A piecewise-homogeneous elastic orthotropic plate, reinforced with a finite patch of the wedge-shaped, which meets the interface at a right angle and is loaded with tangential and normal forces is considered. Using methods of the theory of analytic functions, the problem is reduced to the system of singular integro-differential equations (SIDE) with fixed singularity. Under tension-compression of patch using an integral transformation a Riemann problem is obtained, the solution of which is presented in explicit form. The tangential contact stresses along the contact line are determined and their asymptotic behavior in the neighborhood of singular points is established.
AleksandrovVMMkhitaryanSM.Contact problems for bodies with thin coverings and layers. Moscow: Nauka, 1983 (in Russian).
2.
AntipovYArutyunyanN.A contact problem for an elastic layer with cover plates in the presence of friction and adhesion. J Appl Math Mech1993; 57(1): 159–170.
3.
AntipovYMoiseevN.Exact solution of the two-dimensional problem for a composite plane with a cut that crosses the interface line. J Appl Math Mech1991; 55(4): 531–539.
4.
BantsuriRDShavlakadzeNN.A contact problem for an anisotropic wedge-shaped plate with elastic bracing of variable rigidity. J Appl Math Mech2002; 66(4): 645–650.
5.
BantsuriRD.Contact problem for an anisotropic wedge with elastic mounting. Dokl Akad Nauk SSSR1975; 222: 568–571.
6.
CaoDMalakootiSKulkarniV, et al. The effect of resin uptake on the flexural properties of compression molded sandwich composites. Wind Energy2022; 25: 71–93.
7.
CaoDMalakootiSKulkarniV, et al. Nanoindentation measurement of core–skin interphase viscoelastic properties in a sandwich glass composite. Mech Time Depend Mater2021; 25: 353–363.
8.
NullerBM.On the deformation of an elastic wedge plate reinforced by a variable stiffness bar and a method of solving mixed problems. J Appl Math Mech1976; 40(2): 280–291.
9.
PopovG.Concentration of elastic stresses near punches, cuts, thin inclusion and supports. Moscow: Nauka, 1983 (in Russian).
10.
ShavlakadzeNN.The contact problems of the mathematical theory of elasticity for plates with an elastic inclusion. Acta Appl Math2007; 99(1): 29–51.
11.
TingTCT.Uniform stress inside an anisotropic elliptic inclusion with imperfect interface bonding. J Elasticity2009; 96(1): 43–55.
12.
TsuchidaEMuraTDundursJ.The elastic field of an elliptic inclusion with a slipping interface. J Appl Mech1986; 53(1): 103–107.
13.
WangXXuTAndradeM, et al. The interfacial shear strength of carbon nanotube sheet modified carbon fiber composites. In:SilbersteinMAmirkhiziA (eds) Challenges in mechanics of time dependent materials, volume 2: conference proceedings of the society for experimental mechanics series. Cham: Springer, 2021, pp. 25–32.
14.
KhrapkovAA.First fundamental problem for a piecewise-homogeneous plane with a slit perpendicular to the line of separation. J Appl Math Mech1968; 32(4): 666–678.
15.
BantsuriRD.The first fundamental problem for a piecewise homogeneous orthotropic plane with a cut perpendicular to the line of interface. Soobshch Akad Nauk Gruzin SSR1978; 91(3): 569–572.
16.
UngiadzeAV.The first fundamental problem for a piecewise homogeneous plane that contains a semi-infinite crack crossing the boundary at right angles. Trudy Tbiliss Mat Inst Razmadze Akad Nauk Gruzin SSR1986; 81: 79–86.
17.
BantsuriRDShavlakadzeNN.The contact problem for a piecewise-homogeneous plane with a finite inclusion. J Appl Math Mech2011; 75(1): 93–97.
18.
ShavlakadzeNNOdishelidzeNCriado-AldeanuevaF.The contact problem for a piecewise-homogeneous orthotropic plate with a finite inclusion of variable cross-section. Math Mech Solids2017; 22(6): 1326–1333.
19.
ShavlakadzeNNOdishelidzeNCriado-AldeanuevaF.The investigation of singular integro-differential equations relating to adhesive contact problems of the theory of viscoelasticity. Z Angew Math Phys2021; 72(2): 42.
20.
LubkinJLLewisLC.Adhesive shear flow for an axially-loaded, finite stringer bonded to an infinite sheet. Quart J Mech Appl Math1970; 23(4): 521–533.
MuskhelishviliNI.Singular integral equations: boundary problems of function theory and their application to mathematical physics. Chelmsford, MA: Courier Corporation, 2013.
23.
GahovFDČerskǐJI.Equations of convolution type. Moscow: Nauka, 1978.
