Connecting beams and continua: variational basis and mathematical analysis

TL;DR

This paper introduces a new variational principle that unifies beam and solid models, offering a rigorous mathematical foundation for analyzing systems combining these elements.

Contribution

It develops a joint constrained variational principle that links beam and solid models and proves the well-posedness of the resulting boundary-value problem.

Findings

Unified variational framework for beams and solids

Mathematical proof of well-posedness

Potential for improved structural analysis methods

Abstract

We present a new variational principle for linking models of beams and deformable solids, providing also its mathematical analysis. Despite the apparent differences between the two types of governing equations, it will be shown that the equilibrium of systems combining beams and solids can be obtained from a joint constrained variational principle and that the resulting boundary-value problem is well posed.