Application of Inverse Finite Element Method to Shape Sensing of Curved Beams

Area of Science:

• Structural analysis
• Computational mechanics
• Finite element analysis

Background:

• Curved beam, plate, and shell finite elements are crucial for modeling civil and mechanical structures like tunnels, bridges, pipelines, and domes.
• Curved geometries enhance load transfer efficiency through bending, shear, and membrane actions compared to straight elements.

Purpose of the Study:

• To develop a higher-order curved inverse beam element for the inverse Finite Element Method (iFEM).
• To enable reconstruction of deformed structural shapes from in situ strain measurements.

Main Methods:

• Development of a two-node inverse beam element using quintic-degree polynomial shape functions.
• The element ensures C² continuity and exhibits rapid convergence.
• Analysis of circular arch structures under static loading using linear elasticity and isotropic material assumptions.

Main Results:

• The developed inverse beam finite element demonstrates high efficiency and accuracy.
• Few element subdivisions are sufficient for precise displacement field reconstruction in shallow and deep curved beams.
• Comparisons with direct Finite Element Method (FEM) results validate the iFEM approach.

Conclusions:

• The proposed higher-order curved inverse beam element is a valuable tool for structural analysis.
• iFEM, utilizing this element, offers an efficient and accurate method for shape reconstruction from strain data.
• This advancement has significant implications for real-time structural health monitoring and analysis in civil and mechanical engineering.