Corneliu Cismasiu

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.

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This work studies the low-velocity impact response of 3D-printed layered structures made of thermoplastic materials (PLA and PETg), which form sacrificial claddings for impact protection. The analyzed structures are composed of crushable cellular cores placed in between terminal stiffening plates. The cores tessellate either honeycomb hexagonal unit cells, or hexagonal cells with re-entrant corners, with the latter exhibiting auxetic response. The given results highlight that the examined PETg protectors exhibit higher energy dissipation ratios and lower restitution coefficients, as compared to PLA structures that have the same geometry. It is concluded that PETg qualifies as an useful material for the fabrication of effective impact protection gear through ordinary, low-cost 3D printers.

The present study reports low velocity impact tests on composite laminate plates reinforced either with Kevlar 29 or Dyneema. The tests are produced using a Rosand Precision Impact tester. The experimental results obtained for Kevlar 29 are simulated numerically. The deflection history and the peak of the impact force are compared with experimental data and used to calibrate the numerical model.

Accurate blast models are essential for disaster management and emergency preparedness. Semi-empirical methods, which rely on free-field assumptions, struggle to provide precise data for complex building shapes because they ignore shock wave reflections. This research numerically investigates the effects of an explosion on a large building of complex geometrical configuration using blastFoam, estimating the façade damage and assessing risks to occupants. To evaluate the importance of accurately modelling the building’s geometry, four levels of detail were considered. Additionally, simulations were also performed using the Load Blast Enhanced (LBE) method from LS-DYNA to compare the estimates of this faster semi-empirical approach with those obtained through CFD analyses. The findings reveal that simpler CFD models are adequate for façade analysis and injury assessment around the building but fall short for predicting injury distribution within interior spaces or between buildings. The LBE underestimates both structural damage and human injury levels, while detailed CFD highlights the importance of accounting for interior walls and windows to enhance blast pressure predictions.

The displacement model of the hybrid-{T}refftz finite element formulation is applied to the solution of geometrically and physically linear static and dynamic problems. As the approximation bases solve locally the governing system of differential equations, the errors in the approximation affect only the implementation of the boundary conditions. Potential and elastostatic problems are used to illustrate the enforcement of the boundary conditions and the convergence of the solutions in energy, stresses and displacements, under both p- and h-refinement sequences and their insensitivity to mesh distortion, incompressibility and positioning of the coordinate system of the approximation basis. Also illustrated is the use of elements with arbitrary geometry and the efficiency that can be reached by including in the bases the solutions associated with dominant local effects, in particular those associated with singular stress fields. An adaptive p-refinement algorithm that exploits the naturally hierarchical nature of the approximation bases is presented and assessed. The formulation is generalised for elastodynamic analysis in the frequency domain of both bounded and unbounded domains, which are modelled either with absorbing boundary conditions or with semi-infinite elements that satisfy the Sommerfeld condition. The performance of the formulation is illustrated with tests on the convergence of the solutions in energy, stresses and displacements and on their insensitivity to mesh distortion, wave length and position of the absorbing boundary, for a wide spectrum of forcing frequencies and under both p- and h-refinement sequences.

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 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.

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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.

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.