• Corpus ID: 238744419

# Variational setting for cracked beams and shallow arches

```@inproceedings{Gutman2021VariationalSF,
title={Variational setting for cracked beams and shallow arches},
author={Semion Gutman and Junhong Ha and Sudeok Shon},
year={2021}
}```
• Published 13 October 2021
• Mathematics
We develop a rigorous mathematical framework for the weak formulation of cracked beams and shallow arches problems. First, we discuss the crack modeling by means of massless rotational springs. Then we introduce Hilbert spaces, which are sufficiently wide to accommodate such representations. Our main result is the introduction of a specially designed linear operator that ”absorbs” the boundary conditions at the cracks. We also provide mathematical justification and derivation of the Modified…
1 Citations

## Figures from this paper

Equations of motion for cracked beams and shallow arches
• Mathematics
• 2021
Cracks in beams and shallow arches are modeled by massless rotational springs. First, we introduce a specially designed linear operator that ”absorbs” the boundary conditions at the cracks. Then the

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