Abstract
In this paper, a complex variable function method for solving the hole shape optimization problem in an elastic plane is presented. In this method, the stresses in hole problems are analysed by taking advantage of the efficiency of the complex variable function method. To optimize the hole shape, the coeffecients in conformal mapping functions are taken as design variables, and the sensitivity analysis and gradient methods are used to reduce the largest circumferential stress in absolute value and at the same time to make the second largest circumferential stress in absolute value not to exceed the largest one (in fact, these two stresses are the stationary values of the circumferential stresses). The coefficients in conformal mapping function are revised by iteration step by step until the largest circumferential stress in absolute value is reduced to the second largest stress. This method guarantees the continuity, differentiability and accuracy of the stress solution along the boundary, and it is evident that this method is better than either the difference method or the finite element method.
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References
N.E. Moshihelishivily,Some Basic Problems of Mathematic Theory of Elasticity, Publishing House URSS (1954). (in Russian)
Tang Li-min, Stress analysis for some adjecent circle holes in elastic plane,Science Record, 10 (1959). (in Chinese)
Sun Huan-chun, Stress concentration problems for a rectangular hole in an infinite long narrow strip, Science Ressarch Material of the Department of Engineering Mechanics, Dalian Institute of Technology (1965). (Unpublished), (in Chinese)
Tang Li-min and Sun Huan-chun, Three-dimensional elasticity problems solved by complex variable method,Scientia Sinica,12, 11, Nov. (1963.)
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Huan-chun, S., Ju-yong, Z., Guo-mei, Y. et al. Complex variable function method fob hole shape optimization in an elastic plane. Appl Math Mech 8, 137–146 (1987). https://doi.org/10.1007/BF02019086
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DOI: https://doi.org/10.1007/BF02019086