A new method was presented here based on authors' previous work. This new method can be used to solve the arbitrary nonlinear system of differential equations with variable coefficients. By this method, the genera...A new method was presented here based on authors' previous work. This new method can be used to solve the arbitrary nonlinear system of differential equations with variable coefficients. By this method, the general solution for large deformation of nonhomogeneous circular plates resting on a elastic foundation was derived, and its convergence was proved. Finally, the only thing necessary to solve is a set of nonlinear algebraic equations with three unknowns. The solution obtained by the present method has large convergence range and the computation is simpler and more rapid than other numerical methods. The numerical examples indicate that satisfactory results of stress resultants and displacements can be obtained by the present method. The correctness of the theory in this paper has been confirmed.展开更多
In this paper, a new method, the step-reduction method, is proposed to investigate the dynamic response of the Bernoulli-Euler beams with arbitrary nonhomogeneity and arbitrary variable cross-section under arbitrary l...In this paper, a new method, the step-reduction method, is proposed to investigate the dynamic response of the Bernoulli-Euler beams with arbitrary nonhomogeneity and arbitrary variable cross-section under arbitrary loads. Both free vibration and forced vibration of such beams are studied. The new method requires to discretize the space domain into a number of elements. Each element can be treated as a homogeneous one with uniform thickness. Therefore, the general analytical solution of homogeneous beams with uniform cross-section can be used in each element. Then, the general analytic solution of the whole beam in terms of initial parameters can be obtained by satisfying the physical and geometric continuity conditions at the adjacent elements. In the case of free vibration, the frequency equation in analytic form can be obtained, and in the case of forced vibration, a final solution in analytical form can also be obtained which is involved in solving a set of simultaneous algebraic equations with only two unknowns which are independent of the numbers of elements divided. The present analysis can also be extended to the study of the vibration of such beams with viscous and hysteretic damping and other kinds of beams and other structural elements with arbitrary nonhomogeneity and arbitrary variable thickness.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
In this paper, a new method, the exact analytic method, is presented on the basis of step reduction method. By this method, the general solution for the bending of nonhomogenous circular plates and circular plates wit...In this paper, a new method, the exact analytic method, is presented on the basis of step reduction method. By this method, the general solution for the bending of nonhomogenous circular plates and circular plates with a circular hole at the center resting, on an elastfc foundation is obtained under arbitrary axial symmetrical loads' and boundary conditions. The uniform convergence of the solution is proved. This general solution can also he applied directly to the bending of circular plates without elastic foundation. Finally, it is only necessary to solve a set of binary linear algebraic equation. 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
In this paper, based on the step reduction method and exaet analytic method, a new method, theexacl element method for constructing finite element, is presented. Since the near method doesn't need varialional prin...In this paper, based on the step reduction method and exaet analytic method, a new method, theexacl element method for constructing finite element, is presented. Since the near method doesn't need varialional principle, it can he applied to solve nun-positive and positive definite partial differcntial equations with arbitral varutble coefficients. By this method, a triangle noncompatible element with 15 degrees of freedom is derived to solve the bending of nonhomogenous Reissner's plate. Because the displacement parameters at the nodal point only contain deflection and rotation angle, it is convenient to deal with arbitrary boundary conditions. In this paper, the convergcnceof displacement and stress resultants is proved. The element obtained by the present method can be used for thin and thick plates as well, hour numerical examples are given at the end of this paper, which indicates that we can obtain satisfactory results and have higher numerical precision.展开更多
The exact analytic method was given by [1] . It can be used for arbitrary variable coefficient differential equations and the solution obtained can have the second order convergent precision. In this paper, a new high...The exact analytic method was given by [1] . It can be used for arbitrary variable coefficient differential equations and the solution obtained can have the second order convergent precision. In this paper, a new high precision algorithm is given based on [1], through a bending problem of variable cross-section beams. It can have the fourth convergent precision without increasing computation work. The present computation method is not only simple but also fast. The numerical examples are given at the end of this paper which indicate that the high convergent precision can be obtained using only a few elements. The correctness of the theory in this paper is confirmed.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
基金Project Supported by the National Natural Science Foundation of China
文摘A new method was presented here based on authors' previous work. This new method can be used to solve the arbitrary nonlinear system of differential equations with variable coefficients. By this method, the general solution for large deformation of nonhomogeneous circular plates resting on a elastic foundation was derived, and its convergence was proved. Finally, the only thing necessary to solve is a set of nonlinear algebraic equations with three unknowns. The solution obtained by the present method has large convergence range and the computation is simpler and more rapid than other numerical methods. The numerical examples indicate that satisfactory results of stress resultants and displacements can be obtained by the present method. The correctness of the theory in this paper has been confirmed.
文摘In this paper, a new method, the step-reduction method, is proposed to investigate the dynamic response of the Bernoulli-Euler beams with arbitrary nonhomogeneity and arbitrary variable cross-section under arbitrary loads. Both free vibration and forced vibration of such beams are studied. The new method requires to discretize the space domain into a number of elements. Each element can be treated as a homogeneous one with uniform thickness. Therefore, the general analytical solution of homogeneous beams with uniform cross-section can be used in each element. Then, the general analytic solution of the whole beam in terms of initial parameters can be obtained by satisfying the physical and geometric continuity conditions at the adjacent elements. In the case of free vibration, the frequency equation in analytic form can be obtained, and in the case of forced vibration, a final solution in analytical form can also be obtained which is involved in solving a set of simultaneous algebraic equations with only two unknowns which are independent of the numbers of elements divided. The present analysis can also be extended to the study of the vibration of such beams with viscous and hysteretic damping and other kinds of beams and other structural elements with arbitrary nonhomogeneity and arbitrary variable thickness.
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In this paper, a new method, the exact analytic method, is presented on the basis of step reduction method. By this method, the general solution for the bending of nonhomogenous circular plates and circular plates with a circular hole at the center resting, on an elastfc foundation is obtained under arbitrary axial symmetrical loads' and boundary conditions. The uniform convergence of the solution is proved. This general solution can also he applied directly to the bending of circular plates without elastic foundation. Finally, it is only necessary to solve a set of binary linear algebraic equation. 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In this paper, based on the step reduction method and exaet analytic method, a new method, theexacl element method for constructing finite element, is presented. Since the near method doesn't need varialional principle, it can he applied to solve nun-positive and positive definite partial differcntial equations with arbitral varutble coefficients. By this method, a triangle noncompatible element with 15 degrees of freedom is derived to solve the bending of nonhomogenous Reissner's plate. Because the displacement parameters at the nodal point only contain deflection and rotation angle, it is convenient to deal with arbitrary boundary conditions. In this paper, the convergcnceof displacement and stress resultants is proved. The element obtained by the present method can be used for thin and thick plates as well, hour numerical examples are given at the end of this paper, which indicates that we can obtain satisfactory results and have higher numerical precision.
文摘The exact analytic method was given by [1] . It can be used for arbitrary variable coefficient differential equations and the solution obtained can have the second order convergent precision. In this paper, a new high precision algorithm is given based on [1], through a bending problem of variable cross-section beams. It can have the fourth convergent precision without increasing computation work. The present computation method is not only simple but also fast. The numerical examples are given at the end of this paper which indicate that the high convergent precision can be obtained using only a few elements. The correctness of the theory in this paper is confirmed.
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.
