Abstract
Curved beam, plate, and shell finite elements are commonly used in the finite element modeling of a wide range of civil and mechanical engineering structures. In civil engineering, curved elements are used to model tunnels, arch bridges, pipelines, and domes. Such structures provide a more efficient load transfer than their straight/flat counterparts due to the additional strength provided by their curved geometry. The load transfer is characterized by the bending, shear, and membrane actions. In this paper, a higher-order curved inverse beam element is developed for the inverse Finite Element Method (iFEM), which is aimed at reconstructing the deformed structural shapes based on real-time, in situ strain measurements. The proposed two-node inverse beam element is based on the quintic-degree polynomial shape functions that interpolate the kinematic variables. The element is C2 continuous and has rapid convergence characteristics. To assess the element predictive capabilities, several circular arch structures subjected to static loading are analyzed, under the assumption of linear elasticity and isotropic material behavior. Comparisons between direct FEM and iFEM results are presented. It is demonstrated that the present inverse beam finite element is both efficient and accurate, requiring only a few element subdivisions to reconstruct an accurate displacement field of shallow and deep curved beams.
Highlights
Civil engineering structures are commonly exposed to a series of loading and environmental conditions that impair their structural performance, integrity, and durability
Modern technologies that fall into the general category of Structural Health Monitoring (SHM) can potentially detect real-time information related to on-site structural conditions
Based on a variational principle that compares the analytic and measured section strains in a least-square sense, inverse Finite Element Method (iFEM) reconstructs the full-field displacements and strains using only the discrete strain-sensor measurements and structural topology
Summary
Civil engineering structures are commonly exposed to a series of loading and environmental conditions that impair their structural performance, integrity, and durability. Tessler and Spangler [2] employed Mindlin (first-order shear deformation) theory as the kinematic basis for iFEM, and they developed a three-node triangular inverse shell element (iMIN3) to model plate and shell structures. Curved beams are widely used in a variety of practical applications such as arches, arch bridges, highway construction, tunnels, circumferential stiffeners, airplane wings, blades, and springs Such structures are commonly modeled using curved finite elements. Considerable attention has been devoted to developing suitable element shape functions for curved finite elements that include proper representations of rigid-body modes, bending–membrane coupling, and membrane and shear locking stiffening effects. The formulation based on displacement fields often leads to excessively stiff behavior in thin regimes In such analyses, the phenomenon of shear and membrane locking takes place when lower order shape functions are used. For the inverse FEM, the effects of mesh refinement are studied
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