Mattias Schevenels

Short Note: EDT: An ElastoDynamics Toolbox for MATLAB

The ElastoDynamics Toolbox (EDT) version 2.1 offers an extensive set of MATLAB functions to model elastodynamic wave propagation in horizontally layered media. The toolbox is based on the direct stiffness method and the thin layer method. These methods provide stiffness matrices for a homogeneous layer and a homogeneous halfspace, which are formulated in the frequency-wavenumber domain. EDT 2.1 can be used to solve a variety of problems governed by wave propagation in the soil, such as (1) site amplification, (2) the computation of dispersive wave modes in layered soils, and (3) the calculation of the forced response of the soil due to harmonic and transient loading. The toolbox serves as an electronic learning environment for the simulation and processing of seismic wave propagation in layered media. It has also been used by various authors to model wave propagation in layered soils

Using the PiP Model for Fast Calculation of Vibration from a Railway Tunnel in a Multi-layered Half-Space

This paper presents a new method for calculating vibration from underground railways buried in a multi-layered half-space. The method assumes that the tunnel’s near-field displacements are controlled by the dynamics of the tunnel and the layer that contains the tunnel, and not by layers further away. Therefore the displacements at the tunnel-soil interface can be calculated using a model of a tunnel embedded in a full space. The Pipe-in-Pipe (PiP) model is used for this purpose, where the tunnel wall and its surrounding ground are modelled as two concentric pipes using elastic continuum theory. The PiP model is computationally efficient on account of uniformity along and around the tunnel. The far-field displacement is calculated by using another computationally efficient model that calculates Green’s functions for a multi-layered half-space using the direct stiffness method. The model is based on the exact solution of Navier’s equations for a horizontally layered half-space in the frequency-wavenumber domain.

Geotechnical characterization of a river dyke by surface waves surface waves

The need for effective and reliable methods to survey and monitor the structure of earth-fill dams recently became pressing in light of the increasing number of flood events in central Europe. Among geophysical techniques, dam imaging using electrical resistivity methods is applied in most cases. Occasionally, ground-penetrating radar is applied in the framework of the search for subsurface facilities. Seismic methods are rarely used. This paper focuses on the multichannel analysis of the surface waves (MASW) method to determine dynamic soil properties and aims to extend its application field to dyke and dam structures. The standard processing procedure of the MASW assumes a flat free surface of infinite extension. The flat surfaces of a dyke, in contrast, are in the order of 1–10 times smaller than the wavelengths in the soil; disturbing side reflections will occur. Even though MASW has already been applied on a few dyke sites, the effect of such an obvious breach of preconditions needs to be studied before the method can be recommended. In this paper the influences of the dyke’s topography on the test results are studied by means of a numerical analysis. Typical cross-sections are modelled using 2.5D finite and boundary elements. The results of models taking the topography into account are compared with models neglecting the topography. The differences are evaluated on the level of the dispersion curves and for one cross-section on the level of the S-wave velocity. They were found to be insignificant for dykes with a width-to-height ratio larger than four. A testing campaign was conducted providing the chance to collect experience in the practical use of the MASW method on dykes. Test results obtained at two test sites are selected and compared to the results of borehole logs and cone penetration tests. A remarkable relation between the S-wave velocity and the consistency of the clay sealing was found at one site; a distinct positive correlation to the measured cone tip resistances was achieved on the other test site. Valuable information on the composition of the dyke body and base could be obtained but the resolution of the method to identify small areas of inhomogeneity should not be overestimated.

Global Size Optimization of Statically Determinate Trusses Considering Displacement, Member, and Joint Constraints

AbstractRealistic truss design optimization problems are often governed by practical constraints. Because of the complexity of these constraints, usually only member constraints are taken into account during the optimization, and joint constraints are accounted for in a manual postprocessing step. This paper proposes a method to account for joint constraints in the global discrete size optimization of a steel truss structure. The design of an N-type truss girder is considered first without and then with the joint constraints specified in the Eurocode. To guarantee global optimality in both cases, the optimization problem is reformulated as a mixed-integer linear program. A statically determinate analysis model is adopted so as to ensure that all joint constraints can be reformulated as linear functions. If the joint constraints are not considered in the optimization, a design is obtained where the joints need additional strengthening. This can be done by manually selecting heavier sections, which often le...

The generation of hierarchic structures via robust 3D topology optimisation

Commonly used building structures often show a hierarchic layout of structural elements. It can be questioned whether such a layout originates from practical considerations, e.g. related to its construction, or that it is (relatively) optimal from a structural point of view. This paper investigates this question by using topology optimisation in an attempt to generate hierarchical structures. As an arbitrarily standard design case, the principle of a traditional timber floor that spans in one direction is used. The optimisation problem is first solved using classical sensitivity and density filtering. This leads indeed to solutions with a hierarchic layout, but they are practically unusable as the floor boarding is absent. A Heaviside projection is therefore considered next, but this does not solve the problem. Finally, a robust approach is followed, and this does result in a design similar to floor boarding supported by timber joists. The robust approach is then followed to study a floor with an opening, two floors that span in two directions, and an eight-level concrete building. It can be concluded that a hierarchic layout of structural elements likely originates from being optimal from a structural point of view. Also clear is that this conclusion cannot be obtained by means of standard topology optimisation based on sensitivity or density filtering (as often found in commercial finite element codes); robust 3D optimisation is required to obtain a usable, constructible (or in the future: 3D printable) structural design, with a crisp black-and-white density distribution.

OMAX testing of a steel bowstring footbridge

A recent development in operational modal analysis (OMA) is the possibility of using measured, artificial loads in addition to the unmeasured, ambient excitation, while the ratio between forced and ambient excitation can be low compared to classical experimental modal analysis (EMA). Most of these so-called OMAX algorithms lack the intuitiveness of their EMA and OMA counterparts, since they fit a system model that takes both the measured and the operational excitation into account directly to the measured signals. A more physically intuitive subspace algorithm for OMAX, that starts with an accurate decomposition of the measured joint response in a forced and an ambient part, was recently introduced. In this paper, the performance of this algorithm, which is called CSI-ic/ref, is assessed by means of a case study, where a two-span steel arch footbridge is tested in operational conditions, with and without using additional actuators. From a comparison of the modal parameters with results from a finite elementmodel, an OMA algorithm, and an alternative OMAX algorithm, it can be concluded that CSI-ic/ref yields accurate modal parameter estimates.

A mixed-integer linear programming approach for global discrete size optimization of frame structures

This paper proposes a method to solve discrete size optimization problems of frame structures to global optimality. Global optimality is guaranteed by reformulating the optimization problem as a mixed-integer linear program (MILP) and solving it with the branch-andbound method. The presented mixed variable formulation extends the existing mixed variable formulation for size and topology optimization of truss structures. The MILP is obtained by adopting the simultaneous analysis and design approach. The variables consist of binary decision variables to select a profile section from the catalog, and state variables representing the member end forces. The equilibrium equations and member stiffness relations are included as constraints. The displacement and stress constraints are formulated such that for each member limit values are imposed at predefined locations along the member. The proposed method is applied to a three-bay three-story frame.

The use of the SASW method to determine the shear wave velocity and the material damping ratio of shallow soil layers

This paper focuses on the Spectral Analysis of Surface Waves (SASW) method for the determination of stiffness and damping parameters of shallow soil layers. The paper consists of three parts, addressing (1) the in situ SASW test, (2) the determination of the dispersion and attenuation curves from the measurement data, and (3) the inverse problem where the soil profile is identified. The existing practice is critically reviewed, and a number of improvements to the SASW method are presented. These include a technique to improve the efficiency of the in situ test, and a new method to determine the experimental attenuation curve. The efficiency of the test is improved by monitoring the signal-to-noise ratio during the experiment. The experimental attenuation curve is determined by means of a frequencywavenumber analysis, using the half-power bandwidth method.

The Wave Propagation in a Vertically Inhomogeneou Soil with a Random Dynamic Shear Modulus

Vibrations induced by road and rail traffic are a common source of discomfort to people. Numerical models have been developed for the prediction of traffic induced vibrations in the free field or in the built environment. These models consist of a finite element formulation for the vehicles and the buildings and a boundary element formulation that accounts for the wave propagation in the soil. The latter is based on the Green’s functions of a horizontally layered halfspace. The experimental validation of these models reveals a discrepancy between the predicted and measured response in the higher frequency range. Given the crucial role of the Green’s functions in the prediction model, the dynamic soil characteristics governing these functions are a possible source of the discrepancy. Common techniques for the in-situ measurement of the dynamic soil characteristics such as the spectral analysis of surface waves (SASW) test and the seismic cone penetration test (SCPT) are based on local averages of the soil characteristics and have a limited resolution. The small scale variations of the soil characteristics are not revealed.

Combined Length Scale and Overhang Angle Control in Minimum Compliance Topology Optimization for Additive Manufacturing

This paper focusses on topology optimization for additive manufacturing. Two manufacturing constraints are considered: minimum length scale and maximum overhang angle. The first is needed to ensure that the condition on minimal printable feature sizes is satisfied, while the second eliminates the need for a temporary support structure. Filtering schemes have been proposed in the literature to ensure either a minimum length scale or a maximum overhang angle, but not both simultaneously. In this paper, it is shown that both constraints cannot simultaneously be met by simply applying both filters sequentially, as the effect of the first filter is destroyed by the second. A new, slightly more complex filtering scheme is therefore proposed, which does allow simultaneous control over length scale and overhang angle in a minimum compliance topology optimization problem. The method is successfully applied to a 2D benchmark problem.