Singular Problems in Shell Theory

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.