The draping behavior of fabric is simulated by using four node quadrilateral thin plate elements with finite rotation. The finite element formulation is based on the total Lagrangian approach. An exact representatio...The draping behavior of fabric is simulated by using four node quadrilateral thin plate elements with finite rotation. The finite element formulation is based on the total Lagrangian approach. An exact representation of finite rotation is introduced. The strain energy function accounting for the material symmetry is obtained by the tensor representation theory. To avoid shear locking, the assumed strain technique for transverse shear is adopted. The conjugate gradient method with a proposed line search algorithm is employed to minimize energy and reach the final shape of fabric. The draping behavior of a rectangular piece of fabric over a rectangular table is simulated. (Author abstract) 9 Refs.展开更多
The new technology of welding with impacting rotation is put forward to decrease the wave-like deformation of the TC4 thin plate weldment. The thermal stress and strain are vital to understand the mechanism of control...The new technology of welding with impacting rotation is put forward to decrease the wave-like deformation of the TC4 thin plate weldment. The thermal stress and strain are vital to understand the mechanism of controlling the wave-like deformation. In order to know the development of internal thermal stress and strain, finite element method is utilized for- the stress and strain are difficult to be investigated by experimental methods during the welding process. Temperature field, thermal stress evolution and distortion of thin plate are compared with the test results such as weld thermal cycle, residual stress sectioning measurement, and the deflection of the thin plate respectively. By the finite element analysis and test results verification, the meehaaism of the technology to control the wave-like deformation is brought forward, non-uniform thermal elastic strain between compressive plastic region and elastic extensive region is diminished by a certain amount of extensive plastic deformation by welding with impacting rotation process.展开更多
The typical quadrangular and triangular elements for thin plate bending based on Kirchhoff assumptions are the non- conforming elements with low computational accuracy and limitative application range in fmite element...The typical quadrangular and triangular elements for thin plate bending based on Kirchhoff assumptions are the non- conforming elements with low computational accuracy and limitative application range in fmite element method（FEM）. Some compatible elements can be developed by the means of supplementing correction functions, increasing nodes in element or on the boundaries, expanding nodal degrees of freedom（DOF）, etc, but these elements are inconvenient to apply in practice for the high calculation complexity. In this paper, in order to overcome the defects of thin plate bending finite element, numerical manifold method（NMM） was introduced to solve thin plate bending deformation problem. Rectangular mesh was adopted as mathematical mesh to form f＇mite element cover system, and then 16-cover manifold element was proposed. Numerical manifold formulas were constructed on the basis of minimum potential energy principle, displacement boundary conditions are implemented by penalty function method, and all the element matrixes were derived in details. The 16-cover element has a simple calculation process for employing only the transverse displacement cover DOFs as the basic unknown variables, and has been proved to meet the requirements of completeness and full compatibility. As an application, the presented 16-cover element has been used to analyze bending deformation of square thin plate under different loads and boundary conditions, and the results show that numerical manifold method with compatible element, compared with finite element method, can improve computational accuracy and convergence greatly.展开更多
In this paper, based on the step reduction method, a new method, the exact element method for constructing finite element, is presented. Since the new method doesn 't need the variational principle, it can be appl...In this paper, based on the step reduction method, a new method, the exact element method for constructing finite element, is presented. Since the new method doesn 't need the variational principle, it can be applied to solve non-positive and positive definite partial differential equations with arbitrary variable coefficient. By this method, a triangle noncompatible element with 6 degrees of freedom is derived to solve the bending of nonhomogeneous plate. The convergence of displacements and stress resultants which have satisfactory numerical precision is proved. Numerical examples are given at the end of this paper, which indicate satisfactory results of stress resultants and displacements can be obtained by the present method.展开更多
This paper presents a curvilinear boundary quadrilateral element for the problem of thin plate of bending with curvilinear boundary. A coordinate transformation of two dimensions is performed in the calculation of FEM...This paper presents a curvilinear boundary quadrilateral element for the problem of thin plate of bending with curvilinear boundary. A coordinate transformation of two dimensions is performed in the calculation of FEM. The introduction of an additional stiffness matrix based on the generalized variational principles results in high accuracy and less computation time. The numerical results agree with the analytical solution very well.展开更多
In this paper,a method of constructing displacement-based elment for thick/thin plates is devel- oped by using the technique of generalized compatibility,and a rectangular displacement-based element with 12 degrees of...In this paper,a method of constructing displacement-based elment for thick/thin plates is devel- oped by using the technique of generalized compatibility,and a rectangular displacement-based element with 12 degrees of freedom for thick/thin plates is presented.This method enjoys a good accuracy with simple formulation and is free of shear- locking as the thickness of the plate approaches zero.展开更多
On the basis of the general theory of perforated thin plates under large deflections, variational principles with deflection w and stress function F as variables are stated in detail.Based on these princi- ples,finite...On the basis of the general theory of perforated thin plates under large deflections, variational principles with deflection w and stress function F as variables are stated in detail.Based on these princi- ples,finite element method is established for analysing the buckling and post-buckling of perforated thin plates. It is found that the property of element is very complicated,owing to the multiple connexity of the region.展开更多
Boundary Element Method (BEM) is employed to run theoretical analsis and numerical calculation of dif-fraction of elastic wave and dynamic stress concentration in an infinite then plate with a cireular hole. Based on ...Boundary Element Method (BEM) is employed to run theoretical analsis and numerical calculation of dif-fraction of elastic wave and dynamic stress concentration in an infinite then plate with a cireular hole. Based on the work equivalent law of dynamics,boundary integral equation is established for flexural waves of thin plate. Calculation formulas of influence coefficients are derived using Mathematica software and numerical results are obtained for dynam-ic stress conoentration factors in a then plate with a circular hole.展开更多
This paper presents a new curved quadrilateral plate element with 12-degree freedom by the exact element method[1]. The method can be used to arbitrary non-positive and positive definite partial differential equations...This paper presents a new curved quadrilateral plate element with 12-degree freedom by the exact element method[1]. The method can be used to arbitrary non-positive and positive definite partial differential equations without variation principle. Using this method, the compatibility conditions between element can be treated very easily, if displacements and stress resultants are continuous at nodes between elements. The displacements and stress resultants obtained by the present method can converge to exact solution and have the second order convergence speed. Numerical examples are given at the end of this paper, which show the excellent precision and efficiency of the new element.展开更多
4 semi-analytical approach for the dynamic response of general thin plates whichemployes finite element discretization in space domain and a series of representation intime demain is developed on the basis of Curtin v...4 semi-analytical approach for the dynamic response of general thin plates whichemployes finite element discretization in space domain and a series of representation intime demain is developed on the basis of Curtin variational principles.The formulationof time series is also investigated so that the dynamic response of plates with arbitraryshape and boundary constraints can be achieved with adequate accuracy.展开更多
The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton＇s principle for t...The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton＇s principle for the elastic dynamics system,the dimensionless equations of motion of rectangular plates with finite interior elastic point supports and the edge elastically restrained are established using the element-free Galerkin method.Through numerical calculation,curves of the natural frequency of thin plates with three edges simply supported and one edge elastically restrained,and three edges clamped and the other edge elastically restrained versus the spring constant,locations of elastic point support and the elastic stiffness of edge elastically restrained are obtained.Effects of elastic point supports and edge elastically restrained on the free vibration characteristics of the thin plates are analyzed.展开更多
The FE simulation results of transverse stresses and strains during welding of thin aluminum alloy plate are presented. The results indicate that restraint condition is the main factor that determines whether or not h...The FE simulation results of transverse stresses and strains during welding of thin aluminum alloy plate are presented. The results indicate that restraint condition is the main factor that determines whether or not hot cracking will occur. With rigid restraint hot cracking (crater cracking) will occur at the arc-stopping end, and such cracking usually will not occur without external restraint. But under restraint-free condition it is easy for terminal cracks to occur.展开更多
Some theorems of compactly supported non-tensor product form two-dimension Daubechies wavelet were analysed carefully. Compactly supported non-tensor product form two-dimension wavelet was constructed, then non-tensor...Some theorems of compactly supported non-tensor product form two-dimension Daubechies wavelet were analysed carefully. Compactly supported non-tensor product form two-dimension wavelet was constructed, then non-tensor product form two dimension wavelet finite element was used to solve the deflection problem of elastic thin plate. The error order was researched. A numerical example was given at last.展开更多
In the realization of mechanical structures, achieving stability and balance is a problem commonly encountered by engineers in the field of civil engineering, mechanics, aeronautics, biomechanics and many others. The ...In the realization of mechanical structures, achieving stability and balance is a problem commonly encountered by engineers in the field of civil engineering, mechanics, aeronautics, biomechanics and many others. The study of plate behavior is a very sensitive subject because it is part of the structural elements. The study of the dynamic behavior of free vibration structures is done by modal analysis in order to calculate natural frequencies and modal deformations. In this paper, we present the modal analysis of a thin rectangular plate simply supported. The analytical solution of the differential equation is obtained by applying the method of separating the variables. We are talking about the exact solution of the problem to the limit values. However, numerical methods such as the finite element method allow us to approximate these functions with greater accuracy. It is one of the most powerful computational methods for predicting dynamic response in a complex structure subject to arbitrary boundary conditions. The results obtained by MEF through Ansys 15.0 are then compared with those obtained by the analytical method.展开更多
In this paper, a new method, exact element method for constructing finite element, is presented. It can be applied to solve nonpositive definite or positive definite partial differential equation with arbitrary variab...In this paper, a new method, exact element method for constructing finite element, is presented. It can be applied to solve nonpositive definite or positive definite partial differential equation with arbitrary variable coefficient under arbitrary boundary condition. Its convergence is proved and its united formula for solving partial differential equation is given. By the present method, a noncompatible element can be obtained and the compatibility conditions between elements can be treated very easily. Comparing the exact element method with the general finite element method with the same degrees of freedom, the high convergence rate of the high order derivatives of solution can be obtained. Three numerical examples are given at the end of this paper, which indicate all results can converge to exact solution and have higher numerical precision.展开更多
文摘The draping behavior of fabric is simulated by using four node quadrilateral thin plate elements with finite rotation. The finite element formulation is based on the total Lagrangian approach. An exact representation of finite rotation is introduced. The strain energy function accounting for the material symmetry is obtained by the tensor representation theory. To avoid shear locking, the assumed strain technique for transverse shear is adopted. The conjugate gradient method with a proposed line search algorithm is employed to minimize energy and reach the final shape of fabric. The draping behavior of a rectangular piece of fabric over a rectangular table is simulated. (Author abstract) 9 Refs.
文摘The new technology of welding with impacting rotation is put forward to decrease the wave-like deformation of the TC4 thin plate weldment. The thermal stress and strain are vital to understand the mechanism of controlling the wave-like deformation. In order to know the development of internal thermal stress and strain, finite element method is utilized for- the stress and strain are difficult to be investigated by experimental methods during the welding process. Temperature field, thermal stress evolution and distortion of thin plate are compared with the test results such as weld thermal cycle, residual stress sectioning measurement, and the deflection of the thin plate respectively. By the finite element analysis and test results verification, the meehaaism of the technology to control the wave-like deformation is brought forward, non-uniform thermal elastic strain between compressive plastic region and elastic extensive region is diminished by a certain amount of extensive plastic deformation by welding with impacting rotation process.
基金supported by National Natural Science Foundation of China (Grant No. 50775044, Grant No. 50975050)Guangdong Provincial and Ministry of Education Industry-University-Research Integration Project of China (Grant No. 2009B090300044)
文摘The typical quadrangular and triangular elements for thin plate bending based on Kirchhoff assumptions are the non- conforming elements with low computational accuracy and limitative application range in fmite element method（FEM）. Some compatible elements can be developed by the means of supplementing correction functions, increasing nodes in element or on the boundaries, expanding nodal degrees of freedom（DOF）, etc, but these elements are inconvenient to apply in practice for the high calculation complexity. In this paper, in order to overcome the defects of thin plate bending finite element, numerical manifold method（NMM） was introduced to solve thin plate bending deformation problem. Rectangular mesh was adopted as mathematical mesh to form f＇mite element cover system, and then 16-cover manifold element was proposed. Numerical manifold formulas were constructed on the basis of minimum potential energy principle, displacement boundary conditions are implemented by penalty function method, and all the element matrixes were derived in details. The 16-cover element has a simple calculation process for employing only the transverse displacement cover DOFs as the basic unknown variables, and has been proved to meet the requirements of completeness and full compatibility. As an application, the presented 16-cover element has been used to analyze bending deformation of square thin plate under different loads and boundary conditions, and the results show that numerical manifold method with compatible element, compared with finite element method, can improve computational accuracy and convergence greatly.
文摘In this paper, based on the step reduction method, a new method, the exact element method for constructing finite element, is presented. Since the new method doesn 't need the variational principle, it can be applied to solve non-positive and positive definite partial differential equations with arbitrary variable coefficient. By this method, a triangle noncompatible element with 6 degrees of freedom is derived to solve the bending of nonhomogeneous plate. The convergence of displacements and stress resultants which have satisfactory numerical precision is proved. Numerical examples are given at the end of this paper, which indicate satisfactory results of stress resultants and displacements can be obtained by the present method.
文摘This paper presents a curvilinear boundary quadrilateral element for the problem of thin plate of bending with curvilinear boundary. A coordinate transformation of two dimensions is performed in the calculation of FEM. The introduction of an additional stiffness matrix based on the generalized variational principles results in high accuracy and less computation time. The numerical results agree with the analytical solution very well.
基金The project supported by National Natural Science Foundation of China through Grant No.59208075
文摘In this paper,a method of constructing displacement-based elment for thick/thin plates is devel- oped by using the technique of generalized compatibility,and a rectangular displacement-based element with 12 degrees of freedom for thick/thin plates is presented.This method enjoys a good accuracy with simple formulation and is free of shear- locking as the thickness of the plate approaches zero.
基金Project supported by National Natural Science Foundation of China.
文摘On the basis of the general theory of perforated thin plates under large deflections, variational principles with deflection w and stress function F as variables are stated in detail.Based on these princi- ples,finite element method is established for analysing the buckling and post-buckling of perforated thin plates. It is found that the property of element is very complicated,owing to the multiple connexity of the region.
文摘Boundary Element Method (BEM) is employed to run theoretical analsis and numerical calculation of dif-fraction of elastic wave and dynamic stress concentration in an infinite then plate with a cireular hole. Based on the work equivalent law of dynamics,boundary integral equation is established for flexural waves of thin plate. Calculation formulas of influence coefficients are derived using Mathematica software and numerical results are obtained for dynam-ic stress conoentration factors in a then plate with a circular hole.
基金Outstanding Education Fund and Doctor Point Fund of National Education Committee and the National Science Foundation of China
文摘This paper presents a new curved quadrilateral plate element with 12-degree freedom by the exact element method[1]. The method can be used to arbitrary non-positive and positive definite partial differential equations without variation principle. Using this method, the compatibility conditions between element can be treated very easily, if displacements and stress resultants are continuous at nodes between elements. The displacements and stress resultants obtained by the present method can converge to exact solution and have the second order convergence speed. Numerical examples are given at the end of this paper, which show the excellent precision and efficiency of the new element.
文摘4 semi-analytical approach for the dynamic response of general thin plates whichemployes finite element discretization in space domain and a series of representation intime demain is developed on the basis of Curtin variational principles.The formulationof time series is also investigated so that the dynamic response of plates with arbitraryshape and boundary constraints can be achieved with adequate accuracy.
基金Project supported by the National Natural Science Foundation of China (Grant No.10872163)the Natural Science Foundation of Education Department of Shaanxi Province (Grant No.08JK394)
文摘The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton＇s principle for the elastic dynamics system,the dimensionless equations of motion of rectangular plates with finite interior elastic point supports and the edge elastically restrained are established using the element-free Galerkin method.Through numerical calculation,curves of the natural frequency of thin plates with three edges simply supported and one edge elastically restrained,and three edges clamped and the other edge elastically restrained versus the spring constant,locations of elastic point support and the elastic stiffness of edge elastically restrained are obtained.Effects of elastic point supports and edge elastically restrained on the free vibration characteristics of the thin plates are analyzed.
文摘The FE simulation results of transverse stresses and strains during welding of thin aluminum alloy plate are presented. The results indicate that restraint condition is the main factor that determines whether or not hot cracking will occur. With rigid restraint hot cracking (crater cracking) will occur at the arc-stopping end, and such cracking usually will not occur without external restraint. But under restraint-free condition it is easy for terminal cracks to occur.
文摘Some theorems of compactly supported non-tensor product form two-dimension Daubechies wavelet were analysed carefully. Compactly supported non-tensor product form two-dimension wavelet was constructed, then non-tensor product form two dimension wavelet finite element was used to solve the deflection problem of elastic thin plate. The error order was researched. A numerical example was given at last.
文摘In the realization of mechanical structures, achieving stability and balance is a problem commonly encountered by engineers in the field of civil engineering, mechanics, aeronautics, biomechanics and many others. The study of plate behavior is a very sensitive subject because it is part of the structural elements. The study of the dynamic behavior of free vibration structures is done by modal analysis in order to calculate natural frequencies and modal deformations. In this paper, we present the modal analysis of a thin rectangular plate simply supported. The analytical solution of the differential equation is obtained by applying the method of separating the variables. We are talking about the exact solution of the problem to the limit values. However, numerical methods such as the finite element method allow us to approximate these functions with greater accuracy. It is one of the most powerful computational methods for predicting dynamic response in a complex structure subject to arbitrary boundary conditions. The results obtained by MEF through Ansys 15.0 are then compared with those obtained by the analytical method.
文摘In this paper, a new method, exact element method for constructing finite element, is presented. It can be applied to solve nonpositive definite or positive definite partial differential equation with arbitrary variable coefficient under arbitrary boundary condition. Its convergence is proved and its united formula for solving partial differential equation is given. By the present method, a noncompatible element can be obtained and the compatibility conditions between elements can be treated very easily. Comparing the exact element method with the general finite element method with the same degrees of freedom, the high convergence rate of the high order derivatives of solution can be obtained. Three numerical examples are given at the end of this paper, which indicate all results can converge to exact solution and have higher numerical precision.
