The implicit function theorem is applied to the general three-dimensional equations for the equilibrium of a rectangular nonlinearly elastic plate subjected to suitable applied forces. The plate is assumed to have periodic boundary conditions or else to be with sliding edges. Regularity results in Sobolev spaces are used to define the equations in a suitable Banach space. Then, it is shown that the problem has a solution if the applied forces are small enough in a certain Sobolev norm.
R~nmm6. On applique le th6or~me des fonctions implicites au probl6me non iin~aire de l'&lullibre d'une plaque rectangulalre 6lastique soumise/t des forces convenables. Cette plaque est suppos~e fi bords glissants ou bien soumise ~ des conditions aux limites de type p~riodique. On utilise des r6sultats de r6gularit6 clans les espaces de Sobolev pour poser les &tnations dam un cadre fonetionnel ad&luat. On montre alors que ce probl6me admet une solution si les forces appliqu6es sont assez petites dam une certaine norme de Sobolev.
Contents
- Introduction 2. The three-dimensional plate problem 3. Abstract formulation of the problem 4. Properties of the mappings ~, ~/and ~ 5. The existence Theorem 6. The plate with sliding edges 7. Conciusion Annex References 233 236 238 240 244 245 248 248 251