The methods of complex potentials, singular integral equations and integral transformations in a series of problems for the reinforcement of cracked plates

• Published in: Acta mechanica Vol. 221; no. 1-2; pp. 147 - 174
• Main Authors: Bardzokas, Dimosthenis I., Mkhitaryan, S. M., Sfyris, Georgios I.
• Format: Journal Article
• Language: English
• Published: Vienna Springer Vienna 01-09-2011; Springer; Springer Nature B.V
• Subjects: Boundaries; Classical and Continuum Physics; Contact stresses; Control; Crack initiation; Crack propagation; Cracks; Dynamical Systems; Engineering; Engineering Thermodynamics; Exact sciences and technology; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); Heat and Mass Transfer; Mathematical analysis; Mechanical engineering; Physics; Plates; Shear stress; Singular integral equations; Solid Mechanics; Stringers; Structural and continuum mechanics; Tensile strength; Theoretical and Applied Mechanics; Vibration; Contact Problem; Vertical Crack; Singular Integral Equation; Complex Potential; Logarithmic Singularity; Singularity; Cracked plate; Logarithmic function; Complex potential; Singular equation; Brittle fracture; Modeling; Reinforced structure; Reinforced plate; Exact solution; Infinite medium; Complex method; Transverse crack; Contact stress; Integral equation; Crack tip; Potential method; Integral transformation
• DOI: 10.1007/s00707-011-0473-3
• EISSN: 1619-6937
• ISSN: 0001-5970

We study the initiation and propagation of a vertical crack in an elastic semi-infinite plate, reinforced on its boundary by an infinite discontinuous stringer within the limits of the theory of brittle failure. The plate is subjected to uniform distributed tensile forces at infinity, as well as to contact stresses due to application of forces to the stringer. We find the appropriate loading of the coherent stringer, and consequently we consider a problem where the stringer is cracked and a vertical crack has developed within the plate. We deduce the exact analytical solution for the principal singular integral equation for this case; hence the stringer is perfectly rigid and we calculate characteristic parameters of the problem. The results show that the crack tip has a logarithmic singularity, and the tangential contact stresses under the stringer at that end point are finite and generally differ from zero.