Singular Problems in Shell Theory by Evariste Sanchez-Palencia, Paperback | Indigo Chapters

Thin shells are three-dimensional structures with a dimension (the thickness) small with respect to the two others. Such thin structures are widely used in automobileandaviation industries, or in civil engineering, because they provide animportantsti?ness, due to theircurvature, with a small weight. Fig. 0.1. Airbus A380 Fig. 0.2. Hemispherical roof (Marseille, France) One ofthechallenges is often to reduce the weight (andconsequently the thickness)oftheshells, preservingtheirsti?ness. So that it is essential to have 1 accuratemodelsforthinandevenverythinshells ,andtobeabletocomputethe displacements resultingfromagivenloading. In particular, singularities leading to fractures in some cases must be absolutely predicted a priori and ofcourse avoided (see Fig.0.3 forexample). Since the pioneeringmodels of Novozhilov-Donnell [81] and Koiter [65][66], numerous works havebeen devoted to establish linear and non linear elastic shell model usingdirect orsurfacic approaches [18][25][100]. More recently, the asymptoticmethods [87] havebeen used, to try tojustify rigorously, fromthe three-dimensional equations, the shell models obtained by direct approaches - lying onapriori assumption, andto construct new models [54][55]. This way, 1 Very thin shells are present in certain domains of industry, as plastic ?lms for pa- aging or for electronics, streched sails, or even very thin metal sheets obtained by drawing. E. Sanchez-Palencia et al.: Singular Problems in Shell Theory, LNACM 54, pp. 1-11. | Singular Problems in Shell Theory by Evariste Sanchez-Palencia, Paperback | Indigo Chapters