specimens ranges from 1.27 kJ/m^(3)to 1.43 kJ/m^(3).Machining deformation simulations of an aerospace component incorporating these measured stresses showed minimal final deformation difference between the material sources,with a maximum deviation of only 0.009 mm across specimens.These findings provide critical data for material selection and deformation control in aerospace manufacturing.展开更多
Legendre polynomial method is well-known in modeling acoustic wave characteristics.This method uses for the mechanical displacements a single polynomial expansion over the entire sandwich layers.This results in a limi...Legendre polynomial method is well-known in modeling acoustic wave characteristics.This method uses for the mechanical displacements a single polynomial expansion over the entire sandwich layers.This results in a limitation in the accuracy of the field profile restitution.Thus,it can deal with the guided waves in layered sandwich only when the material properties of adjacent layers do not change significantly.Despite the great efforts regarding this issue in the literature,there remain open questions.One of them is:“what is the exact threshold of contrasting material properties of adjacent layers for which this polynomial method cannot correctly restitute the roots of guided waves?”We investigated this numerical issue using the calculated guided phase velocities in 0°/φ/0°-carbon fibre reinforced plastics(CFRP)sandwich plates with gradually increasing angleφ.Then,we approached this numerical problem by varying the middle layer thickness h90°for the 0°/90°/0°-CFRP sandwich structure,and we proposed an exact thickness threshold of the middle layer for the Legendre polynomial method limitations.We showed that the polynomial method fails to calculate the quasi-symmetric Lamb mode in 0°/φ/0°-CFRP whenφ>25°.Moreover,we introduced a new Lamb mode so-called minimum-group-velocity that has never been addressed in literature.展开更多
In this paper,we define for the trace operator,the solution of certain models of vibrating plates standards with initial data in a strategic region spaces of weak regularities.Indeed,we know that the notion of regiona...In this paper,we define for the trace operator,the solution of certain models of vibrating plates standards with initial data in a strategic region spaces of weak regularities.Indeed,we know that the notion of regional controllability is more adapted to systems described by dynamic systems.Regional controllability results in a strategic area were established for vibrating plates by the Hilbertian Uniqueness Method.展开更多
The bending of rectangular plate is divided into the generalized statically determinate bending and the generalized statically indeterminate bending based on the analysis of the completeness of calculating condition a...The bending of rectangular plate is divided into the generalized statically determinate bending and the generalized statically indeterminate bending based on the analysis of the completeness of calculating condition at the corner point. The former can be solved directly by the equilibrium differential equation and the boundary conditions of four edges of the plate. The latter can be solved by using the superposition principle. Making use of the recommended method, the bending of the plate with all kinds of...展开更多
Based on the Boltzmann’s superposition principles of linear viscoelastic materials and the von K*-rm*-n’s hypotheses of thin plates with large deflections, a mathematical model for quasi-static problems of viscoelas...Based on the Boltzmann’s superposition principles of linear viscoelastic materials and the von K*-rm*-n’s hypotheses of thin plates with large deflections, a mathematical model for quasi-static problems of viscoelastic thin plates was given. By the Galerkin method in spatial domain, the original integro-partial-differential system could be transformed into an integral system. The latter further was reduced to a differential system by using the new method for temporal domain presented in this paper. Numerical results show that compared with the ordinary finite difference method, the new method in this paper is simpler to operate and has some advantages, such as, no storage and quicker computational speed etc.展开更多
The prosperous post buckling load capacity of web plates of box girders can be used.In this article,the post buckling behaviour of web plates of box girders under different loading conditions is theoretically analyz...The prosperous post buckling load capacity of web plates of box girders can be used.In this article,the post buckling behaviour of web plates of box girders under different loading conditions is theoretically analyzed and on the basis of domestic and overseas design codes of steel structures,the corresponding simplified analysis methods are put forward for the engineering design or code revision.It is proved that the simplified methods are safe,efficient and practicable through the comparison between several results.展开更多
In this paper,a deep collocation method(DCM)for thin plate bending problems is proposed.This method takes advantage of computational graphs and backpropagation algorithms involved in deep learning.Besides,the proposed...In this paper,a deep collocation method(DCM)for thin plate bending problems is proposed.This method takes advantage of computational graphs and backpropagation algorithms involved in deep learning.Besides,the proposed DCM is based on a feedforward deep neural network(DNN)and differs from most previous applications of deep learning for mechanical problems.First,batches of randomly distributed collocation points are initially generated inside the domain and along the boundaries.A loss function is built with the aim that the governing partial differential equations(PDEs)of Kirchhoff plate bending problems,and the boundary/initial conditions are minimised at those collocation points.A combination of optimizers is adopted in the backpropagation process to minimize the loss function so as to obtain the optimal hyperparameters.In Kirchhoff plate bending problems,the C^1 continuity requirement poses significant difficulties in traditional mesh-based methods.This can be solved by the proposed DCM,which uses a deep neural network to approximate the continuous transversal deflection,and is proved to be suitable to the bending analysis of Kirchhoff plate of various geometries.展开更多
A new efficient meshless method based on the element-free Galerkin method is proposed to analyze the static deformation of thin and thick plate structures in this paper. Using the new 3D shell-like kinematics in analo...A new efficient meshless method based on the element-free Galerkin method is proposed to analyze the static deformation of thin and thick plate structures in this paper. Using the new 3D shell-like kinematics in analogy to the solid-shell concept of the finite element method, discretization is carried out by the nodes located on the upper and lower surfaces of the structures. The approximation of all unknown field variables is carried out by using the moving least squares （MLS） approximation scheme in the in-plane directions, while the linear interpolation is applied through the thickness direction. Thus, different boundary conditions are defined only using displacements and penalty method is used to enforce the essential boundary conditions. The constrained Galerkin weak form, which incorporates only dis- placement degrees of freedom （d.o.f.s）, is derived. A modified 3D constitutive relationship is adopted in order to avoid or eliminate some self-locking effects. The numeric efficiency of the proposed meshless formulation is illustrated by the numeric examples.展开更多
The mill roller bearing is made up of an internal ring, middlerolls and an external ring, the analysis of which is a multi-bodiescontact problem. In this paper, based on the three-dimensionalelastic contact BEM withou...The mill roller bearing is made up of an internal ring, middlerolls and an external ring, the analysis of which is a multi-bodiescontact problem. In this paper, based on the three-dimensionalelastic contact BEM without friction, and using the structuralcharacteristics of roller bearings, middle rolls are de- scribed byelastic plate units of different shapes, which is placed on theinternal ring.展开更多
This paper presents a combined application of the finite element method （FEM） and the differential quadrature method （DQM） to vibration and buckling problems of rectangular plates. The proposed scheme combines the...This paper presents a combined application of the finite element method （FEM） and the differential quadrature method （DQM） to vibration and buckling problems of rectangular plates. The proposed scheme combines the geometry flexibility of the FEM and the high accuracy and efficiency of the DQM. The accuracy of the present method is demonstrated by comparing the obtained results with those available in the literature. It is shown that highly accurate results can be obtained by using a small number of finite elements and DQM sample points. The proposed method is suitable for the problems considered due to its simplicity and potential for further development.展开更多
The healthy and rapid development of the controlled cooling technology was hampered by the uneven cooling phenomenon. During the process of hot plate production,the homogeneous cooling along the length direction of pl...The healthy and rapid development of the controlled cooling technology was hampered by the uneven cooling phenomenon. During the process of hot plate production,the homogeneous cooling along the length direction of plate was constrained by lots of factors. And because the speed was a flexible control parameter,the calculation method of optimal speed profile was developed based on the measured start cooling temperature and its matrix equation was solved by the Cholesky decomposition method. The optimal speed profile was used in online control system. As a result,the temperature distribution along the plate length direction was relatively uniform,and 95% of measured final cooling temperature difference from the target temperature 700 ℃ was controlled within ±20 ℃.展开更多
A wavelet method for solving strongly nonlinear boundary value problems is described, which has been demonstrated early to have a convergence rate of order 4, almost independent of the nonlinear intensity of the equat...A wavelet method for solving strongly nonlinear boundary value problems is described, which has been demonstrated early to have a convergence rate of order 4, almost independent of the nonlinear intensity of the equations. By using such a method, we study the bending problem of a circular plate with arbitrary large deflection. As the deflection increases, the bending behavior usually exhibits a so-called plate-to-membrane transition. Capturing such a transition has ever frustrated researchers for decades. However, without introducing any addi- tional treatment, we show in this study that the proposed wavelet solutions can naturally cover the plate-membrane transition region as the plate deflection increases. In addition, the high accuracy and efficiency of the wavelet method in solving strongly nonlinear problems is numerically confirmed, and applicable scopes for the linear, the membrane and the yon Karman plate theories are identified with respect to the large deformation bending of circular plates.展开更多
The separation of variables is employed to solve Hamiltonian dual form of eigenvalue problem for transverse free vibrations of thin plates,and formulation of the natural mode in closed form is performed.The closed-for...The separation of variables is employed to solve Hamiltonian dual form of eigenvalue problem for transverse free vibrations of thin plates,and formulation of the natural mode in closed form is performed.The closed-form natural mode satisfies the governing equation of the eigenvalue problem of thin plate exactly and is applicable for any types of boundary conditions.With all combinations of simplysupported(S)and clamped(C)boundary conditions applied to the natural mode,the mode shapes are obtained uniquely and two eigenvalue equations are derived with respect to two spatial coordinates,with the aid of which the normal modes and frequencies are solved exactly.It was believed that the exact eigensolutions for cases SSCC,SCCC and CCCC were unable to be obtained,however,they are successfully found in this paper.Comparisons between the present results and the FEM results validate the present exact solutions,which can thus be taken as the benchmark for verifying different approximate approaches.展开更多
The integrated structure parts are widely used in aircraft. The distortion caused by residual stresses in thick pre-stretched aluminum plates during machining integrated parts is a common and serious problem. To predi...The integrated structure parts are widely used in aircraft. The distortion caused by residual stresses in thick pre-stretched aluminum plates during machining integrated parts is a common and serious problem. To predict and control the machining distortion, the residual stress distribution in the thick plate must be measured firstly. The modified removal method for measuring residual stress in thick pre-stretched aluminum plates is proposed and the stress-strain relation matrix is deduced by elasticity theory. The residual stress distribution in specimen of 7050T7451 plate is measured by using the method, and measurement results are analyzed and compared with data obtained by other methods. The method is effective to measure the residual stress.展开更多
In this study, forced nonlinear vibration of a circular micro-plate under two-sided electrostatic, two-sided Casimir and external harmonic forces is investigated analytically. For this purpose, at first, von Karman pl...In this study, forced nonlinear vibration of a circular micro-plate under two-sided electrostatic, two-sided Casimir and external harmonic forces is investigated analytically. For this purpose, at first, von Karman plate theory including geometrical nonlinearity is used to obtain the deflection of the micro-plate. Galerkin decomposition method is then employed, and nonlinear ordinary differential equations (ODEs) of motion are determined. A harmonic balance method (HBM) is applied to equations and analytical relation for nonlineaT frequency response (F-R) curves are derived for two categories (including and neglecting Casimir force) separately. The analytical results for three cases:(1) semi-linear vibration;(2) weakly nonlinear vibration;(3) highly non linear vibration, are validated by comparing with the numerical solutio ns. After validation, the effects of the voltage and Casimir force on the natural frequency of two-sided capacitor system are investigated. It is shown that by assuming Casimir force in small gap distances, reduction of the natural frequency is considerable. The influences of the applied voltage, damping, micro-plate thickness and Casimir force on the frequency response curves have been presented too. The results of this study can be useful for modeling circular parallel-plates in nano /microelectromechanical transducers such as microphones and pressure sensors.展开更多
Based on the Boltzmann's superposition principles of linear viscoelastic materials and the von Karman's hypotheses of thin plates with large deflections, a mathematical model for quasi-static problems of visco...Based on the Boltzmann's superposition principles of linear viscoelastic materials and the von Karman's hypotheses of thin plates with large deflections, a mathematical model for quasi-static problems of viscoelastic thin plates was given. By the Galerkin method in spatial domain, the original integro-partial-differential system could be transformed into an integral system. The latter further was reduced to a differential system by using the new method for temporal domain presented in this paper. Numerical results show that compared with the ordinary finite difference method, the new method in this paper is simpler to operate and has some advantages, such as, no storage and quicker computational speed etc.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.51975138the High-Tech Ship Scientific Research Project from the Ministry of Industry and Information Technology under Grant No.CJ05N20the National Defense Basic Research Project under Grant No.JCKY2023604C006.
文摘Marine thin plates are susceptible to welding deformation owing to their low structural stiffness.Therefore,the efficient and accurate prediction of welding deformation is essential for improving welding quality.The traditional thermal elastic-plastic finite element method(TEP-FEM)can accurately predict welding deformation.However,its efficiency is low because of the complex nonlinear transient computation,making it difficult to meet the needs of rapid engineering evaluation.To address this challenge,this study proposes an efficient prediction method for welding deformation in marine thin plate butt welds.This method is based on the coupled temperature gradient-thermal strain method(TG-TSM)that integrates inherent strain theory with a shell element finite element model.The proposed method first extracts the distribution pattern and characteristic value of welding-induced inherent strain through TEP-FEM analysis.This strain is then converted into the equivalent thermal load applied to the shell element model for rapid computation.The proposed method-particularly,the gradual temperature gradient-thermal strain method(GTG-TSM)-achieved improved computational efficiency and consistent precision.Furthermore,the proposed method required much less computation time than the traditional TEP-FEM.Thus,this study lays the foundation for future prediction of welding deformation in more complex marine thin plates.
基金funded by research grant OPUS no.2021/41/B/ST8/02432 entitled Probabilistic entropy in engineering computations sponsored by The National Science Center in Polandthe Institute of Structural Analysis of Poznan University of Technology in the framework of the internal research grant 0411/SBAD/0010.
文摘The analysis of the dynamics of surface girders is of great importance in the design of engineering structures such as steel welded bridge plane girders or concrete plate-column structures.This work is an extension of the classical deterministic problem of free vibrations of thin(Kirchhoff)plates.Themain aim of this work is the study of stochastic eigenvibrations of thin(Kirchhoff)elastic plates resting on internal continuous and column supports by the Boundary Element Method(BEM).This work is a continuation of previous research related to the random approach in plate analysis using the BEM.The static fundamental solution(Green’s function)is applied,coupled with a nonsingular formulation of the boundary and domain integral equations.These are derived using a modified and simplified formulation of the boundary conditions,inwhich there is no need to introduce theKirchhoff forces on a plate boundary.The role of the Kirchhoff corner forces is played by the boundary elements placed close to a single corner.Internal column or linear continuous supports are introduced using the Bezine technique,where the additional collocation points are introduced inside a plate domain.This allows for significant simplification of the BEM computational algorithm.An application of the polynomial approximations in the Least Squares Method(LSM)recovery of the structural response is done.The probabilistic analysis will employ three independent computational approaches:semi-analytical method(SAM),stochastic perturbation technique(SPT),and Monte-Carlo simulations.Numerical investigations include the fundamental eigenfrequencies of an elastic,thin,homogeneous,and isotropic plate.
基金supported by the National Natural Science Foundation of China(Grant No.11925204).
文摘The challenge of solving nonlinear problems in multi-connected domains with high accuracy has garnered significant interest.In this paper,we propose a unified wavelet solution method for accurately solving nonlinear boundary value problems on a two-dimensional(2D)arbitrary multi-connected domain.We apply this method to solve large deflection bending problems of complex plates with holes.Our solution method simplifies the treatment of the 2D multi-connected domain by utilizing a natural discretization approach that divides it into a series of one-dimensional(1D)intervals.This approach establishes a fundamental relationship between the highest-order derivative in the governing equation of the problem and the remaining lower-order derivatives.By combining a wavelet high accuracy integral approximation format on 1D intervals,where the convergence order remains constant regardless of the number of integration folds,with the collocation method,we obtain a system of algebraic equations that only includes discrete point values of the highest order derivative.In this process,the boundary conditions are automatically replaced using integration constants,eliminating the need for additional processing.Error estimation and numerical results demonstrate that the accuracy of this method is unaffected by the degree of nonlinearity of the equations.When solving the bending problem of multi-perforated complex-shaped plates under consideration,it is evident that directly using higher-order derivatives as unknown functions significantly improves the accuracy of stress calculation,even when the stress exhibits large gradient variations.Moreover,compared to the finite element method,the wavelet method requires significantly fewer nodes to achieve the same level of accuracy.Ultimately,the method achieves a sixth-order accuracy and resembles the treatment of one-dimensional problems during the solution process,effectively avoiding the need for the complex 2D meshing process typically required by conventional methods when solving problems with multi-connected domains.
基金supported by the National Natural Science Foundation of China(No.52374110)Key scientific and technological projects of Henan province(No.242102320337)Basic Research Fund of Zhongyuan University of Technology(No.K2022QN008).
文摘A mesh-free method is presented to investigate the static bending properties of functionally graded carbon nanotube-reinforced composite(FG-CNTRC)plates.The curvature of the plate is directly interpolated with the nodal deflections due to the higher-order continuity property of the moving leastsquares approximation,establishing a mesh-free computational scheme where the nodal deflections are the only unknowns.The convergence and efficiency of the proposed method are studied based on a homogeneous square plate.The FG-CNTRC plates are modeled with continuously varying Young’s moduli along the thickness direction according to the volume fraction of the carbon nanotubes(CNTs).Detailed studies have been conducted on the effects of different boundary conditions,CNT volume fractions,geometric shapes,and width-to-thickness ratios on bending behavior.CNT efficiency parameters are introduced to account for load transfer between the nanotubes and the matrix,treating the nanocomposites as orthotropic materials.However,in the actual structure,arranging the CNTs in the desired direction is more difficult compared to other fibers.Therefore,in the present study,CNTs in the composites are considered to be arranged randomly,resulting in the composite properties being treated as isotropic.The study includes second-order derivatives of deflections,and the finite element method typically requires C1 continuity for interpolation,which introduces challenges in building elements and constructing interpolation functions.The distinct advantage of the mesh-free method is that it requires only C0 weight functions.A mesh-free computational scheme based on moving leastsquares approximations for composite plates using Kirchhoffplate theory is established.Bending analyses of homogeneous and FG-CNTRC plates are conducted using the proposed method.Aspects such as boundary conditions,CNT volume fractions,geometric shapes,and width-to-thickness ratios are also discussed.Regular node arrangements and background meshes are adopted in the present study.Results are computed using different scalar parameters and numbers of nodes.Convergence properties for the central deflection of isotropic plates are analyzed in terms of the number of nodes and different scalar parameters.The normalized central deflection is defined and examined under various boundary conditions.
基金supported in part by the National Natural Science Foundation of China(Nos.61201048,61107063)the National Science and Technology Major Project(No.2017-VI-001-0094).
文摘To investigate the residual stress distribution and its influence on machining deformation in 6061-T651 aluminum alloy plates,this paper uses the crack compliance method to study the residual stress characteristics of 6061-T651 aluminum alloy plates with a thickness of 75 mm produced by two domestic manufacturers in China.The results indicate that both types of plates exhibit highly consistent and symmetrical M-shaped residual stress profile along the thickness direction,manifested as surface layer compression and core tension.The strain energy density across all specimens ranges from 1.27 kJ/m^(3)to 1.43 kJ/m^(3).Machining deformation simulations of an aerospace component incorporating these measured stresses showed minimal final deformation difference between the material sources,with a maximum deviation of only 0.009 mm across specimens.These findings provide critical data for material selection and deformation control in aerospace manufacturing.
基金supported by the National Natural Science Foundation of China(Grant No.12102131).
文摘Legendre polynomial method is well-known in modeling acoustic wave characteristics.This method uses for the mechanical displacements a single polynomial expansion over the entire sandwich layers.This results in a limitation in the accuracy of the field profile restitution.Thus,it can deal with the guided waves in layered sandwich only when the material properties of adjacent layers do not change significantly.Despite the great efforts regarding this issue in the literature,there remain open questions.One of them is:“what is the exact threshold of contrasting material properties of adjacent layers for which this polynomial method cannot correctly restitute the roots of guided waves?”We investigated this numerical issue using the calculated guided phase velocities in 0°/φ/0°-carbon fibre reinforced plastics(CFRP)sandwich plates with gradually increasing angleφ.Then,we approached this numerical problem by varying the middle layer thickness h90°for the 0°/90°/0°-CFRP sandwich structure,and we proposed an exact thickness threshold of the middle layer for the Legendre polynomial method limitations.We showed that the polynomial method fails to calculate the quasi-symmetric Lamb mode in 0°/φ/0°-CFRP whenφ>25°.Moreover,we introduced a new Lamb mode so-called minimum-group-velocity that has never been addressed in literature.
文摘In this paper,we define for the trace operator,the solution of certain models of vibrating plates standards with initial data in a strategic region spaces of weak regularities.Indeed,we know that the notion of regional controllability is more adapted to systems described by dynamic systems.Regional controllability results in a strategic area were established for vibrating plates by the Hilbertian Uniqueness Method.
文摘The bending of rectangular plate is divided into the generalized statically determinate bending and the generalized statically indeterminate bending based on the analysis of the completeness of calculating condition at the corner point. The former can be solved directly by the equilibrium differential equation and the boundary conditions of four edges of the plate. The latter can be solved by using the superposition principle. Making use of the recommended method, the bending of the plate with all kinds of...
文摘Based on the Boltzmann’s superposition principles of linear viscoelastic materials and the von K*-rm*-n’s hypotheses of thin plates with large deflections, a mathematical model for quasi-static problems of viscoelastic thin plates was given. By the Galerkin method in spatial domain, the original integro-partial-differential system could be transformed into an integral system. The latter further was reduced to a differential system by using the new method for temporal domain presented in this paper. Numerical results show that compared with the ordinary finite difference method, the new method in this paper is simpler to operate and has some advantages, such as, no storage and quicker computational speed etc.
基金Supported by Ministry of Metallurgical Industry of China
文摘The prosperous post buckling load capacity of web plates of box girders can be used.In this article,the post buckling behaviour of web plates of box girders under different loading conditions is theoretically analyzed and on the basis of domestic and overseas design codes of steel structures,the corresponding simplified analysis methods are put forward for the engineering design or code revision.It is proved that the simplified methods are safe,efficient and practicable through the comparison between several results.
文摘In this paper,a deep collocation method(DCM)for thin plate bending problems is proposed.This method takes advantage of computational graphs and backpropagation algorithms involved in deep learning.Besides,the proposed DCM is based on a feedforward deep neural network(DNN)and differs from most previous applications of deep learning for mechanical problems.First,batches of randomly distributed collocation points are initially generated inside the domain and along the boundaries.A loss function is built with the aim that the governing partial differential equations(PDEs)of Kirchhoff plate bending problems,and the boundary/initial conditions are minimised at those collocation points.A combination of optimizers is adopted in the backpropagation process to minimize the loss function so as to obtain the optimal hyperparameters.In Kirchhoff plate bending problems,the C^1 continuity requirement poses significant difficulties in traditional mesh-based methods.This can be solved by the proposed DCM,which uses a deep neural network to approximate the continuous transversal deflection,and is proved to be suitable to the bending analysis of Kirchhoff plate of various geometries.
基金supported by the National Natural Science Foundation of China (11172192)the College Postgraduate Research and Innovation Project of Jiangsu province (CXZZ12 0803)
文摘A new efficient meshless method based on the element-free Galerkin method is proposed to analyze the static deformation of thin and thick plate structures in this paper. Using the new 3D shell-like kinematics in analogy to the solid-shell concept of the finite element method, discretization is carried out by the nodes located on the upper and lower surfaces of the structures. The approximation of all unknown field variables is carried out by using the moving least squares （MLS） approximation scheme in the in-plane directions, while the linear interpolation is applied through the thickness direction. Thus, different boundary conditions are defined only using displacements and penalty method is used to enforce the essential boundary conditions. The constrained Galerkin weak form, which incorporates only dis- placement degrees of freedom （d.o.f.s）, is derived. A modified 3D constitutive relationship is adopted in order to avoid or eliminate some self-locking effects. The numeric efficiency of the proposed meshless formulation is illustrated by the numeric examples.
基金the National Natural Science Foundation of China (50075075)
文摘The mill roller bearing is made up of an internal ring, middlerolls and an external ring, the analysis of which is a multi-bodiescontact problem. In this paper, based on the three-dimensionalelastic contact BEM without friction, and using the structuralcharacteristics of roller bearings, middle rolls are de- scribed byelastic plate units of different shapes, which is placed on theinternal ring.
文摘This paper presents a combined application of the finite element method （FEM） and the differential quadrature method （DQM） to vibration and buckling problems of rectangular plates. The proposed scheme combines the geometry flexibility of the FEM and the high accuracy and efficiency of the DQM. The accuracy of the present method is demonstrated by comparing the obtained results with those available in the literature. It is shown that highly accurate results can be obtained by using a small number of finite elements and DQM sample points. The proposed method is suitable for the problems considered due to its simplicity and potential for further development.
文摘The healthy and rapid development of the controlled cooling technology was hampered by the uneven cooling phenomenon. During the process of hot plate production,the homogeneous cooling along the length direction of plate was constrained by lots of factors. And because the speed was a flexible control parameter,the calculation method of optimal speed profile was developed based on the measured start cooling temperature and its matrix equation was solved by the Cholesky decomposition method. The optimal speed profile was used in online control system. As a result,the temperature distribution along the plate length direction was relatively uniform,and 95% of measured final cooling temperature difference from the target temperature 700 ℃ was controlled within ±20 ℃.
基金Project supported by the National Natural Science Foundation of China(Nos.11472119,11032006 and 11121202)the National Key Project of Magneto-Constrained Fusion Energy Development Program(No.2013GB110002)the Scientific and Technological Self-innovation Foundation of Huazhong Agricultural University(No.52902-0900206074)
文摘A wavelet method for solving strongly nonlinear boundary value problems is described, which has been demonstrated early to have a convergence rate of order 4, almost independent of the nonlinear intensity of the equations. By using such a method, we study the bending problem of a circular plate with arbitrary large deflection. As the deflection increases, the bending behavior usually exhibits a so-called plate-to-membrane transition. Capturing such a transition has ever frustrated researchers for decades. However, without introducing any addi- tional treatment, we show in this study that the proposed wavelet solutions can naturally cover the plate-membrane transition region as the plate deflection increases. In addition, the high accuracy and efficiency of the wavelet method in solving strongly nonlinear problems is numerically confirmed, and applicable scopes for the linear, the membrane and the yon Karman plate theories are identified with respect to the large deformation bending of circular plates.
基金supported by the National Natural Science Foundation of China(10772014)
文摘The separation of variables is employed to solve Hamiltonian dual form of eigenvalue problem for transverse free vibrations of thin plates,and formulation of the natural mode in closed form is performed.The closed-form natural mode satisfies the governing equation of the eigenvalue problem of thin plate exactly and is applicable for any types of boundary conditions.With all combinations of simplysupported(S)and clamped(C)boundary conditions applied to the natural mode,the mode shapes are obtained uniquely and two eigenvalue equations are derived with respect to two spatial coordinates,with the aid of which the normal modes and frequencies are solved exactly.It was believed that the exact eigensolutions for cases SSCC,SCCC and CCCC were unable to be obtained,however,they are successfully found in this paper.Comparisons between the present results and the FEM results validate the present exact solutions,which can thus be taken as the benchmark for verifying different approximate approaches.
文摘The integrated structure parts are widely used in aircraft. The distortion caused by residual stresses in thick pre-stretched aluminum plates during machining integrated parts is a common and serious problem. To predict and control the machining distortion, the residual stress distribution in the thick plate must be measured firstly. The modified removal method for measuring residual stress in thick pre-stretched aluminum plates is proposed and the stress-strain relation matrix is deduced by elasticity theory. The residual stress distribution in specimen of 7050T7451 plate is measured by using the method, and measurement results are analyzed and compared with data obtained by other methods. The method is effective to measure the residual stress.
文摘In this study, forced nonlinear vibration of a circular micro-plate under two-sided electrostatic, two-sided Casimir and external harmonic forces is investigated analytically. For this purpose, at first, von Karman plate theory including geometrical nonlinearity is used to obtain the deflection of the micro-plate. Galerkin decomposition method is then employed, and nonlinear ordinary differential equations (ODEs) of motion are determined. A harmonic balance method (HBM) is applied to equations and analytical relation for nonlineaT frequency response (F-R) curves are derived for two categories (including and neglecting Casimir force) separately. The analytical results for three cases:(1) semi-linear vibration;(2) weakly nonlinear vibration;(3) highly non linear vibration, are validated by comparing with the numerical solutio ns. After validation, the effects of the voltage and Casimir force on the natural frequency of two-sided capacitor system are investigated. It is shown that by assuming Casimir force in small gap distances, reduction of the natural frequency is considerable. The influences of the applied voltage, damping, micro-plate thickness and Casimir force on the frequency response curves have been presented too. The results of this study can be useful for modeling circular parallel-plates in nano /microelectromechanical transducers such as microphones and pressure sensors.
文摘Based on the Boltzmann's superposition principles of linear viscoelastic materials and the von Karman's hypotheses of thin plates with large deflections, a mathematical model for quasi-static problems of viscoelastic thin plates was given. By the Galerkin method in spatial domain, the original integro-partial-differential system could be transformed into an integral system. The latter further was reduced to a differential system by using the new method for temporal domain presented in this paper. Numerical results show that compared with the ordinary finite difference method, the new method in this paper is simpler to operate and has some advantages, such as, no storage and quicker computational speed etc.
