Abstract
This paper considers the elastostatic plane problem of a finite strip. One end of the strip is perfectly bonded to a rigid support while the other is under the action of a uniform tensile load. Solution for the finite strip is obtained by considering an infinite strip containing a transverse rigid inclusion at the middle and two symmetrically located transverse cracks. The distance between the two cracks is equal to twice the length of the finite strip. In the limiting case when the rigid inclusion and the cracks approach the sides of the infinite strip, the region between one crack and the rigid inclusion becomes equivalent to the finite strip. Formulation of the problem is reduced to a system of three singular integral equations using the Fourier transforms. Numerical results for stresses and stress intensity factors are given in graphical form.
Similar content being viewed by others
References
Adams, G. G.; Bogy, D. B. (1975): A note on a paper by G. D. Gupta. J. Appl. Mech. 42, 224–225
Benthem, J. P. (1963): A Laplace transform method for the solution of semi-infinite and finite strip problems in stress analysis. Quart. J. Mech. Appl. Math. 16, 413–429
Bogy, D. B. (1971): Two edge-bonded elastic wedges of different materials and wedge angles under surface tractions. J. Appl. Mech. 38, 377–386
Bogy, D. B. (1975a): Solution of the plane end problem for a semi-infinite elastic strip. ZAMP 26, 749–769
Bogy, D. B. (1975b): The plane solution for joined dissimilar elastic semi-strips under tension. J. Appl. Mech. 42, 93–98
Cook, T. S.; Erdogan, F. (1972): Stresses in bonded materials with a crack perpendicular to the interface. Int. J. Eng. Sci. 10, 677–697
Erdogan, F.; Gupta, G. D. (1972): Stresses near a flat inclusion in bonded dissimilar materials. Int. J. Solid Struct. 8, 533–547
Erdogan, F. (1978): Mixed boundary value problems in mechanics. In: Nemat-Nasser, S. (ed.): Mechanics today, Vol. 4, 1–81. Oxford: Pergamon
Fadle, J. (1941): Die Selbstspannungs-eigenwertfunktionen der quadratischen Scheibe. Österr. Ing. Arch. 11, 125–149
Gaydon, F. A.; Shepherd, W. M. (1964): Generalized plane stress in a semi-infinite strip under arbitrary end-load. Proc. Roy. Soc. London, Series A 281, 184–206
Gecit, M. R. (1983): An integral equation approach for simultaneous solution of rectangular hole and rectangular block problems. Int. J. Eng. Sci. 21, 1041–1051
Gecit, M. R. (1986): Axisymmetric contact problem for a frictionless elastic layer indented by an elastic cylinder. Comp. Mech. 1, 91–104
Gecit, M. R.; Erdogan, F. (1978): The effect of adhesive layers on the fracture of laminated structures. J. Eng. Mat. Tech. 100, 2–9
Goodier, J. N. (1932): Compression of rectangular blocks, and the bending of beams by non-linear distributions of bending forces. Trans. ASME 54, 173–183
Gupta, G. D. (1973): An integral equation approach to the semi-infinite strip problem. J. Appl. Mech. 40, 948–954
Gupta, G. D. (1975): The problem of a finite strip compressed between two rough rigid stamps. J. Appl. Mech. 42, 81–87
Horvay, G. (1953): The end problem of rectangular strips. J. Appl. Mech. 20, 87–94
Horvay, G. (1957): Biharmonic eigenvalue problem of the semi-infinite strip. Quart. Appl. Math. 15, 65–81
Johnson, M. W. Jr.; Little, R. W. (1965): The semi-infinite strip. Quart. Appl. Math. 22, 335–344
Knein, M. (1927): Der Spannungszustand bei ebener Formänderung und Vorkommen verhindert Querdehnung. Abh. Aerodyn. Inst., TH Aachen 7, 43–62
Muskhelishvili, N. I. (1953): Singular integral equations. The Netherlands/Gröningen. P. Noordhoff
Papkovich, P. R. (1940): Über eine Form der Lösung des biharmonischen Problems für das Rechteck. C. R. (Doklady) Acad. Sci. USSR 27, 337
Sneddon, I. N. (1951): Fourier transforms. New York: McGraw-Hill
Theocaris, P. S. (1959): The stress distribution in a semi-infinite strip subjected to a concentrated load. J. Appl. Mech. 26, 401–406
Vorovich, I. I.; Kopasenko, V. V. (1956): Some problems in the theory of elasticity for a semi-infinite strip. Appl. Math. Mech. 30, 128–136
Williams, M. L. (1952): Stress singularities resulting from various boundary conditions in angular corners of plates in extension. J. Appl. Mech. 19, 526–528
Author information
Authors and Affiliations
Additional information
Communicated by S. N. Atluri February 24, 1987
Rights and permissions
About this article
Cite this article
Gecit, M.R., Turgut, A. Extension of a finite strip bonded to a rigid support. Computational Mechanics 3, 398–410 (1988). https://doi.org/10.1007/BF00301140
Issue Date:
DOI: https://doi.org/10.1007/BF00301140