Nonlinear equations of flexible plates deformations

K. G. Koifman   ; S. A. Lychev

Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 30 (2024) no. 4, pp. 53-83

Résumé

Nonlinear equations of deformation of flexible plates are formulated in general nonorthogonal coordinates with taking into account incompatible local deformations. The following assumptions are used. 1. Displacements of the plate from the reference (self-stressed) shape are restricted by the kinematic hypotheses of Kirchhoff — Love. 2. Elementary volumes constituting the reference shape can be locally transformed into an unstressed state by means of a nondegenerate linear transformation (hypothesis of local discharging). 3. Transformations inverse to local unloading, referred to as implants, can be found from the solution of the evolutionary problem simulating the successive deposition of infinitely thin layers on the front boundary surface of the plate. Geometric spaces of affine connection that model the global stress-free reference shape are constructed. The following special cases are considered: Weitzenböck space (with non-zero torsion), Riemann space (with non-zero curvature) and Weyl space (with non-zero non-metricity).

Détail

Keywords: hyperelasticity, flexible plates, kinematic hypothesis, nonlinear equations, asymptotic expansion, material connection.
Mots-clés : incompatible deformations

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