{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T18:07:36Z","timestamp":1754158056617,"version":"3.41.2"},"reference-count":10,"publisher":"Emerald","issue":"5","license":[{"start":{"date-parts":[[1998,8,1]],"date-time":"1998-08-01T00:00:00Z","timestamp":901929600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1998,8,1]]},"abstract":"<jats:p>This paper presents an algorithm for automatic generation of graded initial quadrilateral meshes targeted for the finite element analysis of metal\u2010forming processes. Meshing the domain geometry deals with a universe of shapes, and the procedure therefore takes into account the initial geometry of the billet. A grid\u2010based approach is utilised for generating an initial coarse mesh with well\u2010shaped (internal) elements, and in cases where non\u2010rectangular shapes are to be discretized, linking with the boundary is performed on the basis of constrained Delaunay triangulation. By analysing the contact situation between dies and mesh, an attempt is made to identify regions where plastic deformation is likely to be concentrated during the early stages of processing, and accordingly refinement of the mesh is performed locally by elemental subdivision. Simulation examples for closed\u2010die forging, forward rod and backward can extrusion substantiate the feasibility of this approach in terms of lowering the overall calculation error and limiting the interference between mesh and die.<\/jats:p>","DOI":"10.1108\/02644409810225742","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T02:07:04Z","timestamp":1027735624000},"page":"577-587","source":"Crossref","is-referenced-by-count":7,"title":["A metal\u2010forming approach to automatic generation of graded initial quadrilateral finite element meshes"],"prefix":"10.1108","volume":"15","author":[{"given":"S.B.","family":"Petersen","sequence":"first","affiliation":[]},{"given":"B.P.P.A.","family":"Gouveia","sequence":"additional","affiliation":[]},{"given":"J.M.C.","family":"Rodrigues","sequence":"additional","affiliation":[]},{"given":"P.A.F.","family":"Martins","sequence":"additional","affiliation":[]}],"member":"140","reference":[{"key":"key2022020219580145800_b1","doi-asserted-by":"crossref","unstructured":"1.Mackerle, J., \u201cReview of general purpose pre\u2010 and postprocessor programs for the finite element applications\u201d, Adv. Eng. Software, Vol. 5, 1983, pp. 148\u201059.","DOI":"10.1016\/0141-1195(83)90110-9"},{"key":"key2022020219580145800_b2","doi-asserted-by":"crossref","unstructured":"2.Ho\u2010Le, K., \u201cFinite element mesh generation methods: a review and classification\u201d, Computer\u2010Aided Design, Vol. 20, 1988, pp. 27\u201038.","DOI":"10.1016\/0010-4485(88)90138-8"},{"key":"key2022020219580145800_b3","doi-asserted-by":"crossref","unstructured":"3.Zienkiewicz, O.C., Liu, Y.C. and Huang, G.C., \u201cError estimation and adaptivity in flow formulation for forming problems\u201d, Int. J. Numer. Methods Eng., Vol. 25, 1988, pp. 23\u201042.","DOI":"10.1002\/nme.1620250105"},{"key":"key2022020219580145800_b4","unstructured":"4.Wu, W.T., Oh, S.I., Altan, T. and Miller, R.A., \u201cAutomated mesh generation for forming simulation\u201d, Part I, Proc. Computers in Engineering, Vol. 1, ASME, New York, NY, 1990, p. 507."},{"key":"key2022020219580145800_b5","doi-asserted-by":"crossref","unstructured":"5.Petersen, S.B. and Martins, P.A.F., \u201cFinite element remeshing: a metal forming approach for quadrilateral mesh generation and refinement\u201d, Int. J. Numer. Methods Eng., 1996.","DOI":"10.1002\/(SICI)1097-0207(19970430)40:8<1449::AID-NME121>3.0.CO;2-Z"},{"key":"key2022020219580145800_b6","doi-asserted-by":"crossref","unstructured":"6.Zienkiewicz, O.C. and Zhu, J.Z., \u201cA simple error estimate for adaptive procedure for practical engineering analysis\u201d, Int. J. Numer. Methods Eng., Vol. 24, 1987, pp. 337\u201057.","DOI":"10.1002\/nme.1620240206"},{"key":"key2022020219580145800_b7","doi-asserted-by":"crossref","unstructured":"7.Sloan, S.W., \u201cA fast algorithm for generating constrained Delaunay triangulations\u201d, Comp. Struc., Vol. 47, 1993, pp. 441\u201050.","DOI":"10.1016\/0045-7949(93)90239-A"},{"key":"key2022020219580145800_b8","doi-asserted-by":"crossref","unstructured":"8.Kobayashi, S., Oh, S.I. and Altan, T., Metal Forming and the Finite Element Method, Oxford University Press, Oxford, 1989.","DOI":"10.1093\/oso\/9780195044027.003.0014"},{"key":"key2022020219580145800_b9","doi-asserted-by":"crossref","unstructured":"9.Herrmann, L.R., \u201cLaplacian\u2010isoparametric grid generation scheme\u201d, J. Engng. Mechanics Div., ASCE, Vol. 102, 1976, pp. 749\u201056.","DOI":"10.1061\/JMCEA3.0002158"},{"key":"key2022020219580145800_b10","doi-asserted-by":"crossref","unstructured":"10.Rodrigues, J.M.C., Martins, P.A.F. and Barata Marques, M.J.M., \u201cThe PLAST3 system and its application to the simulation of an open die forging operation\u201d, J. Mat. Proc. Tech., Vol. 47, 1994, pp. 111\u201025.","DOI":"10.1016\/0924-0136(94)90089-2"}],"container-title":["Engineering Computations"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.emeraldinsight.com\/doi\/full-xml\/10.1108\/02644409810225742","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/02644409810225742\/full\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/02644409810225742\/full\/html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,25]],"date-time":"2025-07-25T00:36:00Z","timestamp":1753403760000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.emerald.com\/ec\/article\/15\/5\/577-587\/106779"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,8,1]]},"references-count":10,"journal-issue":{"issue":"5","published-print":{"date-parts":[[1998,8,1]]}},"alternative-id":["10.1108\/02644409810225742"],"URL":"https:\/\/doi.org\/10.1108\/02644409810225742","relation":{},"ISSN":["0264-4401"],"issn-type":[{"type":"print","value":"0264-4401"}],"subject":[],"published":{"date-parts":[[1998,8,1]]}}}