A new method is presented for shape sensitivity analysis of a crack in a homogeneous, isotropic, and linear-elastic body subject to mode-I loading conditions. The method involves the material derivative concept of continuum mechanics, domain integral representation of the J-integral, and direct differentiation. Unlike virtual crack extension techniques, no mesh perturbation is needed in the proposed method. Since the governing variational equation is differentiated prior to the process of discretization, the resulting sensitivity equations are independent of any approximate numerical techniques, such as the finite element method, boundary element method, or others. Since the J-integral is represented by domain integration, only the first-order sensitivity of displacement field is needed. Two numerical examples are presented to illustrate the proposed method. The results show that the maximum difference in calculating the sensitivity of J-integral by the proposed method and reference solutions by analytical or finite-difference methods is less than three percent.
Shape Sensitivity Analysis of Linear-Elastic Cracked Structures Under Mode-I Loading
Contributed by the Pressure Vessels and Piping Division and presented at the Pressure Vessels and Piping Conference, Seattle, Washington, July 23–27, 2000, of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS. Manuscript received by the PVP Division, May 14, 2001; revised manuscript received April 15, 2002. Associate Editor: K. K. Yoon.
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Chen , G., Rahman, S., and Park, Y. H. (November 8, 2002). "Shape Sensitivity Analysis of Linear-Elastic Cracked Structures Under Mode-I Loading ." ASME. J. Pressure Vessel Technol. November 2002; 124(4): 476–482. https://doi.org/10.1115/1.1486017
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