PROBABILISTIC MODELS FOR LONG FATIGUE CRACK GROWTH RATES OF LZ50 AXLE STEEL

IntroductionStudy on the model of fatigue crack growth rate (da/dN) and measurement of theprobabilistic curves of the model are a basis of the fatigue damage tolerate design and theprobabilistic safety assessment. Some benefit efforts have been made in th…     

Positive solutions to （n-1,1） m-point boundary value problems with dependence on the first order derivative

Using the extension of Krasnoselskii＇s fixed point theorem in a cone, we prove the existence of at least one positive solution to the nonlinear nth order m-point boundary value problem with dependence on the first order derivative. The associated Green＇s function for the nth order m-point boundary value problem is given, and growth conditions are imposed on the nonlinear term f which ensures the existence of at least one positive solution. A simple example is presented to illustrate applications of the obtained results.     

Mikusinski’s operators solution of three-order linear difference equation with variable coefficients

This paper proceeds the papers [3] [4], we make use of the idea of the variable number operators and some concepts and conclusions of the shifting operators series with variable coefficients in the operational field of Mikusinski, it is devoted to the solution of the general three-order linear difference equation with variable coefficients, and it is also devoted to the better solution formula for the some special three-order linear difference equations with variable coefficients: in addition, we try to provide the idea and method for realizing solution of the more than three-order linear difference equation with variable coefficients. Project Supported by the Science Foundation of Anhui Province     

Constitutive modelling of nonproportional cyclic plasticity

A multiplicative hardening function and a unified evolution rule of the hardening factors are proposed. The hardening factorf ₁ is introduced to describe cyclic hardening with respect to the plastic strain range, whilef ₂ andf ₃ describe, respectively, instantaneous and hereditary additional hardening with respect to the nonproportionality of the plastic strain path. Two material dependent memory parametersa ₁ anda ₃ are introduced to keep the memory of the largest cyclic and additional hardening in the previous plastic deformation history. Different hardening mechanisms are then embedded into a thermomechanically consistent constitutive equation through the hardening function. The constitutive response of 304 and 316 stainless steels subjected to biaxial nonproportional cyclic loading is analyzed and the proposed model is critically verified by comparing the results with experimental results obtained by Tanaka et al., and Ohashi et al. The project supported by National Natural Science Foundation of China     

A series boundary integration method for the bending analysis of anisotropic plates

A series boundary integration method is given which exactly satisfies the fundamental equation of bending analysis of general anisotropic plates or laminated plates in Kirchhoffs sense. With a unified deflection series, the method may be applied to the plates having different planforms and support conditions. Several groups of representative examples are calculated. The examples include circular, square and triangular plates, and their boundaries include clamped edges, simply supported edges, free edges and free corner. Numerical results indicate rapid convergency for both deflection and stress resultants and demonstrate wide applicability of the method.This subject was supported by the Natural Science Foundation of Guangdong Province.     

The interaction between crack and electric dipole of piezoelectricity

Discrete dipoles located near the crack tip play an important role in nonlinear electric field induced fracture of piezoelectric ceramics. A physico-mathematical model of dipole is constructed of two generalized concentrated piezoelectric forces with equal density and opposite sign. The interaction between crack and electric dipole in piezoelectricity is analyzed. The closed form solutions, including those for stress and electric displacement, crack opening displacement and electric potential, are obtained. The function of piezoelectric anisotropic direction,p _a (θ)=cosθ+p _a sinθ, can be used to express the influence of a dipole's direction. In the case that a dipole locates near crack tip, the piezoelectric stress intensity factor is a power function with −3/2 index of the distance between dipole and crack tip. Supported by National Natural Science Foundation of China(No. 10072033)     

A triangular quasi-conforming finite element for transient dynamic analysis

A type of 3 node triangular element is constructed by the Quasi-conforming method, which may be used to solve the equation of a type of inverse problem of wave propagation after Laplace transformation Δu−A ² u=0. The strains in the element are approximated by an exponential function and the string-net function between neighbouring elements is approximated by one dimensional general solution of the equation. Furthermore the strain field satisfies the equation, and therefore in the derivation of the element formulation, no shape function is needed. In this sense, it is a kind of hybrid element. Compared with the ordinary linear triangular element, the new one features higher precision with coarse meshes. Some numerical tests are presented. The project is supported by the National Natural Science Foundation of China.     

Percolation Approach to the Anisotropy Factor in an Unsaturated Porous Medium

The anisotropy factor is defined as the ratio of the effective (macroscopic) conductivities parallel to the bedding plane and perpendicular to it. The anisotropy factor A(p,a) is a function of both the saturation degree, p, in the void space of the disordered medium and the anisotropy parameter, a, that characterizes the ratio of the local conductivities parallel and normal to the bedding plane. There are two opposite behaviors of the anisotropy factor as a function of the saturation degree described in literature. One presents the anisotropy factor as a curve with a maximum and the other as a curve with a minimum. The main result of calculating the conductivities of a uniaxial percolation anisotropic model is that at the saturation threshold value, p_c, A(p_c, a) = 1, wherefrom it increases at a >1 (or decreases at a < 1) with saturation. An extension of the computed results below the threshold is also proposed.     

The 3-D stress intensity factor for a half plane crack in a transversely isotropic solid due to the motion of loads on the crack faces

Three-dimensional analysis of a half plane crack in a transversely isotropic solid is performed. The crack is subjected to a pair of normal point loads moving in a direction perpendicular to the crack edge on its faces. Transform methods are used to reduce the boundary value problem to a single integral equation that can be solved by the Wiener-Hopf technique. The Cagniard-de Hoop method is employed to invert the transforms. An exact expression is derived for the mode I stress intensity factor as a function of time and position along the crack edge. Some features of the solution are discussed through numerical results. The project supported by the Guangdong Provincial Natural Science Foundation and the Science Foundation of Shantou University     

A survey of exact solutions of inviscid field equations in the theory of shear flow instabilty

This paper presents a survey of undisturbed flows that take one or another of the field equations of inviscid shear flow instability theory (e.g. theRayleigh equation,Taylor-Goldstein-Haurwitz equation or theKuo equation) to a differential equation satisfied by aknown transcendental function forarbitrary complex values of the parameters. Some mean velocity profiles having this feature are well known. Thus, piecewise linear mean velocity profiles take theRayleigh equations to a constant-coefficient differential equation and the exponential mean velocity profile takes theRayleigh equation to theGauss hypergeometric equation. Less well known is the fact that a variety of mean velocity profiles take theRayleigh equation to a differential equation due toKarl Heun. These profiles include: (i) the sinusoidal profile; (ii) the hyperbolic tangent profile (an example pointed out byMiles (1963)); (iii) the profile in the form of the square of a hyperbolic secant (theBickley jet); and, (iv) a skewed velocity profile in which each component has the form of a quadratic function of the variable exp(–z/l) (in whichz is the cross-stream coordinate andl is a length scale). In all of these cases, one or another author has previously identified aregular neutral mode solution of theRayleigh equation and has expressed that solution in the form of elementary functions. Such regular neutral modes apparently represent cases in which the solution ofHeun's equation (which is normally an infinite series) truncates to a single term. The survey concludes by noting that the parabolic mean velocity profile takes theRayleigh equation to thedifferential equation of the spheroidal wave function.Dedicated to Mårten T. Landahl on the occasion of his sixty-fifth birthday by a former apprentice as a token of his respect and gratitude.     

Some problems in the Z-C-X space

The new concepts of the Z-C-X space and excellent cone are introduced. Some problems of random semiclosed 1-set-contractive operator are investigated in the Z-C-X space. At first, an important inequality is proved. Secondly, several new conclusions are proved by means of random fixed point index in the theory of random topological degree. A random solution of a class of random operator equations under conditions of imitating the parallelogram law is obtained, famous Altman’s theorem is generalized in partially ordered Z-C-X space. Therefore, some new results are obtained.     

Applying the generalized step-function to solve the bending problems of nonuniform beams with variable cross section

The bending problems of nonuniform beams with variable cross-section can be approximated by that of a step beam under sectionally uniform load (including both concentrated forces and couples). In this paper, the concept of Heaviside function {x-a}⁰ will be generalized, and a new function {x-a}⁰, n=0,1,2…,will be defined, which may be named as a generalized step function. The rules of operation will also be given to {x-a}ⁿ{x-b}⁰. The reciprocal of the flexural of rigidity 1/EJ and the bending moment M(x) can all be expressed in terms of {x-a}ⁿ,and substituted into the differential equation of the elastic curve of the beam respectively. Thus we may establish a set of unified method to solve various types of bending problems of straight beams. The general solution of the deflection equation will be given.     

The high accuracy explicit difference scheme for solving parabolic equations 3-dimension

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PREDICTION OF MODE Ⅰ CRACK PROPAGATION DIRECTION IN CARBON-FIBER REINFORCED COMPOSITE PLATE

A newly developed Z fracture criterion for the composite materials was introduced, the new concepts of in-plane average strain, in-plane dilatational strain energy density factor and reciprocal characteristic function were presented. Many experimental results show that the Z fracture criterion can be well used to predict the crack propagating direction for mode f crack in carbon-fiber reinforced composite laminates.     

Higher approximations to the homogeneous solutions for toroid

To analyze the strength of the elastic, isotropic toroid with axisymmetrical loads, it is necessary to find the solutions for a nonhomogeneous second-order ordinary-differential equation in complex form. When the parameter = 12(1-v²) a² / (r ₀ h), which occurs in the equation, is large, the asymptotic approach is often used. Up to now, only the first approximations to its homogeneous solutions are found. In this paper the author has obtained higher approximations to the homogeneous solutions, thus, reaching the precision of linear thin shell theory.This work was supported by the National Natural Science Foundation of China.     

TheC k instability of navier-Stokes equation appending polynomials of unknown functions

Applying the theory of stratification, the solution space structure about a class of deformed Navier-Stokes equation isdetermined. It is proved that such kind of equation has no C^k (k≥2) stable solution by the fact that the strate transversale is a null set. Foundation item: the National Natural Science Foundation of China (19971054), Shanghai Natural Science Foundation (99ZA14034) Biography: HE You-hua (1960-)     

Application of differential-integral equation to elliptical crack problem under shear load

Stress intensity factors for an elliptical crack under shear loading are investigated. The differential-integral equation is applied to solve the problem. It is found that, if the integrated function takes the form of (1 − (x/a)² − (y/b)²)^1/2 x^m yⁿ, a and b being the major and minor axis of the ellipse, the relevant differential-integral equation can be evaluated. Using this property, the boundary value problems are solved for the shear loading in the form of power function. Finally, results are presented for twelve particular example problems.     

A form function method for form finding of tension structure

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System of set-valued mixed quasi-variational-like inclusionsinvolving H-η-monotone operators in Banach spaces

A new system of the set-valued mixed quasi-variational-like inclusions （SSMQVLI） involving H-η-monotone operators is studied in general Banach spaces without uniform smoothness. By using the resolvent operator technique of H-η-monotone operators, a new iterative algorithm for finding approximate solutions to SSMQVLI is proposed. It is shown that the iterative sequences generated by the algorithm converge strongly to the exact solution of SSMQVLI under appropriate assumptions. These obtained new results have extended and improved previous results.