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Some links are pointed out to the bubble method in topology optimization: when a small hole is introduced in a given shape, the difference between the perturbed solution and the unperturbed one satisfies the hypotheses of Saint\u2010Venant's principle. An important tool is the Poincar\u00e9\u2010Wirtinger inequality for functions defined on a sphere; results from spectral geometry are used to determine the constant therein.<\/jats:p>","DOI":"10.1002\/zamm.200710357","type":"journal-article","created":{"date-parts":[[2007,11,26]],"date-time":"2007-11-26T10:46:20Z","timestamp":1196073980000},"page":"23-32","source":"Crossref","is-referenced-by-count":4,"title":["Saint\u2010Venant's principle and its connections to shape and topology optimization"],"prefix":"10.1002","volume":"88","author":[{"given":"C.","family":"Barbarosie","sequence":"first","affiliation":[]},{"given":"A.\u2010M.","family":"Toader","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2007,12,20]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"S.Agmon Lectures on Elliptic Boundary Value Problems (Van Nostrand Mathematical Studies 2 1965)."},{"key":"e_1_2_1_3_2","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/s002110050253","volume":"76","author":"Allaire G.","year":"1997","journal-title":"Numer. 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