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
In[1], the exact analytic method for the solution of differential equation with variable coefficients was suggested and an analytic expression of solution was given by initial parameter algorithm. But to some problems...In[1], the exact analytic method for the solution of differential equation with variable coefficients was suggested and an analytic expression of solution was given by initial parameter algorithm. But to some problems such as the bending, free vibration and buckling of nonhomogeneous long cylinders, it is difficult to obtain their solutions by the initial parameter algorithm on computer. In this paper, the substructure computational algorithm for the exact analytic method is presented through the bending of non-homogeneous long cylindrical shell. This substructure algorithm can he applied to solve the problems which can not he calculated by the initial parameter algorithm on computer. Finally, the problems can he reduced to solving a low order system of algehraic equations like the initial parameter algorithm Numerical examples are given and compared with the initial para-algorithm at the end of the paper, which confirms the correctness of the substructure computational algorithm.展开更多
Many engineering problems can be reduced to the solution of a variable coefficient differential equation. In this paper, the exact analytic method is suggested to solve variable coefficient differential equations unde...Many engineering problems can be reduced to the solution of a variable coefficient differential equation. In this paper, the exact analytic method is suggested to solve variable coefficient differential equations under arbitrary boundary condition. By this method, the general computation formal is obtained. Its convergence in proved. We can get analytic expressions which converge to exact solution and its higher order derivatives uniformy Four numerical examples are given, which indicate that satisfactory results can he obtanedby this method.展开更多
In this paper, the nonlinear axial symmetric deformation problem of nonhomogeneous ring- and stringer-stiffened shells is first solved by the exact analytic method. An analytic expression of displacements and stress r...In this paper, the nonlinear axial symmetric deformation problem of nonhomogeneous ring- and stringer-stiffened shells is first solved by the exact analytic method. An analytic expression of displacements and stress resultants is obtained and its convergence is proved. Displacements and stress resultants converge to exact solution uniformly. Finally, it is only necessary to solve a system of linear algebraic equations with two unknowns. Four numerical examples are given at the end of the paper which indicate that satisfactory results can be obtained by the exact analytic 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
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.
文摘In[1], the exact analytic method for the solution of differential equation with variable coefficients was suggested and an analytic expression of solution was given by initial parameter algorithm. But to some problems such as the bending, free vibration and buckling of nonhomogeneous long cylinders, it is difficult to obtain their solutions by the initial parameter algorithm on computer. In this paper, the substructure computational algorithm for the exact analytic method is presented through the bending of non-homogeneous long cylindrical shell. This substructure algorithm can he applied to solve the problems which can not he calculated by the initial parameter algorithm on computer. Finally, the problems can he reduced to solving a low order system of algehraic equations like the initial parameter algorithm Numerical examples are given and compared with the initial para-algorithm at the end of the paper, which confirms the correctness of the substructure computational algorithm.
文摘Many engineering problems can be reduced to the solution of a variable coefficient differential equation. In this paper, the exact analytic method is suggested to solve variable coefficient differential equations under arbitrary boundary condition. By this method, the general computation formal is obtained. Its convergence in proved. We can get analytic expressions which converge to exact solution and its higher order derivatives uniformy Four numerical examples are given, which indicate that satisfactory results can he obtanedby this method.
文摘In this paper, the nonlinear axial symmetric deformation problem of nonhomogeneous ring- and stringer-stiffened shells is first solved by the exact analytic method. An analytic expression of displacements and stress resultants is obtained and its convergence is proved. Displacements and stress resultants converge to exact solution uniformly. Finally, it is only necessary to solve a system of linear algebraic equations with two unknowns. Four numerical examples are given at the end of the paper which indicate that satisfactory results can be obtained by the exact analytic 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.
