Corneliu Cismasiu

The elastodynamic response of saturated poroelastic media is modelled approximating independently the solid and seepage displacements in the domain and the force and pressure components on the boundary of the element. The domain and boundary approximation bases are used to enforce on average the dynamic equilibrium and the displacement continuity conditions, respectively. The resulting solving system is Hermitian, except for the damping term, and its coefficients are defined by boundary integral expressions as a Trefftz basis is used to set up the domain approximation. This basis is taken from the solution set of the governing differential equation and models the free-field elastodynamic response of the medium. This option justifies the relatively high levels of performance that are illustrated with the time domain analysis of unbounded domains.

The hybrid-{T}refftz 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.

The paper reports on the work on hybrid-{T}refftz finite elements developed by the Structural Analysis Research Group, ICIST, Technical University of Lisbon. A dynamic elastoplastic problem is used to describe the technique used to establish the alternative stress and displacement models of the hybrid-{T}refftz finite element formulations. They are derived using independent time, space and finite element bases, so that the resulting solving systems are symmetric, sparse, naturally $p$-adaptive and particularly well suited to parallel processing. The performance of the hybrid-{T}refftz stress and displacement models is illustrated with a number of representative static and dynamic applications of elastic and elastoplastic structural problems.

The numerical implementation of the displacement model of the hybrid-{T}refftz 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.

An adaptive p-refinement procedure for the implementation of the displacement model of the hybrid-{T}refftz 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.

Shock absorbers have been widely used in the automotive and aeronautical industries for many years. Inspired on these devices, the paper presents an analytical and numerical assessment of a high performance protective system for building structures against blast loads, which is composed of a shielding element connected to the main structure, at the floor levels, through ductile Energy Absorbing Connectors (EACs). The EACs exploit the external tube inversion mechanism to absorb a significant part of the imparted kinetic energy from the blast wave. While the system prototype has been developed in laboratory, it was characterized and tested in a full-scale blast testing campaign. A validated finite element model was used next to analyze its performance in a more demanding design scenario. The introduction of EACs notably reduces the peak horizontal loads and the kinetic energy transferred to the protected structure, being expected a significant reduction of the stresses in the supporting vertical elements, in addition to the protection of structural and non-structural members. These results encourage further studies of the presented protective system that can be potentially employed for a large variety of blast threat scenarios, especially when increasing the stand-off is not a possible/viable option and sensitive facilities have to be protected.

Being able to efficiently mitigate the effects of blast loads on structures, sacrificial cladding solutions are increasingly used to protect structural elements from the effects of accidental explosions and/or terrorist attacks. The present study analyses the loss of effectiveness of a deterministically designed sacrificial cladding when variability in the material properties and uncertainties in the mechanical model are considered. The results of an experimental campaign are used to validate the numerical models that allow the deterministic design of a sacrificial cladding which successfully improves the blast resistant capabilities of a given structural element. Nonetheless, it is shown that, taking into account the probabilistic variability of key parameters is of vital importance when designing sacrificial cladding solutions, since, when not properly designed for the structural element it intends to protect, adding a sacrificial cladding might negatively impact its blast resistant capabilities. Additionally, it is concluded that the deterministic approach might be against safety. In the reported case study, when comparing the admissible charge weight yielding from the deterministic and probabilistic approaches, one verifies that the former allows a higher charge weight.

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.