{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T19:04:39Z","timestamp":1754161479442,"version":"3.41.2"},"reference-count":18,"publisher":"Emerald","issue":"8","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2001,12,1]]},"abstract":"<jats:p>An optimisation method for design of intermediate die shapes needed in some forging operations is presented. The basic problem consists of finding an optimal two-step forging sequence by automatically designing the shape of the preforming tools. The optimisation problem is defined based on an inverse formulation. The objective function of the optimisation problem is a function describing the quality of the obtained part by measuring the die underfill. The finite element method is used to simulate the forging problem. The optimisation method is based on a modified sequential unconstrained minimisation technique and a gradient method. The sensitivity-dependent algorithm requires computing the derivatives of the objective function with respect to the design variables defining the preform shapes. A direct differentiation method has been developed for this purpose. The optimisation scheme is demonstrated with two axisymmetric forging examples in which optimal preform dies are obtained.<\/jats:p>","DOI":"10.1108\/02644400110409168","type":"journal-article","created":{"date-parts":[[2003,1,6]],"date-time":"2003-01-06T22:18:30Z","timestamp":1041891510000},"page":"1057-1077","source":"Crossref","is-referenced-by-count":16,"title":["An efficient algorithm to estimate optimal preform die shape parameters in forging"],"prefix":"10.1108","volume":"18","author":[{"given":"Catarina F.","family":"Castro","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, University of Porto, Portugal"}]},{"given":"Lu\u00edsa","family":"Costa Sousa","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of Porto, Portugal"}]},{"given":"C.A.C.","family":"Ant\u00f3nio","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of Porto, Portugal"}]},{"given":"J.M.A.","family":"C\u00e9sar de S\u00e1","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of Porto, Portugal"}]}],"member":"140","reference":[{"key":"2025072818523069800_b1","unstructured":"Castro, C.F.\n          , Costa Sousa, L., Concei\u00e7\u00e3o Ant\u00f3nio, C.A. and C\u00e9sar de S\u00e1, J. 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