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Abstract Under the assumption of pure slip contact along the lining-rock interface and the requirements of the net size and the lining thickness，derivation of shape optimization of a tunnel support was carried out with the objective of the greatest tangential stress along the inner edge of the support being minimized. The optimizing process is to solve a class of inverse geometry problems，and the corresponding forward problem can be solved with the method of conformal mapping of complex variable function in plane elasticity. During the process，the tangential stress along the inner edge of the support was selected as the objective function and coefficients of the mapping function were taken as the design variables. The method of mixed penalty function was used to minimize the objective function. As the objective function reached the minimum value，the optimal shape of support can be obtained. With the optimal shape，stress state in tunnel support was improved most effectively and the tangential stress concentration along the inner edge of support was minimized.
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Received: 09 January 2014
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2014, Vol. 33 
