Elasticity theory problem for a multiconnected anisotropic plate with holes and internal cracks

Kaloerov, S. A.

doi:10.1007/bf00883204

Soviet Applied Mechanics

1983

DOI: 10.1007/bf00883204

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Elasticity theory problem for a multiconnected anisotropic plate with holes and internal cracks

S. A. Kaloerov¹

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1998

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“…I). In this case, as is known [3,4], we have K~ = p,/f{; Kf =0, where l is the half-length of the slit. Computations were performed for a plate made of a composite with an epoxy binder reinforced by unidirectional graphite fibers [5] for which Ex = 14.9.104 MPa, Ev = 0.6-104 MPa, G~y= 0.4.104 MPa, v~= 0.31.…”

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On the problem of the legitimacy of various models of cracks for an anisotropic plate

Kaloerov¹,

Goryanskaya²

1998

J Math Sci

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539.3On the basis of numerical studies of the solution of the problem for an anisotropic plate with an arbitrary elliptic hole it is shown that a rectilinear slit can be modeled as an ellipse when the ratio of the semiaxes is less than 0.001, and as a triangle or other figure when the ratio of the sides is less than 0.001. It is shown that a slit cannot be modeled as a rectangular hole with any nonzero width. Two figures. Bibliography: 5 titles.In a previous paper [1] the authors have developed a method of determining the two-dimensional stressed state of a multiconnected anisotropic body with a finite number of elliptic cavities. In the present 0aper this method is used for numerical study of problems of the legitimacy of various models of cracks.Consider an infinite rectilinearly anisotropic multiconnected plate weakened by elliptic holes with boundaries Ll(l = ~ that may be arbitrarily located relative to one another, or may be tangent, intersect, form boundaries of curvilinear holes, or become rectilinear slits. External forces act on the boundaries of the holes, and also at infinity in the form of constant forces Crx, or, "Cx, ). There is no torque at infinity.Determining the stressed state of this plate reduces to finding the complex potentials r (j = 1, 2) from the boundary conditions [ 1 ] 2 2Re'~,(-I.t j, 1) By *~(zj)=(X,,,, Y,,) on L, (l=l-~), (I) j=l where 8 i =cosny-l.tjcosnx; cosruc dy cosny= dx Ixj are the roots of the known characteristic equation [2]; n is the exterior normal to the curve Lt, and X.l and Y.l are the components of the external forces on the curve L t . In this case the complex potentials *;(zj) defined in the regions Sj outside the ellipses Lit (/= ~ obtained from the given region by the affine transformations z2 = x + btjy have the form [ 1 ] L t=, n=, ;7[' Rjt(;~t-nil)" (2) Here I"j are known constants [1], ~jt are variables computed from the conformal mapping of the exterior of the unit disk I;" I > 1 onto the exterior of the ellipses tjl Zj -Zjl 0 = ejl(;j, Jr" mfl/;fl), and Bit and mjt are constants [1] that depend on the shape and size of the ellipses L t.By applying the method of least squares [1], from the boundary conditions on L t used to determine the unknown constants ajl p that occur in the function (2) we obtain a system of linear differential equations m=l Z Zs=I Zr=l Rsr(~2sr_msr)~sPr-I "I Rsr(~sr_msr)~s ='--g-I :

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On the problem of the legitimacy of various models of cracks for an anisotropic plate

Kaloerov¹,

Goryanskaya²

1998

J Math Sci

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Elasticity theory problem for a multiconnected anisotropic plate with holes and internal cracks

Cited by 1 publication

References 2 publications

On the problem of the legitimacy of various models of cracks for an anisotropic plate

On the problem of the legitimacy of various models of cracks for an anisotropic plate

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