NEW BOUNDARY ELEMENT METHOD FOR TORSION PROBLEMS OF CYLINDER WITH CURVILINEAR CRACKS

The Saint-Venant torsion problems of a cylinder with curvilinear cracks were considered and reduced to solving the boundary integral equations only on cracks. Using the interpolation models for both singular crack tip elements and other crack linear elements, the boundary element formulas of the torsion rigidity and stress intensity factors were given. Some typical torsion problems of a cylinder involving a straight, kinked or curvilinear crack were calculated. The obtained results for the case of straight crack agree well with those given by using the Gauss-Chebyshev integration formulas, which demonstrates the validity and applicability of the present boundary element method.     

A GROUP OF ISOPARAMETRIC ELEMENTS SUITABLE FOR ST．VENANT’S TORSION OF A BAR WITH CRACKS

ＡＧＲＯＵＰＯＦＩＳＯＰＡＲＡＭＥＴＲＩＣＥＬＥＭＥＮＴＳＳＵＩＴＡＢＬＥＦＯＲＳＴ．ＶＥＮＡＮＴ’ＳＴＯＲＳＩＯＮＯＦＡＢＡＲＷＩＴＨＣＲＡＣＫＳＦａｎＸｉｕｃｈａｎｇ（范秀昌）ＷｕＹｕｅｍｉｎｇ（吴月明）（ＴｉａｎｊｉｎＩｎｓｔｉｔｕｔｅｏｆＴｅ...     

SAINT-VENANT’S TORSION PROBLEM FOR A COMPOSITE CIRCULAR CYLINDER WITH ANINTERNAL EDGE CRACK

In this paper the writer uses Muskhelishvili single-layer potential function solutionand single crack solution for the torsion problem of a circular cylinder to discuss thetorsion problem of a composite cylinder with an internal crack,and the problem isreduced to a set of mixed-type integral equation with generalized Cauchy-kernel.Then,by using the integration formula of Gauss-Jacobi.the numerical method isestablished and several numerical examples are calculated.The torsional rigidity andthe stress intensity factors are obtained.The results of these examples fit the resultsobtained by the previous papers better.     

ON THE FINITE DISPLACEMENT PROBLEM OF A HOLLOW CYLINDER UNDER INTERNAL AND EXTERNAL PRESSURES

Using the method of successive approximations we find of this boundary-value problem the first-and second-order solutions. And then we obtain the formulae in the second approximation for the displacement, strain, and stress fields. Also, our results show that after deformation (ⅰ) a cross-section of the cylinder must be displaced into a plane section perpendicular to the central axis of the cylinder; and (ⅱ) neither the sum of the strain components E_(RR)~(2) and E_(φφ)~(2) nor the sum of the stress components ∑_(RR)~(2) and ∑_(φφ)~(2) maintains contant throughout the Cylinder. The latter effect, which is absent from classical elasticity, bears respensibility for the presence of the ∑_(ZZ)~(2). Moreover, there exhibits a linear relation between ∑_(ZZ)~(2) and (∑_(RR)~(2)+∑_(φφ)~(2)). with the proportionality coefficients depending only on the material of the cylinder.     

A SOLUTION OF COSINE PRESSURES ON A HOLLOW CYLINDER AND THE LIMIT WHEN k→0

A new stress function is found in this paper and then the problems of cosine pressures on a hollow cylinder are solved with the new stress function,which provides the basis for the solution of the problems of space symmetrical deformation of a hollow cylinder.When the pressures do not vary in the axial direction,that is,when k→0,the lame formulae can be deduced.     

A SOLUTION OF COSINE PRESSURES ON A HOLLOW CYLINDER AND THE LIMIT WHEN k→0

A new stress function is found in this paper and then the problems of cosine pressures on a hollow cylinder are solved with the new stress function, which provides the basis for the solution of the problems of space symmetrical deformation of a hollow cylinder. When the pressures do not vary in the axial direction, that is, when k→0 the lame formulae can be deduced.     

ON THE JUMPING PROBLEMS OF A CIRCULAR THIN PLATE WITH INITIAL DEFLECTION

In this paper,the jumping problems of a circular thin plate with initial defletion arestudied by using the method of two variables proposed by Jiang Fu-ru and the methodof the normal perturbation(in this paper (1.1), (1.2)).We obtain Nth-order uniformly validasymptotic expansion of the solution of this problem ((1.66), (1.67)).When the initialdeflection vanishes the solution of a circular thinplate with initial deflection is reduced tothe solution of the problems of the nonlinear bending of a circular thin plate.If the initialdeflection is largish and the signs of the initial deflection with the intensity of the transverseload are opposite,when the intensity of the transverse load reaches a certain value,thecircular thin plate with initial deflection should produce the jumping phenomenon.     

ON THE NEW FORMS OF THE DIFFERENTIAL EQUATIONS OF THE SYSTEMS WITH HIGHER-ORDER NONHOLONOMIC CONSTRAINTS

In this paper,the new forms of the differential equations of motion of the systems withhigher-order nonholonomic constraints are obtained at first,and then the equivalencebetween these equations and the known equations is demonstrated.Finally an example isgiven to illustrate the application of our new equations.     

INTERACTION OF ELECTRIC CHARGES IN A PIEZOELECTRIC WITH RIGID EXTERNAL CRACKS

IntroductionRecently much attention has been paid to Green’s functions[1 -7]for anisotropic mediabecause of their important applications in boundary element methods used widely inengineering analysis. Generally speaking, it is relatively easy to obtain G…     

THE STUDY ON A KIND OF CONTROL SYSTEM WITH NONLINEAR PARABOLIC DISTRIBUTED PARAMETERS

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｅａｃｔｉｖｉｔｉｅｓｓｕｃｈａｓｔｈｅａｅｒｏｓｐａｃｅｅｎｇｉｎｅｅｒｉｎｇｈｅａｔｐｒｏｔｅｃｔｉｏｎ[1,2 ],ｔｈｅｌａｒｇｅ＿ｓｃａｌｅｃｏｎｃｒｅｔｅｐｏｕｒｉｎｇ ,ｔｈｅｃｈｅｍｉｃａｌｐｒｏｄｕｃｔｉｏｎ ,ｔｈｅｐｏｗｄｅｒｍｅｔａｌｌｕｒｇｙａｎｄｔｈｅｆｉｒｅｓａｆｅｔｙｅｎｇｉｎｅｅｒｉｎｇ[3,4],ｔｈｅｒｅｉｓｏｎｅｋｉｎｄｏｆｎｏｎｌｉｎｅａｒｐａｒａｂｏｌｉｃｄｉｓｔｒｉｂｕｔｅｄｐａｒａｍｅｔｅｒｃｏｎｔｒｏｌｓｙｓｔｅｍｗｉｔｈｍｏｖｉ…