LaCàN - Laboratori de Càlcul Numèric
http://hdl.handle.net/2117/2072
Tue, 30 Aug 2016 01:47:22 GMT2016-08-30T01:47:22ZLaCàN - Laboratori de Càlcul Numèrichttp://upcommons.upc.edu/bitstream/id/22442/logoLaCaN128.gif
http://hdl.handle.net/2117/2072
The solution of linear mechanical systems in terms of path superposition
http://hdl.handle.net/2117/89392
The solution of linear mechanical systems in terms of path superposition
Magrans Fontrodona, Francesc Xavier; Poblet-Puig, Jordi; Rodríguez Ferran, Antonio
We prove that the solution of any linear mechanical system can be expressed as a linear combination of signal transmission paths. This is done in the framework of the Global Transfer Direct Transfer (GTDT) formulation for vibroacoustic problems. Transmission paths are expressed as powers of the transfer matrix. The key idea of the proof is to generalise the Neumann series of the transfer matrix --which is convergent only if its spectral radius is smaller than one-- into a modified Neumann series that is convergent regardless of the eigenvalues of the transfer matrix. The modification consists in choosing the appropriate combination coefficients for the powers of the transfer matrix in the series. A recursive formula for the computation of these factors is derived. The theoretical results are illustrated by means of numerical examples. Finally, we show that the generalised Neumann series can be understood as an acceleration (i.e. convergence speedup) of the Jacobi iterative method.
Mon, 29 Aug 2016 10:40:45 GMThttp://hdl.handle.net/2117/893922016-08-29T10:40:45ZMagrans Fontrodona, Francesc XavierPoblet-Puig, JordiRodríguez Ferran, AntonioWe prove that the solution of any linear mechanical system can be expressed as a linear combination of signal transmission paths. This is done in the framework of the Global Transfer Direct Transfer (GTDT) formulation for vibroacoustic problems. Transmission paths are expressed as powers of the transfer matrix. The key idea of the proof is to generalise the Neumann series of the transfer matrix --which is convergent only if its spectral radius is smaller than one-- into a modified Neumann series that is convergent regardless of the eigenvalues of the transfer matrix. The modification consists in choosing the appropriate combination coefficients for the powers of the transfer matrix in the series. A recursive formula for the computation of these factors is derived. The theoretical results are illustrated by means of numerical examples. Finally, we show that the generalised Neumann series can be understood as an acceleration (i.e. convergence speedup) of the Jacobi iterative method.Regression curves for vibration transmission across junctions of heavyweight walls and floors based on finite element methods and wave theory
http://hdl.handle.net/2117/89391
Regression curves for vibration transmission across junctions of heavyweight walls and floors based on finite element methods and wave theory
Hopkins, Carl; Crispin, Charlotte; Poblet-Puig, Jordi; Guigou-Carter, Catherine
Sound insulation prediction models in European and International standards use the vibration reduction index to calculate flanking transmission across junctions of walls and floors. These standards contain empirical relationships between the ratio of mass per unit areas for the walls/floors that form the junction and a frequency-independent vibration reduction index. Calculations using wave theory show that there is a stronger relationship between the ratio of characteristic moment impedances and the transmission loss from which the vibration reduction index can subsequently be calculated. In addition, the assumption of frequency-independent vibration reduction indices has been shown to be incorrect due to in-plane wave generation at the junction. Therefore numerical experiments with FEM, SFEM and wave theory have been used to develop new regression curves between these variables for the low-, mid- and high-frequency ranges. The junctions considered were L-, T- and X-junctions formed from heavyweight walls and floors. These new relationships have been implemented in the prediction models and they tend to improve the agreement between the measured and predicted airborne and impact sound insulation.
Mon, 29 Aug 2016 10:34:56 GMThttp://hdl.handle.net/2117/893912016-08-29T10:34:56ZHopkins, CarlCrispin, CharlottePoblet-Puig, JordiGuigou-Carter, CatherineSound insulation prediction models in European and International standards use the vibration reduction index to calculate flanking transmission across junctions of walls and floors. These standards contain empirical relationships between the ratio of mass per unit areas for the walls/floors that form the junction and a frequency-independent vibration reduction index. Calculations using wave theory show that there is a stronger relationship between the ratio of characteristic moment impedances and the transmission loss from which the vibration reduction index can subsequently be calculated. In addition, the assumption of frequency-independent vibration reduction indices has been shown to be incorrect due to in-plane wave generation at the junction. Therefore numerical experiments with FEM, SFEM and wave theory have been used to develop new regression curves between these variables for the low-, mid- and high-frequency ranges. The junctions considered were L-, T- and X-junctions formed from heavyweight walls and floors. These new relationships have been implemented in the prediction models and they tend to improve the agreement between the measured and predicted airborne and impact sound insulation.A modal-spectral model for flanking transmissions
http://hdl.handle.net/2117/89390
A modal-spectral model for flanking transmissions
Poblet-Puig, Jordi
A model for the prediction of direct and indirect (flanking) sound transmissions is presented. It can be applied to geometries with extrusion symmetry. The structures are modelled with spectral finite elements. The acoustic domains are described by means of a modal expansion of the pressure field and must be cuboid-shaped. These reasonable simplifications in the geometry allow the use of more efficient numerical methods. Consequently the coupled vibroacoustic problem in structures such as junctions is efficiently solved.
The vibration reduction index of T-junctions with acoustic excitation and with point force excitation is compared. The differences due to the excitation type obey quite general trends that could be taken into account by prediction formulas. However, they are smaller than other uncertainties not considered in practice. The model is also used to check if the sound transmissions of a fully vibroacoustic problem involving several flanking paths can be reproduced by superposition of independent paths. There exist some differences caused by the interaction between paths, which are more important at low frequencies.
Mon, 29 Aug 2016 10:30:50 GMThttp://hdl.handle.net/2117/893902016-08-29T10:30:50ZPoblet-Puig, JordiA model for the prediction of direct and indirect (flanking) sound transmissions is presented. It can be applied to geometries with extrusion symmetry. The structures are modelled with spectral finite elements. The acoustic domains are described by means of a modal expansion of the pressure field and must be cuboid-shaped. These reasonable simplifications in the geometry allow the use of more efficient numerical methods. Consequently the coupled vibroacoustic problem in structures such as junctions is efficiently solved.
The vibration reduction index of T-junctions with acoustic excitation and with point force excitation is compared. The differences due to the excitation type obey quite general trends that could be taken into account by prediction formulas. However, they are smaller than other uncertainties not considered in practice. The model is also used to check if the sound transmissions of a fully vibroacoustic problem involving several flanking paths can be reproduced by superposition of independent paths. There exist some differences caused by the interaction between paths, which are more important at low frequencies.Tutorial on Hybridizable Discontinuous Galerkin (HDG) for second-order elliptic problems
http://hdl.handle.net/2117/88137
Tutorial on Hybridizable Discontinuous Galerkin (HDG) for second-order elliptic problems
Sevilla Càrdenas, Ruben; Huerta, Antonio
The HDG is a new class of discontinuous Galerkin (DG) methods that shares favorable properties with classical mixed methods such as the well known Raviart-Thomas methods. In particular, HDG provides optimal convergence of both the primal and the dual variables of the mixed formulation. This property enables the construction of superconvergent solutions, contrary to other popular DG methods. In addition, its reduced computational cost, compared to other DG methods, has made HDG an attractive alternative for solving problems governed by partial differential equations. A tutorial on HDG for the numerical solution of second-order elliptic problems is presented. Particular emphasis is placed on providing all the necessary details for the implementation of HDG methods.
Fri, 17 Jun 2016 14:10:02 GMThttp://hdl.handle.net/2117/881372016-06-17T14:10:02ZSevilla Càrdenas, RubenHuerta, AntonioThe HDG is a new class of discontinuous Galerkin (DG) methods that shares favorable properties with classical mixed methods such as the well known Raviart-Thomas methods. In particular, HDG provides optimal convergence of both the primal and the dual variables of the mixed formulation. This property enables the construction of superconvergent solutions, contrary to other popular DG methods. In addition, its reduced computational cost, compared to other DG methods, has made HDG an attractive alternative for solving problems governed by partial differential equations. A tutorial on HDG for the numerical solution of second-order elliptic problems is presented. Particular emphasis is placed on providing all the necessary details for the implementation of HDG methods.Master-slave approach for the modelling of joints with dependent degrees of freedom in flexible mechanisms
http://hdl.handle.net/2117/87479
Master-slave approach for the modelling of joints with dependent degrees of freedom in flexible mechanisms
Muñoz Romero, José; Jelenic, Gordan; Crisfield, M. A.
The analysis of multibody systems requires an exact description of the kinematics of the joints involved. In the present work the master–slave approach is employed and endowed with the possibility of including several more complex types of joints. We present the formulation for joints where some relation between the different released degrees of freedom exists such as the screw joint, the rack-and-pinion joint or the cam joint. These joints are implemented in conjunction with geometrically exact beams and an energy-momentum conserving time-stepping algorithm
Mon, 30 May 2016 08:41:00 GMThttp://hdl.handle.net/2117/874792016-05-30T08:41:00ZMuñoz Romero, JoséJelenic, GordanCrisfield, M. A.The analysis of multibody systems requires an exact description of the kinematics of the joints involved. In the present work the master–slave approach is employed and endowed with the possibility of including several more complex types of joints. We present the formulation for joints where some relation between the different released degrees of freedom exists such as the screw joint, the rack-and-pinion joint or the cam joint. These joints are implemented in conjunction with geometrically exact beams and an energy-momentum conserving time-stepping algorithmSpectral analysis of the Beznar dam accelerogram. Comparison with results in the northeastern of Spain
http://hdl.handle.net/2117/87083
Spectral analysis of the Beznar dam accelerogram. Comparison with results in the northeastern of Spain
Canas Torres, José Antonio; Barbat Barbat, Horia Alejandro; Pujades Beneit, Lluís; Egozcue Rubí, Juan José; Sarrate Ramos, Josep
Numerical analysis applied to the Beznar dam accelerograms (longitudinal and transversal components) shows that the Fourier amplitude spectrum is a good approximation to the pseudo-velocity spectra. Thís fact makes possible to use displacement ar velocíty seismograrns to generate acceleration of the ground in places
where acceleration data are not available.
Maximae accelerations determined near and at the Beznar dam are compared wíth the predicted acceleration values far the regían compressed by the Pyrenees Mountains, the lberic System and the Catalonia Coastal Mountains usíng a established theoretical formula
far this region. Theoretical and observad values are consistent among them.
Tue, 17 May 2016 07:55:41 GMThttp://hdl.handle.net/2117/870832016-05-17T07:55:41ZCanas Torres, José AntonioBarbat Barbat, Horia AlejandroPujades Beneit, LluísEgozcue Rubí, Juan JoséSarrate Ramos, JosepNumerical analysis applied to the Beznar dam accelerograms (longitudinal and transversal components) shows that the Fourier amplitude spectrum is a good approximation to the pseudo-velocity spectra. Thís fact makes possible to use displacement ar velocíty seismograrns to generate acceleration of the ground in places
where acceleration data are not available.
Maximae accelerations determined near and at the Beznar dam are compared wíth the predicted acceleration values far the regían compressed by the Pyrenees Mountains, the lberic System and the Catalonia Coastal Mountains usíng a established theoretical formula
far this region. Theoretical and observad values are consistent among them.Boundary element method based on preliminary discretization
http://hdl.handle.net/2117/87019
Boundary element method based on preliminary discretization
Poblet-Puig, Jordi; Valyaev, Valery; Shanin, Andrey
A new numerical method for solving wave diffraction problems is given. The method is based on the concept of boundary elements; i.e., the unknown values are the field values on the surface of the scatterer. An analog of a boundary element method rather than a numerical approximation of the initial (continuous) problem is constructed for an approximate statement of the problem on the discrete lattice. Although it reduces the accuracy of the method, it helps to simplify the implementation significantly since the Green functions of the problem are no longer singular. In order to ensure the solution to the diffraction problem is unique (i.e., to suppress fictitious resonances), a new method is constructed similarly to the CFIE approach developed for the classical boundary element method.
The final publication is available at Springer via http://dx.doi.org/10.1134/S2070048214020082
Thu, 12 May 2016 13:41:06 GMThttp://hdl.handle.net/2117/870192016-05-12T13:41:06ZPoblet-Puig, JordiValyaev, ValeryShanin, AndreyA new numerical method for solving wave diffraction problems is given. The method is based on the concept of boundary elements; i.e., the unknown values are the field values on the surface of the scatterer. An analog of a boundary element method rather than a numerical approximation of the initial (continuous) problem is constructed for an approximate statement of the problem on the discrete lattice. Although it reduces the accuracy of the method, it helps to simplify the implementation significantly since the Green functions of the problem are no longer singular. In order to ensure the solution to the diffraction problem is unique (i.e., to suppress fictitious resonances), a new method is constructed similarly to the CFIE approach developed for the classical boundary element method.An error estimator for separated representations of highly multidimensional models
http://hdl.handle.net/2117/87000
An error estimator for separated representations of highly multidimensional models
Asaad Ammaar, Mouafk; Chinesta, F.; Díez, F.; Huerta, Antonio
Thu, 12 May 2016 10:49:40 GMThttp://hdl.handle.net/2117/870002016-05-12T10:49:40ZAsaad Ammaar, MouafkChinesta, F.Díez, F.Huerta, AntonioNumerical modeling of undersea acoustics using a partition of unity method with plane waves enrichment
http://hdl.handle.net/2117/86965
Numerical modeling of undersea acoustics using a partition of unity method with plane waves enrichment
Hospital Bravo, Raúl; Sarrate Ramos, Josep; Díez, Pedro
A new 2D numerical model to predict the underwater acoustic propagation is obtained by exploring the potential of the Partition of Unity Method (PUM) enriched with plane waves. The aim of the work is to obtain sound pressure level distributions when multiple operational noise sources are present, in order to assess the acoustic impact over the marine fauna. The model takes advantage of the suitability of the PUM for solving the Helmholtz equation, especially for the practical case of large domains and medium frequencies. The seawater acoustic absorption and the acoustic reflectance of the sea surface and sea bottom are explicitly considered, and perfectly matched layers (PML) are placed at the lateral artificial boundaries to avoid spurious reflexions. The model includes semi-analytical integration rules which are adapted to highly oscillatory integrands with the aim of reducing the computational cost of the integration step. In addition, we develop a novel strategy to mitigate the ill-conditioning of the elemental and global system matrices. Specifically, we compute a low-rank approximation of the local space of solutions, which in turn reduces the number of degrees of freedom, the CPU time and the memory footprint. Numerical examples are presented to illustrate the capabilities of the model and to assess its accuracy.
The final publication is available at Springer via http://dx.doi.org/10.1007/s00466-015-1257-8
Wed, 11 May 2016 17:52:15 GMThttp://hdl.handle.net/2117/869652016-05-11T17:52:15ZHospital Bravo, RaúlSarrate Ramos, JosepDíez, PedroA new 2D numerical model to predict the underwater acoustic propagation is obtained by exploring the potential of the Partition of Unity Method (PUM) enriched with plane waves. The aim of the work is to obtain sound pressure level distributions when multiple operational noise sources are present, in order to assess the acoustic impact over the marine fauna. The model takes advantage of the suitability of the PUM for solving the Helmholtz equation, especially for the practical case of large domains and medium frequencies. The seawater acoustic absorption and the acoustic reflectance of the sea surface and sea bottom are explicitly considered, and perfectly matched layers (PML) are placed at the lateral artificial boundaries to avoid spurious reflexions. The model includes semi-analytical integration rules which are adapted to highly oscillatory integrands with the aim of reducing the computational cost of the integration step. In addition, we develop a novel strategy to mitigate the ill-conditioning of the elemental and global system matrices. Specifically, we compute a low-rank approximation of the local space of solutions, which in turn reduces the number of degrees of freedom, the CPU time and the memory footprint. Numerical examples are presented to illustrate the capabilities of the model and to assess its accuracy.Sliding contact conditions using the master-slave approach with application on geometrically non-linear beams
http://hdl.handle.net/2117/86751
Sliding contact conditions using the master-slave approach with application on geometrically non-linear beams
Muñoz Romero, José; Jelenic, Gordan
Frictionless sliding conditions between two bodies are usually defined using either the method of Lagrangian multipliers or by prescribing an artificial (penalty) stiffness which resists the penetration at the contact point. Both of these methods impose the condition that the contact force should be normal to the contact surface, with the Lagrangian multiplier or the penalty parameter serving as a measure of this force. In this work, an alternative approach is undertaken: the frictionless sliding condition is defined through a relationship between nodal parameters of the virtual displacements of a discretised principle of virtual work. This method, which does not involve additional force parameters or degrees of freedom, is known as the master–slave or the minimum-set method and is particularly convenient for displacement-based finite-element implementation. The method is analysed in detail in context of bilateral sliding constraints characteristic of prismatic and cylindrical joints in flexible beam assemblies undergoing large overall motion. Two numerical examples are presented and assessed against the results in the literature.
Mon, 09 May 2016 09:26:06 GMThttp://hdl.handle.net/2117/867512016-05-09T09:26:06ZMuñoz Romero, JoséJelenic, GordanFrictionless sliding conditions between two bodies are usually defined using either the method of Lagrangian multipliers or by prescribing an artificial (penalty) stiffness which resists the penetration at the contact point. Both of these methods impose the condition that the contact force should be normal to the contact surface, with the Lagrangian multiplier or the penalty parameter serving as a measure of this force. In this work, an alternative approach is undertaken: the frictionless sliding condition is defined through a relationship between nodal parameters of the virtual displacements of a discretised principle of virtual work. This method, which does not involve additional force parameters or degrees of freedom, is known as the master–slave or the minimum-set method and is particularly convenient for displacement-based finite-element implementation. The method is analysed in detail in context of bilateral sliding constraints characteristic of prismatic and cylindrical joints in flexible beam assemblies undergoing large overall motion. Two numerical examples are presented and assessed against the results in the literature.