Integral Equation Methods and Numerical Solutions of Crack and Inclusion Problems in Planar Elastostatics

We present algorithms for crack and inclusion problems in planar linear elastostatics. The algorithms are based on new integral equations. For the pure crack problem the integral equations are of Fredholm's second kind. Our algorithms show great stability and allow for solutions to problems more complex than have previously been possible. Our results are orders of magnitudes more accurate than those of previous investigators, which rely on integral equations of Fredholm's first kind.

[1]  F. Smithies,et al.  Singular Integral Equations , 1955, The Mathematical Gazette.

[2]  J. Dundurs,et al.  Discussion of Edge-Bonded Dissimilar Orthogonal Elastic Wedges under Normal and Shear Loading , 1969 .

[3]  N. Muskhelishvili.  Some basic problems of the mathematical theory of elasticity , 1953 .

[4]  John Milnor,et al.  On total curvatures of closed space curves , 1953 .

[5]  F. Erdogan,et al.  On the numerical solution of singular integral equations , 1972 .

[6]  L. Greengard,et al.  On the numerical evaluation of elastostatic fields in locally isotropic two-dimensional composites , 1998 .

[7]  Peter Gudmundson,et al.  An integral equation method for piece-wise smooth cracks in an elastic half-plane , 1989 .

[8]  V. Z. Parton,et al.  Mathematical methods of the theory of elasticity , 1985 .

[9]  V. Hutson.  Integral Equations , 1967, Nature.

[10]  Norio Hasebe,et al.  Fredholm integral equation for the multiple circular arc crack problem in plane elasticity , 1997 .

[11]  M. A. JASWON,et al.  Integral Equation Methods in Elasticity , 1963, Nature.

[12]  Kevin K. Lo,et al.  Analysis of Branched Cracks , 1978 .

[13]  G. Golub,et al.  Gmres: a Generalized Minimum Residual Algorithm for Solving , 2022 .

[14]  D. Roylance.  INTRODUCTION TO COMPOSITE MATERIALS , 2000 .

[15]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[16]  K. X. Hu,et al.  Stiffness Evaluation for Solids Containing Dilute Distributions of Inclusions and Microcracks , 1995 .

[17]  S. Tsai,et al.  Introduction to composite materials , 1980 .

[18]  Johan Helsing,et al.  Thin Bridges in Isotropic Electrostatics , 1996 .