Publications

Bender elements are shear wave transducers, used for the computation of small strain shear moduli of geomaterials. However, the distortion of the output signal caused by residual compression waves may lead to important errors in the shear modulus estimates. We present a novel procedure for the optimisation of the location of the receiver bender element, to avoid regions where the distortion of the output signal is strong, without compromising the strength of the shear wave signal. The procedure is based on a computational technique naturally able to distinguish between the compression and shear waves present in the seismic response of geomaterials. This property enables the construction of compression and shear amplitude maps, that can be used to decide the best location for the receiver prior to running the experiment. The experimental validation of the procedure confirms that it leads to output signals which are easier to interpret than those obtained with the transmitter and receiver in the conventional, tip-to-tip configuration.

A new hybrid-Trefftz finite element for the solution of transient, non-homogeneous parabolic problems is formulated. The governing equations are first discretized in time and reduced to a series of non-homogeneous elliptic problems in space. The complementary and particular solutions of each elliptic problem are approximated independently. The complementary solution is expanded in Trefftz bases, designed to satisfy exactly the homogeneous form of the problem. Trefftz bases are regular, and defined independently for each finite element, using arbitrary orders. A novel dual reciprocity method is used for the approximation of the particular solution, to avoid domain integration. The same, regular basis is used for the expansions of the source function and particular solution, avoiding the cumbersome expressions of the latter that typify conventional dual reciprocity techniques. Moreover, the bases of the complementary and particular solutions are defined by the same expressions, with different wave numbers. The finite element formulation is obtained by enforcing weakly the domain equations and boundary conditions. To enhance the reproducibility of this work, the formulation is implemented in the computational platform FreeHyTE, where it takes advantage of the pre-programmed numerical procedures and graphical user interfaces. The resulting software is open-source, user-friendly and freely distributed to the scientific community through the FreeHyTE web page.

In the last decades, the long-term structural health monitoring of civil structures has been mainly performed using two approaches: model based and data based. The former approach tries to identify damage by relating the monitoring data to the prediction of numerical (e.g., finite-element) models of the structure. The latter approach is data driven, where measured data from a given state condition are compared to the baseline or reference condition. A challenge in both approaches is to make the distinction between the changes of the structural response caused by damage and environmental or operational variability. This issue was tackled here using a hybrid technique that integrates model- and data-based approaches into structural health monitoring. Data recorded in situ under normal conditions were combined with data obtained from finite-element simulations of more extreme environmental and operational scenarios and input into the training process of machine-learning algorithms for damage detection. The addition of simulated data enabled a sharper classification of damage by avoiding false positives induced by wide environmental and operational variability. The procedure was applied to the Z-24 Bridge, for which 1 year of continuous monitoring data were available.

With the continuous evolution of the numerical methods and the availability of advanced constitutive models, it became a common practice to use complex physical and geometrical nonlinear numerical analyses to estimate the structural behavior of reinforced concrete elements. Such simulations may yield the complete time history of the structural behavior, from the first moment the load is applied until the total collapse of the structure. However, the evolution of the cracking pattern in geometrical discontinuous zones of reinforced concrete elements and the associated failure modes are relatively complex phenomena and their numerical simulation is considerably challenging. The objective of the present paper is to assess the applicability of the Applied Element Method in simulating the development of distinct failure modes in reinforced concrete walls subjected to monotonic loading obtained in experimental tests. A pushover test was simulated numerically on three distinct RC shear walls, all presenting an opening that guarantee a geometrical discontinuity zone and, consequently, a relatively complex cracking pattern. The presence of different reinforcement solutions in each wall enables the assessment of the reliability of the computational model for distinct failure modes. Comparison with available experimental tests allows concluding on the advantages and the limitations of the Applied Element Method when used to estimate the behavior of reinforced concrete elements subjected to monotonic loading.

A new approach to the solution of non-homogeneous hyperbolic boundary value problems is casted here using the hybrid-Trefftz stress/flux elements. Similarly to the Dual Reciprocity Method, the technique adopted in this paper uses a Trefftz-compliant set of functions to approximate the complementary solution of the problem and an additional trial basis to approximate its particular solution. However, the particular and complementary solutions are obtained here in a single step, and not sequentially, as typical of the Dual Reciprocity Method. The trial functions used for both particular and complementary solutions are merged together in the same basis and offered full flexibility to combine so as to recover the enforced equations in the best possible way. This option enables Trefftz-compliant functions to compensate for deficiencies of the particular solution basis, meaning that accurate total solutions can be obtained with relatively poor particular solution approximations. The formulation preserves the Hermitian, sparse and localized structure that typifies the matrix of coefficients of hybrid-Trefftz finite elements and avoids the drawbacks of the collocation procedures that arise in the Dual Reciprocity Method. Moreover, all terms of the matrix of coefficients are reduced to boundary integral expressions provided the particular solution trial functions satisfy the static problem obtained after discarding both non-homogeneous and time derivative terms from the governing equation.

A new dual reciprocity-type approach to approximating the solution of non-homogeneous hyperbolic boundary value problems is presented in this paper. Typical variants of the dual reciprocity method obtain approximate particular solutions of boundary value problems in two steps. In the first step, the source function is approximated, typically using radial basis, trigonometric or polynomial functions. In the second step, the particular solution is obtained by analytically solving the non-homogeneous equation having the approximation of the source function as the non-homogeneous term. However, the particular solution trial functions obtained in this way typically have complicated expressions and, in the case of hyperbolic problems, points of singularity. Conversely, the method presented here uses the same trial functions for both source function and particular solution approximations. These functions have simple expressions and need not be singular, unless a singular particular solution is physically justified. The approximation is shown to be highly convergent and robust to mesh distortion.

Any boundary method can be used to approximate the complementary solution of the boundary value problem, once its particular solution is known. The option here is to use hybrid-Trefftz finite elements for this purpose. This option secures a domain integral-free formulation and endorses the use of super-sized finite elements as the (hierarchical) Trefftz bases contain relevant physical information on the modeled problem.

The purpose of this paper is to report the implementation of an alternative time integration procedure for the dynamic non-linear analysis of structures. The time integration algorithm discussed in this work corresponds to a spectral decomposition technique implemented in the time domain. As in the case of the modal decomposition in space, the numerical efficiency of the resulting integration scheme depends on the possibility of uncoupling the equations of motion. This is achieved by solving an eigenvalue problem in the time domain that only depends on the approximation basis being implemented. Complete sets of orthogonal Legendre polynomials are used to define the time approximation basis required by the model. A classical example with known analytical solution is presented to validate the model, in linear and non-linear analysis. The efficiency of the numerical technique is assessed. Comparisons are made with the classical Newmark method applied to the solution of both linear and non-linear dynamics. The mixed time integration technique presents some interesting features making very attractive its application to the analysis of non-linear dynamic systems. It corresponds in essence to a modal decomposition technique implemented in the time domain. As in the case of the modal decomposition in space, the numerical efficiency of the resulting integration scheme depends on the possibility of uncoupling the equations of motion. One of the main advantages of this technique is the possibility of considering relatively large time step increments which enhances the computational efficiency of the numerical procedure. Due to its characteristics, this method is well suited to parallel processing, one of the features that have to be conveniently explored in the near future.

The displacement model of the hybrid-Trefftz finite element is formulated for elastodynamic problems defined on unsaturated soils. The mathematical formulation is based on the theory of mixtures with interfaces. The model considers the full coupling between the solid, fluid and gas phases, including the effects of relative (seepage) accelerations. The hyperbolic problem is integrated in time using a step-by-step implicit scheme that transforms it into a series of elliptic problems in space. The free-field solutions of these problems are derived in cylindrical coordinates and used to construct the domain approximation of the hybrid-Trefftz displacement element. This builds relevant physical information in the approximation basis, increasing the convergence of the elements under p-refinement and their robustness to wide variations of the frequency of the propagating wave.

The hybrid-Trefftz displacement and stress elements for poroelasticity are applied here to the spectral analysis of bounded saturated porous media. The displacement model is derived from the direct approximation of the displacement and fluid seepage fields in the domain of the element and of the tractions and pore pressures in the solid and fluid phases, respectively, on the Dirichlet boundary of the element. Conversely, the stress model is obtained by the direct approximation of the total stress and pore pressure fields in the domain, while independent approximations of the displacement and fluid seepage fields are enacted on the Neumann boundaries. As typical of the Trefftz methods, for both models, the domain approximation bases are constrained to satisfy locally all field equations.

The central objective of the paper is to present a consistent set of tests designed to evaluate the ability of the proposed models to accurately predict the response of saturated porous media subjected to harmonic excitation and to assess the corresponding convergence patterns. Emphasis is placed on some key advantages of the presented formulation, namely the insensitivity of the results to gross mesh distortion, to near-incompressibility of the medium and to the wavelength content of the propagating wave, which enables the use of frequency-independent finite element meshes.

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 displacement and stress models of the hybrid-Trefftz finite element formulation are applied to the dynamic analysis of two-dimensional bounded and unbounded saturated porous media problems. The formulation develops from the classical separation of variables in time and space. A finite element approach is used for the discretization in time of the governing differential equations. It leads to a series of uncoupled problems in the space dimension, each of which is subsequently discretized using either the displacement or the stress model of the hybrid-Trefftz finite element formulation. As typical of the Trefftz methods, the domain approximation bases are constrained to satisfy locally all domain equations. An absorbing boundary element is adopted in the extension to the analysis of unbounded media. The paper closes with the illustration of the application of the alternative hybrid-Trefftz stress and displacement elements to the solution of bounded and unbounded consolidation problems.

The solution of transient parabolic problems using a novel hybrid-Trefftz finite element is presented in this chapter. The governing equations are first discretized in time and reduced to a series of non-homogeneous elliptic problems in space variables only. The complementary and particular solutions of each elliptic problem are approximated independently. The complementary solution is expanded in Trefftz bases, designed to satisfy exactly the homogeneous form of the problem. Trefftz bases include regular functions of arbitrary orders and are defined independently for each finite element. A novel dual reciprocity method is used for the approximation of the particular solution, to avoid domain integration. The same regular basis is used for the expansions of the source function and particular solution, avoiding the cumbersome expressions of the latter that typify conventional dual reciprocity techniques. Moreover, the bases of the complementary and particular solutions are defined by the same expressions, with different wave numbers. The finite element formulation is obtained by enforcing weakly the domain equations and boundary conditions. The formulation is implemented in the computational platform FreeHyTE, where it takes advantage of the pre-programmed numerical procedures and graphical user interfaces. The resulting software is open-source, user-friendly and freely distributed to the scientific community.

The displacement and stress models of the hybrid-Trefftz finite element formulation are applied to the dynamic analysis of two-dimensional bounded and unbounded saturated porous media problems. The formulation develops from the classical separation of variables in time and space. Periodic problems are discretized in time using Fourier analysis. Conversely, a finite element approach is used for the discretization in time of transient problems. Either strategy leads to a series of uncoupled problems in the space dimension, which are subsequently discretized using either the displacement or the stress model of the hybrid-Trefftz finite element formulation. As is typical of Trefftz methods, for both models, the approximation bases are constrained to satisfy locally all domain equations. The displacement model is based on the direct approximation of the solid displacement and fluid seepage fields in the domain of the element and of the forces and pore pressures on the solid and fluid phases, respectively, on the boundary of the element. Conversely, to derive the stress model, the stress and pore pressure fields are approximated in the domain, while independent approximations of the displacement and fluid seepage fields are assumed on the boundary of the element.

Two alternative approaches are used to extend the proposed formulations to semi-infinite (half-space) media, namely a finite element with absorbing boundary and an infinite element. For the displacement (stress) model, the tractions (displacements) are approximated independently on the absorbing boundary and used to enforce on average the asymptotic approximation of the Sommerfeld radiation condition. The domain approximations used in the derivation of infinite elements satisfy explicitly the Sommerfeld radiation condition, thus eliminating the uncertainties regarding possible spurious reflections in the vicinity of the absorbing boundary.