Papers by Mattias Schevenels
Computer Methods in Applied Mechanics and Engineering, 2011
This paper presents a robust approach for the design of macro-, micro-, or nano-structures by mea... more This paper presents a robust approach for the design of macro-, micro-, or nano-structures by means of topology optimization, accounting for spatially varying manufacturing errors. The focus is on structures produced by milling or etching; in this case over-or under-etching may cause parts of the structure to become thinner or thicker than intended. This type of error is modeled by means of a projection technique: a density filter is applied, followed by a Heaviside projection, using a low projection threshold to simulate under-etching and a high projection threshold to simulate over-etching. In order to simulate the spatial variation of the manufacturing error, the projection threshold is represented by a (non-Gaussian) random field. The random field is obtained as a memoryless transformation of an underlying Gaussian field, which is discretized by means of an EOLE expansion. The robust optimization problem is formulated in a probabilistic way: the objective function is defined as a weighted sum of the mean value and the standard deviation of the structural performance. The optimization problem is solved by means of a Monte Carlo method: in each iteration of the optimization scheme, a Monte Carlo simulation is performed, considering 100 random realizations of the manufacturing error. A more thorough Monte Carlo simulation with 10000 realizations is performed to verify the results obtained for the final design. The proposed methodology is successfully applied to two test problems: the design of a compliant mechanism and a heat conduction problem.
Structural and Multidisciplinary Optimization, 2011
The paper presents an efficient 88 line MATLAB code for topology optimization. It has been develo... more The paper presents an efficient 88 line MATLAB code for topology optimization. It has been developed using the 99 line code presented by Sigmund (Struct Multidisc Optim 21(2):120–127, 2001) as a starting point. The original code has been extended by a density filter, and a considerable improvement in efficiency has been achieved, mainly by preallocating arrays and vectorizing loops. A speed improvement with a factor of 100 is obtained for a benchmark example with 7,500 elements. Moreover, the length of the code has been reduced to a mere 88 lines. These improvements have been accomplished without sacrificing the readability of the code. The 88 line code can therefore be considered as a valuable successor to the 99 line code, providing a practical instrument that may help to ease the learning curve for those entering the field of topology optimization. The paper also discusses simple extensions of the basic code to include recent PDE-based and black-and-white projection filtering methods. The complete 88 line code is included as an appendix and can be downloaded from the web site www.topopt.dtu.dk.
Computer Methods in Applied Mechanics and Engineering, 2010
This paper presents a general 2.5D coupled finite element-boundary element methodology for the co... more This paper presents a general 2.5D coupled finite element-boundary element methodology for the computation of the dynamic interaction between a layered soil and structures with a longitudinally invariant geometry, such as railway tracks, roads, tunnels, dams, and pipelines. The classical 2.5D finite element method is combined with a novel 2.5D boundary element method. A regularized 2.5D boundary integral equation is derived that avoids the evaluation of singular traction integrals. The 2.5D Green's functions of a layered halfspace, computed with the direct stiffness method, are used in a boundary element method formulation. This avoids meshing of the free surface and the layer interfaces with boundary elements and effectively reduces the computational efforts and storage requirements. The proposed technique is applied to four examples: a road on the surface of a halfspace, a tunnel embedded in a layered halfspace, a dike on a halfspace and a vibration isolating screen in the soil.
Soil Dynamics and Earthquake Engineering, 2010
Ground vibrations induced by railway traffic at grade and in tunnels are often studied by means o... more Ground vibrations induced by railway traffic at grade and in tunnels are often studied by means of two-and-half dimensional (2.5D) models that are based on a Fourier transform of the coordinate in the longitudinal direction of the track. In this paper, the need for 2.5D coupled finite element-boundary element models is demonstrated in two cases where the prediction of railway
Because numerical simulation parameters may significantly influence the accuracy of the results, ... more Because numerical simulation parameters may significantly influence the accuracy of the results, evaluating the sensitivity of simulation results to variations in parameters is essential. Although the field of sensitivity analysis is well developed, systematic application of such methods to complex biological models is limited due to the associated high computational costs and the substantial technical challenges for implementation. In the specific case of the forward problem in electrocardiography, the lack of robust, feasible, and comprehensive sensitivity analysis has left many aspects of the problem unresolved and subject to empirical and intuitive evaluation rather than sound, quantitative investigation. In this study, we have developed a systematic, stochastic approach to the analysis of sensitivity of the forward problem of electrocardiography to the parameter of inhomogeneous tissue conductivity. We apply this approach to a two-dimensional, inhomogeneous, geometric model of a slice through the human thorax. We assigned probability density functions for various organ conductivities and applied stochastic finite elements based on the generalized polynomial chaos-stochastic Galerkin (gPC-SG) method to obtain the standard deviation of the resulting stochastic torso potentials. This method utilizes a spectral representation of the stochastic process to obtain numerically accurate stochastic solutions in a fraction of the time required when employing classic Monte Carlo methods. We have shown that a systematic study of sensitivity is not only easily feasible with the gPC-SG approach but can also provide valuable insight into characteristics of the specific simulation.
Vibrations induced by road and rail traffic are a common source of discomfort to people. Numerica... more 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. In this paper, the influence of the small scale variations of the dynamic shear modulus on the Green’s functions of a vertically inhomogeneous soil is studied. A probabilistic approach is followed where the mean soil is modelled using the results of the aforementioned measurement techniques. Superimposed on the mean profile is a zero mean random process that represents the small scale variations of the dynamic shear modulus. This process is characterized by a marginal probability density function and a correlation function, estimated by means of a cone penetration test (CPT). The resolution of the CPT test is high as compared to the SASW and the SCPT tests. The non-Gaussian random process is discretized by means of a Hermite polynomial expansion and a Karhunen-Loeve decomposition [1]. The methodology of the stochastic finite element method [2] is applied to a hybrid thin layer - direct stiffness formulation [3] in order to assemble the stochastic system equations. These are solved by means of a Monte Carlo simulation to obtain the stochastic Green’s functions. The results of the simulation are in good correspondence with the discrepancy observed in the validation of the deterministic vibration prediction models. In the low frequency range, the small scale variations of the dynamic shear modulus are not resolved by the waves and all realizations of the stochastic Green’s functions tend to the Green’s functions of the mean soil. In the high frequency range, the waves do resolve the small scale variations. As a result, phase shifts and variations of the amplitude occur between different realizations of the stochastic Green’s functions.
Journal of Geotechnical and Geoenvironmental Engineering, 2008
ABSTRACT
Probabilistic Engineering Mechanics, 2007
This paper presents a study of wave propagation in an infinite beam on a random Winkler foundatio... more This paper presents a study of wave propagation in an infinite beam on a random Winkler foundation. The spatial variation of the foundation spring constant is modelled as a random field and the influence of the correlation length is studied. As it is impossible to determine the general stochastic Green's function, the configurational average of the Green's function and its correlation function are considered. These functions are found through the transformation of the stochastic equation of motion into the Dyson equation for the mean or coherent field and the Bethe-Salpeter equation for the field correlation, as used in the study of wave propagation in random media. The approximate solutions of the Dyson and the Bethe-Salpeter equations are validated by means of a Monte Carlo simulation and compared with the results of a classical Neumann expansion method. Although both methods only involve the second order statistics of the random field, the approximation of the Dyson and the Bethe-Salpeter equations gives better results than the Neumann expansion, at the expense of a larger computational effort. Furthermore, the results show that a small spatial variation of the spring constant has an influence on the response if the correlation length and the wavelength have a similar order of magnitude, while the waves in the beam cannot resolve the spatial variation in the case where the correlation length is much smaller than the wavelength.
Computers & Geosciences, 2009
Probabilistic Engineering Mechanics, 2007
This paper deals with the study of the Green's functions of a layered soil with random characteri... more This paper deals with the study of the Green's functions of a layered soil with random characteristics. The dynamic shear modulus of the soil is modelled as a non-Gaussian random process that varies in the vertical direction and is characterized by a marginal probability density function and a correlation function. The stochastic finite element method is applied to a hybrid thin layer -direct stiffness formulation in order to obtain the stochastic system equations, which are solved by means of a Monte Carlo simulation. The influence of the variations of the dynamic shear modulus on the Green's functions is illustrated for different excitation frequencies and receiver positions.
A recent development in operational modal analysis (OMA) is the possibility of using measured, ar... more 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.
This paper presents a robust approach for the design of macro-, micro-, or nanostructures by mean... more This paper presents a robust approach for the design of macro-, micro-, or nanostructures by means of topology optimization, accounting for spatially varying manufacturing errors. The focus is on structures produced by milling or etching; in this case over-or under-etching may cause parts of the structure to become thinner or thicker than intended. This type of errors is modeled by means of a projection technique: a density filter is applied, followed by a Heaviside projection, using a low projection threshold to simulate under-etching and a high projection threshold to simulate over-etching. In order to simulate the spatial variation of the manufacturing error, the projection threshold is represented by a (non-Gaussian) random field. The random field is obtained as a memoryless transformation of an underlying Gaussian field, which is discretized by means of an EOLE expansion. The robust optimization problem is formulated in a probabilistic way: the objective function is defined as a weighted sum of the mean value and the standard deviation of the structural performance. The optimization problem is solved by means of a Monte Carlo method: in each iteration of the optimization scheme, a Monte Carlo simulation is performed, considering 100 random realizations of the manufacturing error. A more thorough Monte Carlo simulation with 10000 realizations is performed to verify the results obtained for the final design. The proposed methodology is successfully applied to two test problems: the design of a compliant mechanism and a heat conduction problem.
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Papers by Mattias Schevenels