Showing papers in "Applied Mathematics and Mechanics-english Edition in 1981"
TL;DR: In this article, the authors present a review of recent laboratory studies of the flow and fracture of rocks under general triaxial compression and show that three principal stresses and strains are different.
Abstract: Recent laboratory studies of the flow and fracture of rocks under general triaxial compression are reviewed. New developments in laboratory techniques have made it possible to measure three principal stresses and strains under general triaxial stress states, in which all three principal stresses are different.
37 citations
TL;DR: In this article, the exact solution for the unsteady radial flow equations of the slightly compressible liquid through a medium with triple-porosity was obtained by using the method of decomposition.
Abstract: This paper obtains the exact solution for the unsteady radial flow equations of the slightly compressible liquid through a medium with triple-porosity by using the method of decomposition This solution not only reveals the essential characters of the unsteady flow of liquid through a medium with multiple-porosity, but also comprises the existing primal results
34 citations
TL;DR: In this article, the variational principle is used for the solution of large deflection of clamped circular plates under uniformly distributed loads, various perturbation parameters relating to load, deflection, slope of deflection and membrane force are studied.
Abstract: In the problems of large deflection of clamped circular plates under uniformly distributed loads, various perturbation parameters relating to load, deflection, slope of deflection, membrane force, etc, are studied. For a general perturbation parameter, the variational principle is used for the solution of such a problem. The applicable range of these perturbation parameters are studied in detail. In the case of uniformly loaded plate, perturbation parameter relating to central deflection seems to be the best among all others. The method of determination of perturbation solution by means of variational principle can be used to treat a variety of problems, including the large deflection problems under combine loads.
31 citations
TL;DR: In this paper, the authors presented the solution of symmetrical deformation of circular membrane under the action of uniformly distributed loads in its central portion, which is the third solution of the circular membrane problems after the well-known Hencky's solution.
Abstract: This paper presents the solution of symmetrical deformation of circular membrane under the action of uniformly distributed loads in its central portion. Its limiting case is the solution of circular membrane under concentrated load at the center. This solution is the third solution of the circular membrane problems after the well-known Hencky's solution
27 citations
TL;DR: In this paper, the fundamental equations and boundary conditions of nonlinear axisymmetrical bending theory for the circular sandwich plates with a soft core are derived by means of the method of calculus of variations.
Abstract: In this paper, fundamental equations and boundary conditions of nonlinear axisymmetrical bending theory for the circular sandwich plates with a soft core are derived by means of the method of calculus of variations. Especially in the case of very thin faces, the preceding fundamental epuations and boundary conditions simplity considerably. For example, a circular sandwich plate with edge clamped but free to siip under the action of uniform lateral load is considered. A more accurate solution of this problem has been obtained by means of the modified iteration method.
23 citations
TL;DR: In this paper, the defect of the traditional boundary layer methods (including the matched asymptotic expansions and the method of Visik-Lyusternik) is noted, from those methods, from which we can not construct the expansion of boundary layer term substantially.
Abstract: In this paper, the defect of the traditionary boundary layer methods (including the method of matched asymptotic expansions and the method of Visik-Lyusternik) is noted, from those methods we can not construct the asymptotic expansion of boundary layer term substantially. So the method of multiple scales is proposed for constructing the asymptotic expansion of boundary layer term, the reasonable result is obtained. Furthermore, we compare this method with the method used by Levinson, and find that both methods give the same asymptotic expansion of boundary layer term, but our method is simpler.
13 citations
TL;DR: In this paper, two simple integral equation methods are proposed for the analysis of vertical loaded piles in elastic half-space, where the axisymmetrical loads formed by Mindlin's horizontal point forces are distributed along the axisz in [0,L] of the elastic half space, and composed with Boussinesq's point force.
Abstract: Two simple integral equation methods are proposed for the analysis of vertical loaded pile. One of them is: let the axisymmetrical loads formed by Mindlin's horizontal point forces be distributed along the axisz in [0,L] of the elastic half-space, and composed with the Boussinesq's point force. The other is: in addition to the above fictitious loads, the Mindlin's vertical forces are distributed along the axisz in [0,L]. The former reduces the problem of a vertical loaded pile embedded in a half-space with the following boundary conditions.
to a Fredholm integral equation of the first kind; the latter reduces the same problem but with boundary conditions only differed from the second term of (0.1), i.e.
$$0 \leqslant z \leqslant L,U(e,z) = a - e,(e \to a);W(a,z) = const,$$
to two coupled Fredholm integral equations of the first kind. For a loaded rigid pile, the former suits for the cases which permit slides between the pile and the medium, but the latter suits the cases of no slides between the pile and the medium.
13 citations
TL;DR: In this paper, the case of a discontinuously loaded rectangular cantilever plate is considered and the problem to be solved will involve a concentrated load at the center of the plate, as shown in Fig. 1.
Abstract: The cantilever rectangular plates discussed previously are all loaded continuously. For example, the load may be either a uniform or a concentrated load at the free ledge of the plate. Now we go a step further to deal with the case of a discontinuously loaded rectangular cantilever plate. The problem to be solved will involve a concentrated load at the center of the plate, as shown in Fig. 1. The method of solution used is the same as before.
12 citations
TL;DR: In this paper, the deformation and stress distribution in semi-circular corrugated tube under axial force are calculated by means of the general solutions of circular ring shell given in previous paper.
Abstract: In this paper, the deformation and stress distribution in semi-circular corrugated tube under axial force are calculated by means of the general solutions of circular ring shell given in previous paper[1].
11 citations
TL;DR: In this article, the first term of its asymptotic solution, travel speed of soiltary waves and the relation between the amplitude of wave and the geometric size of channel were derived.
Abstract: In this paper, the solitary waves in an arbitrary cross-section channel which gradually changes in the streamwise have been studied. TheKdV equation with slowly varying coefficients is derived. Thus, we produced the first term of its asymptotic solution, travel speed of soiltary waves and the relation between the amplitude of wave and the geometric size of channel. The results have been applied to the cases of triangular and rectangular channels. For the channel with varying depths and breadths they are fairly consistent with those of Johnson, Shuto and Mile.
7 citations
TL;DR: In this article, the completeness of Hu Hai-chang's solution for convex regions in z-direction under a supplementary condition was proved for both convex and non-convex regions.
Abstract: In this paper, the completeness of Hu Hai-chang's solution is proved in the case of convex regions in z-direction under a supplementary condition On the other hand, for those non-convex regions in z-direction, Hu Hai-chang's solution is proved to be incomplete
TL;DR: In this article, the unit-dummy load method is generalized on the basis of Castigliano's Theorem, and the general equations of deflection surfaces of the structures, such as a kind of beams, plates and shells, are directly derived by the force method.
Abstract: In this paper the unit-dummy-load method is generalized on the basis of Castigliano's Theorem. On these grounds the general equations of deflection surfaces of the structures, such as a kind of beams, plates and shells, are directly derived by the force method.
TL;DR: In this article, a dynamic analysis of the viscoelastic simple supported beam was made in accordance with the relationship between stress and strain expressed by the simplest Voigt mechanical model, from which several analytic expressions have been obtained.
Abstract: Dynamic analysis of the viscoelastic simple supported beam has been made in accordance with the relationship between stress and strain expressed by the simplest Voigt mechanical model, from which several analytic expressions have been obtained. It is shown that the reduction of the ratio of natural frequencies progresses with the increase of the exciting frequency for high modes (Tab.1). In the final part of this paper, the forced vibration of simple supported beam subjected to a random and harmonic excitation has also been dealt with, and the representations of the beam deflection have been derived.
TL;DR: The eigenvalue problem and expansion theorems associated with Orr-Sommerfeld equation are fundamental for the investigation of the stability of laminar fluid motion and have been studied by many authors as discussed by the authors.
Abstract: The eigenvalue problem and expansion theorems associated with Orr-Sommerfeld equation are fundamental for the investigation of the stability of laminar fluid motion and have been studied by many authors. Nevertheless, the results are still incomplete[6]. In this paper, this problem is investigated again and some new results have been obtained, namely: (1) The expansion series converges uniformly and absolutely. (2) The coefficients of the expansion series satisfy an inequality of Paley-Wiener type, which is the natural extension of the well-known Bessel equality of a complete orthogonal set.
TL;DR: In this article, a numerical analysis of the propagation of stress waves and the allied scabbing phenomena in a steel plate under explosive attack is made, by using a model of one-dimensional flow.
Abstract: A numerical analysis of the propagation of stress waves and the allied scabbing phenomena in a steel plate under explosive attack is made, by using a model of one-dimensional flow. The results are compared with our experimental results which were carried out several years ago. It is found that, in case the hydrodynamic-elastoplastic model for steel plate and the cumulative damage spall criterion are used, the calculated thickness of the major spall is in reasonable agreement with that obtained in the experiments. An approximate formula for the thickness of the major spall is presented and the “mica-splitting” phenomenon about the minor spalls observed in the experiments is satisfactorily explained.
TL;DR: In this article, an axial compressive ellipsoid was analyzed using integral equation method and photoelastic experiment, and the results showed that σ 2 is quite nearly to those obtained by integral equation methods.
Abstract: Integral equation method and photoelastic experiment are used for the stress analysis of an axial compressive ellipsoid. Let the concentrated forces and the centers of compression, with symmetrical unknown intensive functions X1(c)=X1(−c) and X2(c)=X2(−c) respectively, be distributed symmetrically to =0 plane along the axis z(=−c) in [a,∞) and [−a,−∞) of the elastic space, in addition to a pair of equal and opposite axial forces acting on z=a and z=−a. We can reduce the problem of an axial compressive ellipsoid to two coupled Fredholm integral equations of the first kind. Furthermore, numerical calculation is then made. Two photo-elastic models of ellipsoid were analysed by “Freezing and Cutting” method, and the results, in which σ2 is quite nearly to those obtained by integral equation method, had been used in the analysis of the data of compressive rock specimens.
TL;DR: In this article, compressive tests of the bones along the axial direction have been carried out on some wet specimens of the right femur and humerus, from which there have been obtained the elastic modulus of femur E=9.98×109N/m2 and that of humus E=11.37×109 N/m 2.
Abstract: In this study, compressive tests of the bones along the axial direction have been carried out on some wet specimens of the right femur and humerus, from which there have been obtained the elastic modulus of femur E=9.98×109N/m2 and that of humerus E=11.37×109N/m2. Also comparisons and discussions have been made with reference to the available data reported abroad and at home.
TL;DR: In this paper, the problem of bending elastic circular rings of non-homogeneous and variable cross section under the actions of arbitrary loads is investigated, and the general solution of this problem is obtained so that it can be used for the calculations of strength and rigidity of practical problems such as arch, tunnel etc.
Abstract: On the basis of the stepped reduction method suggested in [1], we investigate the problem of the bending of elastic circular ring of non-homogeneous and variable cross section under the actions of arbitrary loads. The general solution of this problem is obtained so that it can be used for the calculations of strength and rigidity of practical problems such as arch, tunnel etc. In order to examine results of this paper and explain the application of this new method, an example is brought out at the end of this paper.
TL;DR: In this article, the authors discuss the extended graphical representation of the fraction of complex variables in the form of a complex variable fraction, where K is confined to be real and K is a real parameter.
Abstract: In this paper, we discuss the extended graphical representation of the fraction of a complex variables
$${{K = \sum\limits_{i = 0}^n {a_i s^{n - i} } } \mathord{\left/ {\vphantom {{K = \sum\limits_{i = 0}^n {a_i s^{n - i} } } {\sum\limits_{j = 0}^m {b_j s^{m - j} } }}} \right. \kern-
ulldelimiterspace} {\sum\limits_{j = 0}^m {b_j s^{m - j} } }}$$
WhereK is confined to be real. Three figures of the above fraction can be used in feedback systems as well as to study the properties of figures for any one coefficient of a characteristic equation as a real parameter.
TL;DR: In this article, a finite element method using linear elements in which the influence of curvature is considered and the angular displacements are treated as continuous parameters has been provided for the analysis of axisymmetrical shells with abrupt curvature change.
Abstract: It has been noted in the present paper that the finite element method using linear elements for solving axisymmetrical shells cannot be applied to the analysis of axisymmetrical shells with abrupt curvature change, owing to the fact that the influence of the curvature upon the angular displacements has been neglected. The present paper provides a finite element method using linear elements in which the influence of curvature is considered and the angular displacements are treated as continuous parameters. This method has been applied to the calculation of corrugated shells of the type C, and compared with the experimental results obtained by Turner-Ford as well as with the analytical solution given by Prof. Chien Wei-zang. The comparisons have been proved that this theory is correct.
TL;DR: In this article, it was proved that the Maxwell equation is equivalent to a fourth order equation under a certain condition, and its general solution is given by the same authors. But this condition is not satisfied in this paper.
Abstract: In this paper it is proved that Maxwell equation is equivalent to a fourth order equation. Under a certain condition, its general solution is given by
TL;DR: In this article, a new solid variational principle of discrete form is proposed, based on the true case of the discrete analysis by the finite element method and considering the variable boundaries of the elements and the unknown functions of piecewise approximation.
Abstract: This paper suggests a new solid variational principle of discrete form. Basing on the true case of the discrete analysis by the finite element method and considering the variable boundaries of the elements and the unknown functions of piecewise approximation, the unknown functions have various discontinuities at the interfaces between successive element.
TL;DR: In this article, the polynomial of a complex variable (≡x+iy) with real coefficients is graphically represented by three plane curves which are the projections of a space curve on three coordinate planes of the coordinate system (x, iy).
Abstract: In this paper, the polynomial of a complex variables(≡x+iy) with real coefficients
$$K = a_0 s^n + a_1 s^{n - 1} + \cdots \cdots + a_{n - 1} s + a_n $$
is graphically represented by three plane curves which are the projections of a space curve on three coordinate planes of the coordinate system (x, iy. K) in whichK is confined to be real. The projection on (x, iy) plane is just the root locus of the polynomial withK as a real parameter. It is remarkable that the equation of the root-locus ism-th degree iny2, whethern=2m+1 orn=2m+2. In addition to the real curveKr=f(x) in the figure (K, x) there exists another curveKc which is plotted by the real parts of all complex roots againstK. The (K, x) curve is particularly important to determine the absolute as well as the relative stable interval ofK for linear systems. For cybernetics, the (K, iy) curve can be used to show the relation between the nature frequency ω and the gainK. Such three figures are useful for studying the theory of equation and cybernetics.
TL;DR: The multi-element static and dynamic structural analysis program makes possible the analysis of main components in various computing models by solving eigen pairs by the transfer subspace iterative method with the advantages of high efficiency and precision.
Abstract: Dynamic characteristics have been studied for main components of machine tools by finite element method. The multi-element static and dynamic structural analysis program makes possible the analysis of main components in various computing models.
TL;DR: In this paper, the fracture process of small scale yielding for reinforced composites was considered and the solution of the problem by using the combined boundary-layer nonlinear finite element method was constructed.
Abstract: In this paper, we consider the fracture process of small scale yielding for reinforced composites. In the outer region of the crack tip, we use the anisotropic continuum description, while for the crack tip region we use the heterogeneous micromechanical model. Three components in heterogeneous region, namely, fibre, interface and matrix, may be considered as nonlinear. The effect of finite deformation is also considered. We construct the solution of the problem by using the combined boundary-layer nonlinear finite element method.
TL;DR: In this paper, the central deflection was used as the perturbation parameter for nonlinear circular plates by means of W. Z. Chien's method, which is an extension of the W. W. Chan's method.
Abstract: In this paper, we analyzed some problems of nonlinear circular plates by means of perturbation method. The perturbation parameters chosen here are obtained from solving the equations and are not certain mechanical quantities given precedently. This is an extension of W. Z. Chien's perturbation method, which uses the central deflection as the perturbation parameter.
TL;DR: In this article, the boundary conditions which govern the concentrated force equal to zero at the four corner points are shown to be indispensable if the problem is properly set, and it is shown that the Ritz method adopted by the author concerned in the illustrative example will not converge in the best way.
Abstract: This paper points out the former work does not fulfill the boundary conditions that the concentrated force at the four corner points should not exist. Therefore, Ritz method adopted by the author concerned in the illustrative example will not be convergent in the best way. Moreover, Garlerkin method which is illustrated in this paper may carry out incorrect results if we apply its formulae. We have proved that the boundary conditions which govern the concentrated force equal to zero at the four corner points are indispensable if the problem is properly set.
TL;DR: In this article, it was shown that the foundation of mathematical theory of finite deformation by the method of co-moving coordinate is identical to the Moire method in experimental mechanics.
Abstract: It is justified in this paper that the foundation of mathematical theory (12) of finite deformation by the method of co-moving coordinate is identical to Moire method in experimental mechanics. Hence, the important practical value of this theory is further ascertained.
TL;DR: In this article, singular perturbations of first boundary value problem for higher order elliptic equations of two parameters were discussed and the asymptotic expression for the formal solution containing two-parameter as well as the estimation of its remainder term were derived.
Abstract: In this paper we discuss singular perturbations of first boundary value problem for higher order elliptic equations of two parameter and obtain the asymptotic expression for the formal solution containing two-parameter as well as the estimation of its remainder term. These results are the extensions of (2) and (3).