C. Cismaşiu

Hybrid-Trefftz displacement element for spectral analysis of bounded and unbounded media

The hybrid-Trefftz displacement element is applied to the elastodynamic analysis of bounded and unbounded media in the frequency domain. The displacements are approximated in the domain of the element using local solutions of the wave equation, the Neumann conditions are enforced directly and the surface forces are approximated on the Dirichlet and inter-element boundaries of the finite element mesh. Two alternative elements are developed to model unbounded media, namely a finite element with absorbing boundaries and an unbounded element that satisfies explicitly the Sommerfeld condition. The finite element equations are derived from the fundamental relations of elastodynamics written in the frequency domain. The numerical implementation of these equations is discussed and numerical tests are presented to assess the performance of the formulation.

Numerical implementation of hybrid-Trefftz displacement elements

Abstract The numerical implementation of the displacement model of the hybrid-Trefftz finite element formulation is presented. The geometry of the supporting element is not constrained a priori. Unbounded, non-convex and multiply connected elements can be used. The approximation basis is naturally hierarchical and very rich. It is constructed on polynomial solutions of the governing differential equation, and extended to include the particular terms known to model accurately important local effects, namely the singular stress patterns due to cracks or point loads. Numerical and semi-analytical methods are used to compute the finite element matrices and vectors, all of which present boundary integral expressions. Appropriate procedures to store, manipulate and solve symmetric highly sparse systems are used. The characteristics of the finite element solving system in terms of sparsity and conditioning are analysed, as well as its sensitivity to the effects of mesh distortion, incompressibility and rotation of the local reference systems. Benchmark tests are used also to illustrate the performance of the element in the estimation of displacements, stresses and stress intensity factors.

Numerical simulation of superelastic shape memory alloys subjected to dynamic loads

Superelasticity, a unique property of shape memory alloys (SMAs), allows the material to recover after withstanding large deformations. This recovery takes place without any residual strains, while dissipating a considerable amount of energy. This property makes SMAs particularly suitable for applications in vibration control devices. Numerical models, calibrated with experimental laboratory tests from the literature, are used to investigate the dynamic response of three vibration control devices, built up of austenitic superelastic wires. The energy dissipation and re-centering capabilities, important features of these devices, are clearly illustrated by the numerical tests. Their sensitivity to ambient temperature and strain rate is also addressed. Finally, one of these devices is tested as a seismic passive vibration control system in a simplified numerical model of a railway viaduct, subjected to different ground accelerations.

Comparative analysis of hybrid-trefftz stress and displacement elements

SummaryThe alternative stress and displacement models of the hybrid-Trefftz finite element formulation for the analysis of linear boundary value problems are derived in parallel form to emphasise the complementary nature of the fundamental concepts they develop from. In the stress model the stresses in the structural domain and the boundary displacements are independently approximated and inter-element stress continuity is enforced explicitly. Conversely, in the displacement model the displacements in the structural domain and the boundary tractions are independently approximated and inter-element linkage is enforced in the form of displacement continuity. In both models the approximation in the domain is constrained to satisfy locally all field equations, a feature typical of the Trefftz method. Duality is used to interpret physically the finite element equations, which are derived from the fundamental relations of elastostatics. Numerical tests are presented to compare the relative performance of the alternative stress and displacement models.

Experimental Dynamic Characterization and Finite-Element Updating of a Footbridge Structure

AbstractNowadays, modern analysis of civil engineering structures implies the use of increasingly sophisticated computer models, designed not only to predict the response of actual structures to different loadings, but also to simulate the effects of eventual modifications in their structural configuration. Nevertheless, it is often discovered that when the numerical simulations are compared with experimental data, the degree of correlation is weak, thus preventing the use of the finite-element (FE) models with confidence in further analyses. In such cases, FE updating techniques are available to correct the FE models, based on dynamic response records of the real structures. These updating processes usually consist of four phases: preliminary FE modeling, experimental modal identification, manual sensitivity analysis and, finally, updating the FE model. The present paper presents all four phases of a successful updating process for the FE model of a footbridge structure. It is shown how the last phase of...

Adaptive p-refinement of hybrid-Trefftz finite element solutions

An adaptive p-refinement procedure for the implementation of the displacement model of the hybrid-Trefftz finite element formulation is presented. The procedure is designed to select and implement automatically the degrees of freedom in the domain (displacements) and on the boundary (surface forces) of the element to attain a prescribed level of accuracy. This accuracy is measured on the strain energy of the system for a prescribed finite element mesh. Local measures of error can be easily accounted for. The performance of the adaptive procedure suggested is illustrated using two-dimensional potential problems.

Comparison Between Two SMA Constitutive Models for Seismic Applications

This paper analyses and compares the dynamic behavior of superelastic shape memory alloy (SMA) systems based on two different constitutive models. The first model, although being able to describe the response of the material to complex uniaxial loading histories, is temperature and rate independent. The second model couples the mechanical and kinetic laws of the material with a balance equation considering the thermal effects. After numerical validation and calibration, the behavior of these two models is tested in single degree of freedom dynamic systems, with SMAs acting as restoring elements. Different dynamic loads are considered, including artificially generated seismic actions, in a numerical model of a railway viaduct. Finally, it is shown that, in spite of its simplicity, the temperature- and rate-independent model produces a set of very satisfying results. This, together with its robustness and straightforward computational implementation, yields a very appealing numerical tool to simulate superelastic passive control applications.

Adaptive underslung beam using shape-memory alloys for frequency-tuning

The present article addresses the study of an adaptive-passive beam structure with a shape-memory alloy based actuator. In order to mitigate adverse dynamic effects resulting from externally induced vibrations, the structure is able to automatically tune its natural frequency to avoid resonance. The adaptive-passive beam configuration is based on an underslung cable-stayed girder concept. Its frequency tuning is achieved by temperature modulation of the shape-memory alloy elements through a closed-loop control process based on a proportional-integral-derivative algorithm. The effectiveness of the proposed control solution is substantiated by numerical simulations and experimental tests on a small-scale prototype. The validated numerical model enables the simulation of the proposed control approach in a real-scale footbridge, subjected to a prescribed pedestrian loading. The results are very encouraging and show that, by activating the shape-memory alloy elements, the system is able to successfully shift its natural frequency and to mitigate the effects of induced vibrations.

Seismic Vulnerability Assessment of a RC Pedestrian Crossing

ABSTRACT The paper addresses the seismic vulnerability assessment of a multi-span footbridge, prone to span unseating due to shorter seat lengths. The structure is representative of a series of pedestrian crossings located in the Southern part of Portugal, a region with a relevant seismicity. A probabilistic approach allows considering the variability of the seismic action and uncertainties in the definition of the material properties and/or structural behavior. Based on incremental dynamic analyses and corresponding fragility curves, it is shown that, for code compliance design acceleration, there is a significant probability that the structure will only suffer minor damage.

Numerical Simulation of Blast Effects on Fibre Grout Strengthened RC Panels

The present paper aims to examine the potential of the Applied Element Method (AEM) in simulating the blast effects in RC panels. The numerical estimates are compared with the results obtained in an experimental campaign designed to investigate the effectiveness of fibre grout for strengthening full scale RC panels by comparing the effects that a similar blast load produces in a reference and the strengthened panel. First, a numerical model of the reference specimen was created in the software Extreme Loading for Structures and calibrated to match the experimental results. With no further calibration, the fibre reinforced grout strengthening was added and the resulting numerical model subjected to the same blast load. The experimental blast effects on both reference and strengthened panels, despite the lack of high speed measurement equipment (pressure, strains and displacements sensors), compare well with the numerical estimates in terms of residual and maximum displacements, showing that, once calibrated, the AEM numerical models can be successfully used to simulate blast effects in RC panels.