Showing papers in "Applied Mathematics and Mechanics-english Edition in 2000"
TL;DR: Based on the nonlinear geometric theory of extensible rods, an exact mathematical model of thermal postbuckling behavior of uniformly heated elastic rods with axially immovable ends is developed, in which the arc length s(x) of axial line and the longitudinal displacement u(x), are taken as the basic unknown functions as mentioned in this paper.
Abstract: Based on the nonlinear geometric theory of extensible rods, an exact mathematical model of thermal post-buckling behavior of uniformly heated elastic rods with axially immovable ends is developed, in which the arc length s(x) of axial line and the longitudinal displacement u(x) are taken as the basic unknown functions. This is a two point boundary value problem of first order ordinary differential equations with strong nonlinearity. By using shooting method and analytical continuation, the nonlinear boundary value problems are numerically solved. The thermal post-buckled states of the rods with transversely simply supported and clamped ends are obtained respectively and the corresponding numerical data tables and characteristic curves are also given.
40 citations
TL;DR: In this paper, the free vibration of clamped circular plate when temperature and stress fields were coupled was analyzed and a nonlinear differential equation about time was obtained by using Galerkin's method.
Abstract: An analysis was given for the free vibration of clamped circular plate when temperature and stress fields were coupled. A nonlinear differential equation about time was obtained by using Galerkin's method. The numerical results of vibration amplitude vs time were compared with the uncoupled case. It is found that if the given initial displacement is small, the effect of thermoelastical coupling will make the natural frequency increase; if the given initial displacement is large, it will be the opposite case. Effects of some different vibration factors are also discussed.
31 citations
TL;DR: In this paper, a quasi wavelet-based numerical method was introduced for solving the evolution of the solutions of nonlinear paritial differential Burgers' equations, which has distinctive local property.
Abstract: A quasi-wavelet based numerical method was introduced for solving the evolution of the solutions of nonlinear paritial differential Burgers' equations. The quasi wavelet based numerical method was used to discrete the spatial derivatives, while the fourth-order Runge-Kutta method was adopted to deal with the temporal discretization. The calculations were conducted at a variety of Reynolds numbers ranging from 10 to unlimited large. The comparisons of present results with analytical solutions show that the quasi wavelet based numerical method has distinctive local property, and is efficient and robust for numerically solving Burgers' equations.
27 citations
TL;DR: In this article, a semi-inverse method was proposed to establish generalized variational principles with multi-variables without any variational crisis phenomenon, which is an integration and an extension of Hu' s try-and-error method, Chien' s veighted residual method, and Liu' s systematic method.
Abstract: Semi-inverse method, which is an integration and an extension of Hu' s try-and-error method, Chien' s veighted residual method and Liu' s systematic method, is proposed to establish generalized variational principles with multi-variables without any variational crisis phenomenon. The method is to construct an energy trial-functional with an unknown function F , which can be readily identifled by making the trial-functional stationary and using known constraint equations. As a result generalized variational principles with two kinds of independent variables ( such as well-known Hellinger-Reissner variational principle and Hu-Washizu principle ) and generalized variational principles with three kinds of independent variables ( such as Chien' s generalized variational principles) in elasticity have been deduced without using Lagrange multiplier method. By semi-inverse method, the author has also proved that Hu-Washizu principle is actually a variational principle with only two kinds of independent variables, stress-strain relations are still its constraints.
24 citations
TL;DR: In this article, the exact relation between strain and displacement for nonlinear deformation of thin shells is given for cylinder shell deformed cylindrical shaped, and the fundamental formula of large deformation when the deflection is on the same class with the thickness of the shell is derived after simplified rationally.
Abstract: The exact relation between strain and displacement is given for nonlinear deformation of thin shell. The fundamental formula of large deformation when the deflection is on the same class with the thickness of the shell is derived after simplified rationally. The fundamental formula of large deformation when the deflection is on the same class with the length of the shell is derived exactly for cylinder shell deformed cylindrical shaped.
22 citations
TL;DR: In this paper, a general solution of coupled thermoelastic problems is derived from the linearized basic equations for coupled thermodynamic problems, which involves one less potential function than Biot's solution.
Abstract: A new type of general solution of thermoelasticity is derived from the linearized basic equations for coupled thermoelastic problem. In the case of quasi-static problem, the present general solution is simpler since it involves one less potential function than Biot's solution.
19 citations
TL;DR: In this article, the generalized quasi-symmetry of the infinitesimal transformation for the transformation group G is presented and two examples to illustrate the application of the result are given.
Abstract: Noether's theory of dynamical systems with unilateral constraints by introducing the generalized quasi-symmetry of the infinitesimal transformation for the transformation group G, is presented and two examples to illustrate the application of the result are given.
17 citations
TL;DR: In this paper, the vector V -function method used to judge the stability is generalized for infinite interconnected systems and sufficient conditions which guarantee the asymptotic string stability of a class of interconnected systems are given.
Abstract: The notion of string stability of a countably infinite interconnection of a class of nonlinear system was introduced. Intuitively, string stability implies uniform boundedness of all the states of the interconnected system for all time if the initial states of the interconnected system are uniformly bounded. Vector V -function method used to judge the stability is generalized for infinite interconnected system and sufficient conditions which guarantee the asymptotic string stability of a class of interconnected system are given. The stability regions obtained here are much larger than those in previous papers. The method given here overcomes some difficulties to deal with stability of infinite nonlinear interconnected system in previous papers.
17 citations
TL;DR: Using the homogeneous balance method introduced by Wang Mingliang, the multi-solitary wave solutions were obtained for the variant Boussinesq equation and Kupershmidt equation.
Abstract: Using the homogeneous balance method introduced by Wang Mingliang, the multi— solitary wave solutions are obtained for the variant Boussinesq equation and Kupershmidt equation. The Wang's result is a special case of above results for the variant Boussinesq equation.
15 citations
Journal Article•
TL;DR: In this paper, a quasi wavelet based numerical method was introduced for solving the evolution of the solutions of nonlinear partial differential Burgers' equations, which has distinctive local property, and is efficient and robust for numerically solving Burgers's equations.
Abstract: A quasi_wavelet based numerical method was introduced for solving the evolution of the solutions of nonlinear partial differential Burgers' equations. The quasi wavelet based numerical method was used to discrete the spatial deriatives, while the fourth_order Runge_Kutta method was adopted to deal with the temporal discretization. The calculations were conducted at a variety of Reynolds numbers ranging from 10 to unlimited large. The comparisons of present results with analytical solutions show that the quasi wavelet based numerical method has distinctive local property, and is efficient and robust for numerically solving Burgers' equations.
15 citations
TL;DR: In this article, the analytic solution for simply supported piezoelectric beams under uniform exterior pressure was derived, and the results were also compared with the ones of FEM.
Abstract: On the basis of two-dimensional constitutive relationships of piezoelectric materials, the analytic solution for simply supported piezoelectric beams under uniform exterior pressure was derived. Furthermore the results were also compared with the ones of FEM for piezoelectric materials. Thus the foundation for further research of piezoelectric materials' distribution sensing mechanism and the validation of numerical methods such as FEM is provided.
TL;DR: In this article, a smooth model of topology optimization for continuum structures is established which has weight objective considering stress and displacement constraints based on the independent-continuous topological variable concept and mapping transformation method proposed by Sui Yunkang and Yang Deqing.
Abstract: Topology optimization design of continuum structures that can take account of stress and displacement constraints simultaneously is difficult to solve at present. The main obstacle lies in that, the explicit function expressions between topological variables and stress or displacement constraints can not be obtained using homogenization method or variable density method. Furthermore, large quantities of design variables in the problem make it hard to deal with by the formal mathematical programming approach. In this paper, a smooth model of topology optimization for continuum structures is established which has weight objective considering stress and displacement constraints based on the independent-continuous topological variable concept and mapping transformation method proposed by Sui Yunkang and Yang Deqing. Moreover, the approximate, explicit expressions are given between topological variables and stress or displacement constraints. The problem is well solved by using dual programming approach, and the proposed element deletion criterion implements the inversion of topology variables from the discrete to the continuous. Numerical examples verify the validity of proposed method.
TL;DR: In this paper, the integro-partial-differential equation that governs the dynamical behavior of homogeneous viscoelastic beams was established and the material of the beams obeys the Leaderman nonlinear constitutive relation.
Abstract: The integro-partial-differential equation that governs the dynamical behavior of homogeneous viscoelastic beams was established. The material of the beams obeys the Leaderman nonlinear constitutive relation. In the case of two simply supported ends, the mathematical model is simplified into an integro-differential equation after a 2nd-order truncation by the Galerkin method. Then the equation is further reduced to an ordinary differential equation which is convenient to carry out numerical experiments. Finally, the dynamical behavior of 1 st-order and 2 nd-order truncation are numerically compared.
TL;DR: In this article, the steady-state response solutions of mechanical displacement, stresses, strains, potential and electric displacement were derived from constitutive relations, geometric and motion equations for the piezoelectric medium under external excitation (i.e. applied surface traction and potential) in spherical coordinate system.
Abstract: Spherical-symmetric stead-state response problem of piezoelectric spherical shell in the absence of body force and free charges is discussed. The steady-state response solutions of mechanical displacement, stresses, strains, potential and electric displacement were derived from constitutive relations, geometric and motion equations for the piezoelectric medium under external excitation ( i. e. applied surface traction and potential) in spherical coordinate system. As an application of the general solutions, the problem of an elastic spherical shell with piezoelectric actuator and sensor layers was solved. The results could provide good theoretical basis for the spherical symmetric dynamic control problem of piezoelectric intelligent structure. Furthermore, the solutions can serve as reference for the research of general dynamic control problem.
TL;DR: In this article, a discrete model of flexible cable with large sag is established by using multiple rigid body-spherical hinge model, and dynamic equation of that discrete model is derived according to dynamics theory of multiple rigid bodies system.
Abstract: Discrete model of flexible cable with large sag is established by using multiple rigid body-spherical hinge model, and dynamic equation of that discrete model is derived according to dynamics theory of multiple rigid body system. Displacement and velocity of system are revised to elininate violation phenomenon of the differential-algebra equation in numerical simulation based on the theory of generalized inverse of matrices. Numerical simulation proves the validity of our method.
TL;DR: In this article, an improved MAC method proposed by Chen Suqin et al., which uses three order upwind scheme to discretize the convection term and uses multigrid method to solve the Poisson equation for pressure is applied to simulate the flow around two square cylinders arranged side-by-side.
Abstract: The numerical method is used to calculate the flow around two square cylinders arranged side-by-side and the mean and fluctuating aerodynamic forces, and Strouhal numbers and power spectrum of lift force and drag force are obtained. An improved MAC method proposed by Chen Suqin et al., which uses three order upwind scheme to discretize the convection term and uses multigrid method to solve the Poisson equation for pressure is applied to simulate the flow around two square cylinders arranged side-by-side. Results show that the interference characteristic of two square cylinders arranged side-by-side is completely different with the different spacing ratio. When the spacing ratio is smaller than a certain critical value, the gap flow between two cylinders is biased to one side in a stable or unstable manner.
TL;DR: In this paper, a new algorithm to construct solitary wave solutions for systems of nonlinear evolution equations is put forward, which is better than what the hyperbolic function method known does and simpler in use.
Abstract: According to the improved sine-cosine method and Wu-elimination method, a new algorithm to construct solitary wave solutions for systems of nonlinear evolution equations is put forward. The algorithm has some conclusions which are better than what the hyperbolic function method known does and simpler in use. With the aid of MATHEMATICA, the algorithm can be carried out in computer.
TL;DR: In this paper, the critical velocity and complex frequency of pipe conveying fluid on Winkler elastic foundation and two-parameter foundation were calculated by power series method, and the numerical results showed that elastic foundation can increase the critical flow velocity of static instability and dynamic instability of pipe.
Abstract: The governing equation of solid-liquid couple vibration of pipe conveying fluid on the elastic foundation was derived. The critical velocity and complex frequency of pipe conveying fluid on Winkler elastic foundation and two-parameter foundation were calculated by power series method. Compared with pipe without considering elastic foundation, the numerical results show that elastic foundation can increase the critical flow velocity of static instability and dynamic instability of pipe. And the increase of foundation parameters may increase the critical flow velocity of static instability and dynamic instability of pipe, thereby delays the occurrence of divergence and flutter instability of pipe. For higher mass ratio β, in the combination of certain foundation parameters, pipe behaves the phenomenon of restabilization and redivergence after the occurrence of static instability, and then coupled-mode flutter takes place.
TL;DR: In this article, a convergence analysis of a more stable identification algorithm-recursive damped least square is proposed, which is done by normalizing the measurement vector entering into the identification algorithm, and it is shown that the parametric distance converges to a zero mean random variable.
Abstract: The recursive least square is widely used in parameter identification. But it is easy to bring about the phenomena of parameters burst-off. A convergence analysis of a more stable identification algorithm-recursive damped least square is proposed. This is done by normalizing the measurement vector entering into the identification algorithm. It is shown that the parametric distance converges to a zero mean random variable. It is also shown that under persistent excitation condition, the condition number of the adaptation gain matrix is bounded, and the variance of the parametric distance is bounded.
TL;DR: In this article, a new concept of the X-M-PN space is introduced, and the acute angle principle in the X -MPN space was proved, and some new results were obtained.
Abstract: A new concept of the X-M-PN space is introduced, and the acute angle principle in the X-M-PN space is proved. Meanwhile, some new results are obtained.
TL;DR: In this article, some new equilibrium existence theorems of quasi-equilibrium problems are proved in non-compact generalized convex spaces by applying a new fixed point theorem due to the author.
Abstract: By applying a new fixed point theorem due to the author, some new equilibrium existence theorems of quasi-equilibrium problems are proved in noncompact generalized convex spaces. These theorems improve and generalize a number of important known results in recent literature.
TL;DR: In this article, the axisymmetric large amplitude free vibration for circular sandwich plates under static load is derived, and a set of nonlinearly coupled algebraic and differential eigenvalue equations of the problem are formulated following an assumed time mode approach.
Abstract: The differential equations of the axisymmetric large amplitude free vibration for circular sandwich plates under static load are derived, and a set of nonlinearly coupled algebraic and differential eigenvalue equations of the problem are formulated following an assumed time mode approach suggested. The analytic solutions are presented and a relation for amplitude frequency-load of the plates with edge clamped is derived by modified iteration method. The effects of static load on vibrations of plates are investigated.
TL;DR: In this paper, a generalized Lyness equation is investigated and necessary and sufficient conditions for the periodicity of the solutions of Eq. (*) and a sufficient condition for the strict oscillation of all solutions of * are obtained.
Abstract: A generalized Lyness equation is investigated as follows
$$x_{n + 1} = \frac{{x_n }}{{(a + bx_n )x_{n - 1} }}, n = 0,1,2, \cdot \cdot \cdot$$
(*)
where a, b ∈[0,∞) with a+b>0 and where the initial values x−1, xo are arbitrary positive numbers. Some new results, mainly a necessary and sufficient condition for the periodicity of the solutions of Eq. (*) and a sufficient condition for the strict oscillation of all solutions of Eq(*), are obtained. As an application the results solve an open problem presented by G. Ladas.
TL;DR: In this article, inductance-based electromagnetic tomography (EMT) is used for industrial process tomographic technique and exact expressions of the magnetic field distribution in a two-dimensional object space are derived by analytically solving the forward problem for a particular two-component flow.
Abstract: Inductance-based electromagnetic tomography (EMT) is a novel industrial process tomographic technique. Exact expressions of the magnetic field distribution in a two-dimensional object space were derived by analytically solving the forward problem for a particular two-component flow. The physical mechanisms within the sensor and the detectability limits of the EMT technique were quantitatively analyzed. Direct mathematical expressions for the field sensitivity and the sensitivity maps were established. To a certain extent, mathematical and theoretical bases are given for quantitative design of the sensor, detectability analysis of the EMT technique and image reconstruction of two-component processes based on the linear back-projection algorithm.
TL;DR: In this article, the authors introduce the concept of pseudo contractive type mapping and study the convergence problem of Ishikawa and Mann iterative processes with error for this kind of mappings.
Abstract: The purpose of this paper is to introduce the concept of Φ-pseudo contractive type mapping and to study the convergence problem of Ishikawa and Mann iterative processes with error for this kind of mappings. The results presented in this paper improve and extend many authors' recent results.
TL;DR: In this paper, the electroelastic interaction of a piezoelectric screw dislocation with a elliptical inclusion in PEG materials is considered, and the perturbation concept and the method of Laurent series expansion are used to derive the image force.
Abstract: The electroelastic interaction of a piezoelectric screw dislocation with a elliptical inclusion in piezoelectric materials is considered. The electroelastic fields in both the matrix and the inclusion were given explicitly by using the perturbation concept and the method of Laurent series expansion. Furthermore, the expressions of the image force acting on a piezoelectric screw disolcation were obtained. Numerical examples are provided to reveal the effect of piezoelectricity and the relative stiffness between the inclusion and the matrix on the image force. Consequently, the new interaction mechanism is found.
TL;DR: In this paper, the state space was reconstructed using the method of Legendre coordinate and several different scaling regimes for lag time τ were identified, and the influence for state space reconstruction of Lag time τ was discussed.
Abstract: The state space reconstruction is the major important quantitative index for describing non-linear chaotic time series. Based on the work of many scholars, such as: N. H. Packard, F. Takens, M. Casdagli, J. F. Bibson, CHEN Yu-shu et al, the state space was reconstructed using the method of Legendre coordinate. Several different scaling regimes for lag time τ were identified. The influence for state space reconstruction of lag time τ was discussed. The result tells us that is a good practical method for state space reconstruction.
TL;DR: It can be proved that the amount of the solution is nearly as much as that with the general stochastic finite element method (SFEM).
Abstract: For some cases the rules of monosource fuzzy numbers can be used into the solution of fuzzy stochastic finite element equations in engineering. This method can reduce the computing quantity of the solution. It can be proved that the amount of the solution is nearly as much as that with the general stochastic finite element method (SFEM). In addition, a new method to appreciate the structural fuzzy failure probability is presented for the needs of the modern engineering design.
TL;DR: In this paper, a new automatic constraint violation stabilization method for numerical integration of Euler-Lagrange equations of motion in dynamics of multibody systems is presented, where parameters a, β used in the traditional constraint violation stabilisation method are determined according to the integration time time step size and Taylor expansion method automatically.
Abstract: A new automatic constraint violation stabilization method for numerical integration of Euler-Lagrange equations of motion in dynamics of multibody systems is presented. The parameters a, β used in the traditional constraint violation stabilization method are determined according to the integration time time step size and Taylor expansion method automatically. The direct integration method, the traditional constraint violation stabilization method and the new method presented in this paper are compared finally.
TL;DR: Pseudo-division algorithm for matrix multivariable polynomial is given, and sufficient and necessary conditions for transforming a class of partial differential equations into infinite dimensional Hamiltonianian system and its concrete form are obtained as mentioned in this paper.
Abstract: Pseudo-division algorithm for matrix multivariable polynomial are given, thereby with the view of differential algebra, the sufficient and necessary conditions for transforming a class of partial differential equations into infinite dimensional Hamiltonianian system and its concrete form are obtained. Then by combining this method with Wu's method, a new method of constructing general solution of a class of mechanical equations is got, which several examples show very effective.