Showing papers in "Applied Mathematics and Mechanics-english Edition in 1997"
TL;DR: In this article, the effects of initial geometric imperfections of the plate are included in the present study which also includes the thermal effects, and the analysis uses a mixed Galerkinperturbation technique to determine thermal buckling loads and postbuckling equilibrium paths.
Abstract: Karman-type nonlinear large deflection equations are derived according to the Reddy's higher-order shear deformation plate theory and used in the thermal postbuckling analysis. The effects of initial geometric imperfections of the plate are included in the present study which also includes the thermal effects. Simply supported, symmetric cross-ply laminated plates subjected to uniform or nonuniform parabolic temperature distribution are considered. The analysis uses a mixed Galerkinperturbation technique to determine thermal buckling loads and postbuckling equilibrium paths. The effects played by transverse shear deformation, plate aspect ratio, total number of plies, thermal load ratio and initial geometric imperfections are also studied.
122 citations
TL;DR: In this paper, a Banach space ZH is defined, and it is proved that there is completeness of eigenfunction systems (symplectic orthogonal system) of a class of Hamiltonian system in ZH space.
Abstract: In this paper, a new Banach space ZH is defined, and it is proved that there is completeness of eigenfunction systems (symplectic orthogonal system) of a class of Hamiltonian system in ZH space. We have also proved the following results: ZH space can be continuously imbedded toL
2
[0, 1]×L
2
[0, 1], butZH ≠ L
2
[0,1] × L
1
[0, 1].
24 citations
TL;DR: In this paper, the generalized Almansi's theorem was used to simplify the problem of point forces and point charge acting on the line boundary of a piezoelectric half-plane.
Abstract: First, based on the basic equations of two-dimensional piezoelectroelasticity, a displacement function is introduced and the general solution is then derived. Utilizing the generalized Almansi's theorem, the general solution is so simplified that all physical quantities can be expressed by three “harmonic functions”. Second, solutions of problems of a wedge loaded by point forces and point charge at the apex are also obtained in the paper. These solutions can be degenerated to those of problems of point forces and point charge acting on the line boundary of a piezoelectric half-plane.
21 citations
TL;DR: Based on the fundamental principles of meteorology and thermodynamics, the calculation theory of the nonlinear unstable pavement temperature fields of two-dimensional layered system by analytic theory is established and the calculation methods of surface temperature, ground temperature and temperature distribution along the thickness under different climate conditions are put forward respectively as mentioned in this paper.
Abstract: Based on the fundamental principles of meteorology and thermodynamics, the calculation theory of the nonlinear unstable pavement temperature fields of two-dimension layered system by analytic theory is established and the calculation methods of surface temperature, ground temperature and temperature distribution along the thickness under different climate conditions are put forward respectively.
14 citations
TL;DR: A new group decision eigenvalue method abbreviated as GEM is proposed, which overcomes the non-consistence of judgement matrix and will open up a new route for the selection of experts in the decision system.
Abstract: In this paper, a new group decision eigenvalue method abbreviated as GEM is proposed. It overcomes the non-consistence of judgement matrix and will open up a new route for the selection of experts in the decision system.
14 citations
TL;DR: In this paper, it was shown that a Beltrami flow can sustain a steady force-free magnetic field in a perfectly conducting fluid, provided the magnetic field is parallel to the velocity everywhere.
Abstract: Solenoidal vector fields, which satisfy the condition that the field vector everywhere parallels to its curl, have complex topological structures, and usually show chaotic behaviors. In this paper, analytical solutions for vector fields with constant proportional factor in three basic coordinate systems are presented and it is pointed out that a Beltrami flow can sustain a steady force-free magnetic field in a perfectly conducting fluid, provided the magnetic field is parallel to the velocity everywhere.
12 citations
TL;DR: In this paper, the multivariable spline element equations are derived, based on the mixed variational principle, for bending, vibration and stability of the plates on elastic foundation.
Abstract: In this paper, the bicubic splines in product form are used to construct the multifield functions for bending moments, twisting moment and transverse displacement of the plate on elastic foundation. The multivariable spline element equations are derived, based on the mixed variational principle. The analysis and calculations of bending, vibration and stability of the plates on elastic foundation are presented in the paper. Because the field functions of plate on elastic foundation are assumed independently, the precision of the field variables of bending moments and displacement is high.
11 citations
TL;DR: In this paper, the interaction problem of a rigid line inclusion and an elastic circular inclusion has been reduced to solve a normal Cauchy-type singular integral equation and the stress intensity factors at the ends of the rigid line inclusions and the interface stresses of the inclusions are obtained.
Abstract: In this paper, the interaction problem of a rigid line inclusion and an elastic circular inclusion has been reduced to solve a normal Cauchy-type singular integral equation The stress intensity factors at the ends of the rigid line inclusion and the interface stresses of the inclusions are obtained
10 citations
TL;DR: In this paper, the state equation for the continuous orthotropic open cylindrical shells was established and an identical exact solution was presented for the statics of thin, moderately thick and thick laminated continuous OCLS shells.
Abstract: Discarding any assumption about displacement models and stress distribution and introducing δ-function into the present study, we established the state equation for the continuous orthotropic open cylindrical shells. An identical exact solution is presented for the statics of thin, moderately thick and thick laminated continuous open cylindrical shells. Numerical results are obtained and compared with those calculated using SAP5.
10 citations
TL;DR: In this paper, the authors used the conforma mapping method to analyze and evaluate the ground displacement and scattering of incident SH-waves on the surface of semi-canyon topography of arbitrary shape with lining in anisotropic media.
Abstract: The purpose of this paper is to use the conforma mapping method[1] to analyze and evaluate the ground displacement and scattering of incident SH-waves, on the surface of semi-canyon topography of arbitrary shape with lining in anisotropic media. The problem to be solved can be reduced to the solution of an infinite algebraic equation set by using the method of full-space expansion of Fourier progression. Using the mapping function and scattering theory to solve problems due to semi-canyon topography with lining is just like mapping the semi-cylindrical canyon of arbitrary shape into a cylindrical canyon in full-space. Moreover, it is far practical in engineering practice. From the computational examples, it is obvious that the variation of displacement amplitudes on the surface near the lining and the canyon topography is rather sharp, especially when the freqencies of incident SH-waves increase.
10 citations
TL;DR: In this article, a new production form for a hierarchy of nonlinear evolution equations (NLEEs) is given, which contains productions of isospectral and non-isosorral hierarchy under a generalized structure of Lax representations for the hierarchy of NLEEs.
Abstract: A new production form for a hierarchy of nonlinear evolution equations (NLEEs) is given in this paper The form contains productions of isospectral and non-isospectral hierarchy Under this form a generalized structure of Lax representations for the hierarchy of NLEEs is this presented As a concrete example, the Levi-hierarchy of evolution equations are discussed at the end of this paper
TL;DR: In this paper, the fixed point theorem of increasing operator with non-continuity is utilized to discuss the existence and uniqueness of positive solution for a class of nonlinear Volterra integral equations.
Abstract: In this paper, the fixed point theorem of increasing operator with non-continuity is utilized to discuss the existence and uniqueness of positive solution for a class of nonlinear Volterra integral equations. An important condition of continuity can be replaced by weak condition.
TL;DR: In this article, a speedy accurate solution to structural fuzzy finite element equilibrium equations (SFFEEE), by combining the definition of the solution of interval equations with the mechanical meaning of the structural finite element equilibria (SFEEE), was put forward.
Abstract: A speedy accurate solution to structural fuzzy finite element equilibrium equations (SFFEEE), by combining the definition of the solution of interval equations with the mechanical meaning of the structural finite element equilibrium equations (SFEEE), was put forward. The fuzzification of the SFFEEE, which is discussed in this paper, originates from that of material property, structural boundary conditions and external loading. The computing quantity of this solution is almost equal to that of the general finite element method (GFEM).
TL;DR: In this article, the authors studied the distribution of zeroes of solutions of neutral delay differential equations and established an estimate for the distance between adjacent zeros of the solutions of such equations under less restrictive hypotheses on the variable coefficients.
Abstract: The purpose of this paper is to study the distribution of zeroes of solutions of the neutral delay differential equations. An estimate is established for the distance between adjacent zeroes of the solutions of such equations under less restrictive hypotheses on the variable coefficients. The results obtained improve and extend some known results in the literature.
TL;DR: In this article, the axisymmetric nonlinear free vibration problems of cylindrically orthotropic shallow thin spherical and conical shells under uniformly distributed static loads are studied by using MWR and Lindstedt-Poincare perturbation method, from which, the characteristic relation between frequency ratio and amplitude is obtained.
Abstract: In this paper, the axisymmetric nonlinear free vibration problems of cylindrically orthotropic shallow thin spherical and conical shells under uniformly distributed static loads are studied by using MWR and Lindstedt-Poincare perturbation method, from which, the characteristic relation between frequency ratio and amplitude is obtained. The effects of static loads, geometric and material parameters on vibrational behavior of shells are also discussed.
TL;DR: In this article, the authors studied the asymptotic theory of initial value problems for a semilinear perturbed telegraph equation and constructed formal approximations on a long timescale O(∣e∣−1).
Abstract: This paper is devoted to studying the asymptotic theory of initial value problems for a semilinear perturbed telegraph equation. The asymptotic theory and validity of formal approximations are constructed on long timescale O(∣e∣−1. As an application of the asymptotic theory, the initial value problems for a special telegraph equation are studied and two asymptotic solutions of order O(∣e∣−1 are presented.
TL;DR: In this article, the fundamental solutions for a concentrated force in a three-dimensional biphase-infinite solid were expressed in the tensor form, which enables them to be directly applied to the boundary integral equation and the boundary element method for solving elastic mechanics problems of the bimaterial space.
Abstract: In this paper, by using the method of tensor operation, the fundamental solutions, given in the refernces listed, for a concentrated force in a three-dimensional biphase-infinite solid were expressed in the tensor form, which enables them to be directly applied to the boundary integral equation and the boundary element method for solving elastic mechanics problems of the bimaterial space. The fundamental solutions for Mindlin's problem, Lorentz's problem and homogeneous space problem are involved in the present results.
TL;DR: In this paper, a theoretical analysis for the snap-buckling behavior of dished shallow shells under uniform loads is presented by means of the modified iteration method, and the second approximate formula of elastic behaviour and a set of numerical solutions are given.
Abstract: A theoretical analysis is presented for the snap-buckling behaviour of dished shallow shells under uniform loads. By means of the modified iteration method, the second approximate formula of elastic behaviour and a set of numerical solutions are given. And effects of parameters β and k on the snap-buckling behaviour are discussed.
TL;DR: In this paper, the electro-elastic solutions for a piezoelectric halfspace subjected to a line force, a line charge and a line dislocation were derived on the basis of Stroh formalism and analytical continuation.
Abstract: In this paper, as is studied are the electro-elastic solutions for a piezoelectric halfspace subjected to a line force, a line charge and a line dislocation, i. e., Green's functions on the basis of Stroh formalism and the concept of analytical continuation, explicit expressions for Green's functions are derived. As a direct application of the results obtained, an infinite piezoelectric solid containing a semi-infinite crack is examined. Attention if focused on the stress and electric displacement fields of a crack tip. The stress and electric displacement intensity factors are given explicitly.
TL;DR: In this paper, the fracture of materials under the action of compressive forces, directed along cracks which are parallel in plane cannot be described within the framework of the linear fracture mechanics, since these forces have no influence on stress intensity coefficients and on values of cracks opening.
Abstract: The fracture of materials under the action of compressive forces, directed along cracks which are parallel in plane cannot be described within the framework of the linear fracture mechanics. The criteria of fracture of the Griffith-Irvin or COC type, used in classical linear fracture mechanics, are not applicable in this problem, since these forces have no influence on stress intensity coefficients and on values of cracks opening. The problems of such a class may be described only by using new approaches. One of possible approaches is presented by the first author, which involves using linearized relations, derived from exact non-linear equations of deformable solid body mechanics. It should be remarked here that this approach has been widely used in problems of deformable bodies stability. As a criterion of the initiation of fracture the criterion of local instability near defects of the crack type is used. In these cases the process of loss of stability initiates the fracture process.
TL;DR: The random interval equilibrium equation (RIEE) is obtained by λ-level cutting the fuzzy-stochastic finite element equilibrium equations (FSFEEE) by derived from the small-parameter perturbation theory.
Abstract: In this paper, the random interval equilibrium equations (RIEE) is obtained by λ-level cutting the fuzzy-stochastic finite element equilibrium equations (FSFEEE). Based on the relations between the variables of equilibrium equations, solving RIEE is transformed into solving two kinds of general random equilibrium equaltions (GREE). Then the recursive equations of evaluating the random interval displacement is derived from the small-parameter perturbation theory. The computational formulae of statistical characteristic of the fuzzy random displacements, the fuzzy random strains and the fuzzy random stresses are also deduced in detail.
TL;DR: Explicit fomulas for 2D electroelastic fundamental solutions in general anisotropic piezoelectric media subjected to a line force and a line charge are obtained by using the plane wave decomposition method and a subsequent application of the residue calculus as discussed by the authors.
Abstract: Explicit fomulas for 2-D electroelastic fundamental solutions in general anisotropic piezoelectric media subjected to a line force and a line charge are obtained by using the plane wave decomposition method and a subsequent application of the residue calculus “Anisotropic” means that any material symmetry restrictions are not assumed “Two dimensional” includes not only in-plane problems but also anti-plane problems and problems in which in-plane and anti-plane deformations couple each other As a special case, the solutions for transversely isotropic piezoelectric media are given
TL;DR: In this paper, the existence and uniqueness of a classical solution locally in time of the Verigin problem with kinetic condition is investigated. But the uniqueness of the solution is not proven.
Abstract: In this paper a Verigin problem with kinetic condition is considered. The existence and uniqueness of a classical solution locally in time of this problem are obtained.
TL;DR: In this article, a complete set of higher order sensitivity expressions has been presented based on the complex variables theory, which have solid mathematical foundation and practical significance, and they have been used to solve the inverse algebraic eigenvalue problem.
Abstract: In this paper, structural static design is considered as a kind of inverse algebraic eigenvalue problem. It is the most important task for the inverse problem to compute the sensitivities of eigenvalues and eigenvectors. Therefore, a complete set of higher order sensitivity expressions has been presented based on the complex variables theory. These expressions have solid mathematical foundation and practical significance.
TL;DR: In this paper, the S-R decomposition unique existence theorem is proved, by employing matrix and tensor method, and a brief proof of its objectivity is given, where the deformation gradient function F can be decomposed into direct sum of a symmetric tensor S and an orthogonal tensor R.
Abstract: For a physically possible deformation field of a continuum, the deformation gradient function F can be decomposed into direct sum of a symmetric tensor S and an orthogonal tensor R, which is called S-R decomposition theorem. In this paper, the S-R decomposition unique existence theorem is proved, by employing matrix and tensor method. Also, a brief proof of its objectivity is given.
TL;DR: In this paper, one sufficient condition for a graph to be (g, f)-factorable is given, where the edges of a graph G can be decomposed into some edge disjoint factorizations.
Abstract: Let G be a graph and g, f be two nonnegative integer-valued functions defined on the vertices set V(G) of G and g≤f. A (g, f)-factor of a graph G is a spanning subgraph F of G such that g(x)≤dF(x)≤f(x) for all x∈V(G). If G itself is a (g, f)-factor, then it is said that G is a (g, f)-graph. If the edges of G can be decomposed into some edge disjoint (g, f)-factors, then it is called that G is (g, f)-factorable. In this paper, one sufficient condition for a graph to be (g, f)-factorable is given.
TL;DR: In this article, a method based on a line-spring model was proposed to analyze approximately vibration responses of cracked beams, in conjunction with the Euler-Bernoulli beam theory, modal analysis and fracture mechanics principle was applied to derive a characteristic equation for the cracked beam vibration.
Abstract: In this paper a method based on a line-spring model was proposed to analyze approximately vibration responses of cracked beams. The method in conjunction with the Euler-Bernoulli beam theory, modal analysis and fracture mechanics principle was applied to derive a characteristic equation for the cracked beam vibration. As application examples, natural frequency responses for a cracked hinged-hinged beam and a cracked cantilever beam were examined. It was shown that the present solutions obtained are quite in agreement with the solutions or experimental results in available references.
TL;DR: In this paper, a boundary element method for solving the dynamical response of viscoelastic thin plate is given, which is based on the improved Bellman's numerical inversion of the Laplace transform.
Abstract: In this paper, a boundary element method for solving dynamical response of viscoelastic thin plate is given. In Laplace domain, we propose two methods to approximate the fundamental solution and develop the corresponding boundary element method. Then using the improved Bellman's numerical inversion of the Laplace transform, the solution of the original problem is obtained. The numerical results show that this method has higher accuracy and faster convergence.
TL;DR: In this article, the second-order perturbation results of non-repeated singular values and the corresponding left and right singular vectors are obtained, and the results can meet the general needs of most problems of various practical applications.
Abstract: The perturbational reanalysis technique of matrix singular value decomposition is applicable to many theoretical and practical problems in mathematics, mechanics, control theory, engineering, etc.. An indirect perturbation method has previously been proposed by the author in this journal, and now the direct perturbation method has also been presented in this paper. The second-order perturbation results of non-repeated singular values and the corresponding left and right singular vectors are obtained. The results can meet the general needs of most problems of various practical applications. A numerical example is presented to demonstrate the effectiveness of the direct perturbation method.
TL;DR: In this article, it is shown that there exists approximate inertial manifolds in weakly damped forced KdV equation with periodic boundarý conditions, which provide approximant of the attractor by finite dimensional smooth manifolds which are explicitly defined.
Abstract: It is presented that there exists approximate inertial manifolds in weakly damped forced KdV equation with periodic boundarý conditions. The approximate inertial manifolds provide approximant of the attractor by finite dimensional smooth manifolds which are explicitly defined. And the concept leads to new numerical schemes which are well adapted to the longtime behavior of dynamical system.