An elastic rod perfectly bonded to a fold on a von Karman elastic surface

Abstract

An elastic rod perfectly bonded to an elastic von Kármán plate is considered. The bonding is such that no relative displacements, except for a relative twist, are allowed between the rod and the plate. A recently proposed framework (Journal of Elasticity, 156, 1015–1044, 2024) is extended to allow the rod-plate system to develop a fold (slope discontinuity) coinciding with the rod in the deformed configuration. A boundary value problem is derived for the determination of the deformed shape, the fold angle, and the internal forces/moments in the rod-plate system for a given inelastic strain distribution in the rod as well as in the plate. The governing equations are posed in terms of a scalar stress function and a scalar transverse displacement field, both piecewise-smooth over the plate domain.

Keywords

Rod under flexible confinement plate reinforced by a rod interfaces in von Kármán surfaces non-smooth von Kármán equations folds in plates

Get full access to this article

View all access options for this article.

References

Raj

Pandey

Gupta

. Growth of an elastic rod perfectly bonded to a von Kármán elastic surface. J Elast 2024; 156: 1015–1044.

Pandey

Gupta

. Singular points and singular curves in von Kármán elastic surfaces. J Elast 2023; 153: 681–713.

Mansfield

. The bending and stretching of plates. Cambridge: Cambridge University Press, 1989.

Pandey

Gupta

. Topological defects and metric anomalies as sources of incompatibility for piecewise smooth strain fields. J Elast 2020; 139: 237–267.

Pandey

Gupta

. Point singularities in incompatible elasticity. J Elast 2021; 147: 229–256.

Pandey

Gupta

. Some consequences of the distributional stress equilibrium condition. Z Angew Math Phys 2022; 73: 203:1–7.