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"Elastic analysis"
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Guided waves in structures for SHM
Understanding and analysing the complex phenomena related to elastic wave propagation has been the subject of intense research for many years and has enabled application in numerous fields of technology, including structural health monitoring (SHM).
eBook
Elastic Shape Analysis of Surfaces with Second-Order Sobolev Metrics: A Comprehensive Numerical Framework
This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic distances between parametrized or unparametrized immersed surfaces represented as 3D meshes. Building on this, we develop tools for the statistical shape analysis of sets of surfaces, including methods for estimating Karcher means and performing tangent PCA on shape populations, and for computing parallel transport along paths of surfaces. Our proposed approach fundamentally relies on a relaxed variational formulation for the geodesic matching problem via the use of varifold fidelity terms, which enable us to enforce reparametrization independence when computing geodesics between unparametrized surfaces, while also yielding versatile algorithms that allow us to compare surfaces with varying sampling or mesh structures. Importantly, we demonstrate how our relaxed variational framework can be extended to tackle partially observed data. The different benefits of our numerical pipeline are illustrated over various examples, synthetic and real.
Journal Article
Definition and validation of a valley amplification factor for seismic linear response of 2D homogeneous alluvial basins
The paper presents findings from a parametric study analysing geometric (e.g., shape ratio, edge inclination) and stratigraphic factors (e.g. impedance ratio) influencing ground motion in trapezoidal valleys. The study involved 2160 visco-elastic analyses, considering 180 2D models with diverse shapes and soil properties, undergoing 12 synthetic input motions. Analyses results showed that the motion at the valley centre increases with both shape and impedance ratios, while it is independent of the edge slope; on the other hand, the maximum amplification at the edges depends on their inclination and on the impedance ratio, while it is independent of the valley shape. The position and size of the zone of maximum amplification at the edges depend on all the previous parameters. A valley amplification factor (VAF) is introduced to quantify spectral acceleration increase due to 2D effects. Closed-form equations are proposed to evaluate VAF based on valley properties. The proposed VAF is then applied to predict seismic amplification in two central Italian valleys, providing results well-comparable to those obtained from 2D numerical analyses. The described approach can be easily implemented into codes of practice as a conservative design tool to estimate 2D amplification along the surface of ‘shallow valleys’ subjected to moderate seismic actions.
Journal Article
Elastic–Plastic Deformation Analysis of Cantilever Beams with Tension–Compression Asymmetry of Materials
In the elastic–plastic analysis of structures, the deformation problem of cantilever beams is a classical problem, in which it is usually assumed that the material constituting the beam has an identical elastic modulus and identical yield strength when it is tensioned and compressed. These characteristics are manifested graphically as the symmetry of tension and compression. In this work, we will give up the general assumption and consider that the material has the property of tension–compression asymmetry, that is, the material presents different moduli in tension and compression and different yield strengths in tension and compression. First, the elastic–plastic response of the cantilever beam with a concentrated force acting at the fixed end in the loading stage is theoretically analyzed. When the plastic hinge appears at the fixed end, the maximum deflection at the free end is derived, and in the unloading stage the residual deflection at the free end is also given. At the same time, the theoretical solution obtained is validated by the numerical simulation. The results indicate that when considering the tension–compression asymmetry of materials, the plastic zone length from the fixed end no longer keeps the classical value of 1/3 and will become bigger; the tension–compression asymmetry will enlarge the displacement during the elastic–plastic response; and the ultimate deflection in loading and the residual deflection in unloading are both greater than the counterparts in the classical problem. The research results provide a theoretical reference for the fine analysis and optimal design of cantilever beams.
Journal Article
The Elastic-Analysis-Based Study on the Internal Force and Deformation of the Double-System Composite Guideway
To fill the gaps in the theoretical research on the internal force and deformation of the DSCG, the development law of the internal force and deformation of DSCG was explored in conjunction with the theory of elastic analysis. In addition, a finite element model was established to validate the calculation results. The results showed that using different pre-stressing increment calculation methods affected the calculation results of the composite interface deformation, with the equivalent section method accounting for 0.74% and the principle of the virtual work method for 0.03%. On the other hand, the development of internal forces and deformations in the DSCG was closely related to the magnitude of the load forms and axle weights. At the same time, material non-linearity had less influence on these factors. Finally, the development patterns of the internal forces and deformations of the DSCG with different spans were similar. The specific values were closely related to the span of the guideway, and the interfacial slip, axial force, and deflection of the DSCG with span L = 25 m were 0.60, 0.41, and 0.23 times those of the DSCG with span L = 35 m, respectively. The conclusions of this paper fill the gaps in the theoretical study of multi-system guideways.
Journal Article
Basis Restricted Elastic Shape Analysis on the Space of Unregistered Surfaces
This paper introduces a new framework for surface analysis derived from the general setting of elastic Riemannian metrics on shape spaces. Traditionally, those metrics are defined over the infinite dimensional manifold of immersed surfaces and satisfy specific invariance properties enabling the comparison of surfaces modulo shape preserving transformations such as reparametrizations. The specificity of our approach is to restrict the space of allowable transformations to predefined finite dimensional bases of deformation fields. These are estimated in a data-driven way so as to emulate specific types of surface transformations. This allows us to simplify the representation of the corresponding shape space to a finite dimensional latent space. However, in sharp contrast with methods involving e.g. mesh autoencoders, the latent space is equipped with a non-Euclidean Riemannian metric inherited from the family of elastic metrics. We demonstrate how this model can be effectively implemented to perform a variety of tasks on surface meshes which, importantly, does not assume these to be pre-registered or to even have a consistent mesh structure. We specifically validate our approach on human body shape and pose data as well as human face and hand scans for problems such as shape registration, interpolation, motion transfer or random pose generation.
Journal Article
Approximate Solutions for Displacements in an Elastic Layer Subjected to Circular or Square Loads
This paper presents new approximate formulas for evaluating the maximum displacements of an elastic layer loaded on a circular or square area. The approximate formulas are based on the exact solutions of the theory of elasticity for a half-space and the elastic layer and offer a simple and quick way to obtain the values of displacements. The novelty of these formulas lies in their ease of application while maintaining high accuracy with respect to the exact solution of the theory of elasticity, which can make them useful in engineering practice and allows for the quick and efficient estimation of displacement values without the need for complex numerical methods—merely a pocket calculator is enough. This is beneficial from an engineering point of view, where time and resources may be limited. This article also provides an analysis of the maximum displacements of different elastic layers—slipping on a non-deformable base (a load on a circular or square area) or fixed on a non-deformable base (a load on a circular area).
Journal Article