A BEM based on the Bézier/Bernstein polynomial for acoustic waveguide modelization

42nd International Conference on Boundary Elements and other Mesh Reduction Methods, BEM/MRM 2019; ITeCons-University of CoimbraCoimbra; Portugal; 2 July 2019 through 4 July 2019; Code 155806. Publicado en WIT Transactions on Engineering Sciences, Vol 126This paper proposes a novel boundary element approach formulated on the Bézier–Bernstein basis to yield a geometry-independent field approximation. The proposed method is geometrically based on both computer aided design (CAD) and isogeometric analysis (IGA), but field variables are independently approximated from the geometry. This approach allows the appropriate approximation functions for the geometry and variable field to be chosen. We use the Bézier–Bernstein form of a polynomial as an approximation basis to represent both geometry and field variables. The solution of the element interpolation problem in the Bézier–Bernstein space defines generalised Lagrange interpolation functions that are used as element shape functions. The resulting Bernstein–Vandermonde matrix related to the Bézier–Bernstein interpolation problem is inverted using the Newton–Bernstein algorithm. The applicability of the proposed method is demonstrated by solving the Helmholtz equation over an unbounded region in a two-and-a-half dimensional (2.5D) domain.Ministerio de Economía y Competitividad BIA2016-75042-C2-1-

A 2.5D BEM-FEM using a spectral approach to study scattered waves in fluid–solid interaction problems

42nd International Conference on Boundary Elements and other Mesh Reduction Methods, BEM/MRM 2019; ITeCons-University of Coimbra, Coimbra; Portugal; 2 July 2019 through 4 July 2019. - Publicado en WIT Transactions on Engineering Sciences, Volume 126, 2019, Pages 111-123This work presents a two-and-a-half dimensional (2.5D) spectral formulation based on the finite element method (FEM) and the boundary element method (BEM) to study wave propagation in acoustic and elastic waveguides. The analysis involved superposing two dimensional (2D) problems with different longitudinal wavenumbers. A spectral finite element (SFEM) is proposed to represent waveguides in solids with arbitrary cross-section. Moreover, the BEM is extended to its spectral formulation (SBEM) to study unbounded fluid media and acoustic enclosures. Both approaches use Lagrange polynomials as element shape functions at the Legendre–Gauss–Lobatto (LGL) points. The fluid and solid subdomains are coupled by applying the appropriate boundary conditions at the limiting interface. The proposed method is verified by means of a benchmark problem regarding the scattering of waves by an elastic inclusion. The convergence and the computational effort are evaluated for different h-p strategies. Numerical results show good agreement with the reference solution. Finally, the proposed method is used to study the pressure field generated by an array of elastic fluid-filled scatterers immersed in an acoustic mediumMinisterio de Economía y Competitividad BIA2016-75042-C2-1-

A novel 2.5D spectral approach for studying thin-walled waveguides with fluid-acoustic interaction

This paper presents a novel formulation of two spectral elements to study guided waves in coupled problems involving thin-walled structures and fluid-acoustic enclosures. The aim of the proposed work is the development of a new efficient computational method to study problems where geometry and properties are invariant in one direction, commonly found in the analysis of guided waves. This assumption allows using a two-and-a-half dimensional (2.5D) spectral formulation in the wavenumber-frequency domain. The novelty of the proposed work is the formulation of spectral plate and fluid elements with an arbitrary order in 2.5D. A plate element based on a Reissner-Mindlin/Kirchhoff-Love mixed formulation is proposed to represent the thin-walled structure. This element uses approximation functions to overcome the difficulties to formulate elements with an arbitrary order from functions. The proposed element uses a substitute transverse shear strain field to avoid shear locking effects. Three benchmark problems are studied to check the convergence and the computational effort for different strategies. Accurate results are found with an appropriate combination of element size and order of the approximation functions allowing at least six nodes per wavelength. The effectiveness of the proposed elements is demonstrated studying the wave propagation in a water duct with a flexible side and an acoustic cavity coupled to a Helmholtz resonator.Ministerio de Economía y Competitividad BIA2013-43085-P y BIA2016-75042-C2-1-RCentro Informático Científico de Andalucía (CICA

Modeling elastic wave propagation in fluid-filled boreholes drilled in nonhomogeneous media: BEM – MLPG versus BEM-FEM coupling

The efficiency of two coupling formulations, the boundary element method (BEM)-meshless local Petrov–Galerkin (MLPG) versus the BEM-finite element method (FEM), used to simulate the elastic wave propagation in fluid-filled boreholes generated by a blast load, is compared. The longitudinal geometry is assumed to be invariant in the axial direction (2.5D formulation). The material properties in the vicinity of the borehole are assumed to be nonhomogeneous as a result of the construction process and the ageing of the material. In both models, the BEM is used to tackle the propagation within the fluid domain inside the borehole and the unbounded homogeneous domain. The MLPG and the FEM are used to simulate the confined, damaged, nonhomogeneous, surrounding borehole, thus utilizing the advantages of these methods in modeling nonhomogeneous bounded media. In both numerical techniques the coupling is accomplished directly at the nodal points located at the common interfaces. Continuity of stresses and displacements is imposed at the solid–solid interface, while continuity of normal stresses and displacements and null shear stress are prescribed at the fluid–solid interface. The performance of each coupled BEM-MLPG and BEM-FEM approach is determined using referenced results provided by an analytical solution developed for a circular multi-layered subdomain. The comparison of the coupled techniques is evaluated for different excitation frequencies, axial wavenumbers and degrees of freedom (nodal points).Ministerio de Economía y Competitividad BIA2013-43085-PCentro Informático Científico de Andalucía (CICA

On the formulation of a BEM in the Bézier–Bernstein space for the solution of Helmholtz equation

This paper proposes a novel boundary element approach formulated on the Bézier-Bernstein basis to yield a geometry-independent field approximation. The proposed method is geometrically based on both computer aid design (CAD) and isogeometric analysis (IGA), but field variables are independently approximated from the geometry. This approach allows the appropriate approximation functions for the geometry and variable field to be chosen. We use the Bézier–Bernstein form of a polynomial as an approximation basis to represent both geometry and field variables. The solution of the element interpolation problem in the Bézier–Bernstein space defines generalised Lagrange interpolation functions that are used as element shape functions. The resulting Bernstein–Vandermonde matrix related to the Bézier–Bernstein interpolation problem is inverted using the Newton-Bernstein algorithm. The applicability of the proposed method is demonstrated solving the Helmholtz equation over an unbounded region in a two-and-a-half dimensional (2.5D) domainMinisterio de Economía y Competitividad BIA2016-75042-C2-1-RFondos FEDER POCI-01-0247-FEDER-01775

A 2.5D spectral approach to represent acoustic and elastic waveguides interaction on thin slab structures

Faculty of Civil and Industrial Engineering; Rome; Italy; 10 September 2017 through 13 September 2017In this paper, we propose a spectral element method (SEM) to study guided waves in coupled problems involving thin-walled structures and fluid-acoustic cavities. The numerical method is based on the subdomain decomposition of the fluid-structure system. Two spectral elements are developed to represent the fluid and the structure. A plate element based on a mixed ReissnerMindlin and Kirchhoff-Love formulation is proposed to represent the thin-walled structure. This element uses C0 approximation functions to overcome the difficulties to formulate elements with arbitrary order from C1 functions. The proposed element uses a substitute transverse shear strain field resulting free shear locking. The fluid element is derived from the Helmholtz equation. These elements use Lagrange polynomials as shape functions at the Legendre-Gauss-Lobatto (LGL) points. The analysis is carried out by a two-and-a-half dimension (2.5D) approach in the wavenumber-frequency domain. The guided wave in a fluid cavity with a flexible side is analysed.Ministerio de Economía y Competitividad. BIA2013-43085-PMinisterio de Economía y Competitividad. BIA2016-75042-C2-1-

Acoustic waves scattered by elastic waveguides using a spectral approach with a 2.5D coupled boundary-finite element method

This work presents a two-and-a-half dimensional (2.5D) spectral formulation based on the finite element method (FEM) and the boundary element method (BEM) to study wave propagation in acoustic and elastic waveguides. The analysis involved superposing two dimensional (2D) problems with different longitudinal wavenumbers. A spectral finite element (SFEM) is proposed to represent waveguides in solids with arbitrary cross-section. Moreover, the BEM is extended to its spectral formulation (SBEM) to study unbounded fluid media and acoustic enclosures. Both approaches use Lagrange polynomials as element shape functions at the Legendre–Gauss–Lobatto (LGL) points. The fluid and solid subdomains are coupled by applying the appropriate boundary conditions at the limiting interface. The proposed method is verified by means of two benchmark problems: wave propagation in an unbounded acoustic medium and the scattering of waves by an elastic inclusion. The convergence and the computational effort are evaluated for different strategies. Numerical results show good agreement with the reference solution. Finally, the proposed method is used to study the pressure field generated by an array of elastic fluid-filled scatterers immersed in an acoustic mediumMinisterio de Economía y Competitividad BIA2016-75042-C2-1-RFondos FEDER POCI-01-0247-FEDER-01775

Modelling of acoustic and elastic wave propagation from underground structures using a 2.5D BEM-FEM approach

This paper presents a numerical method based on a two-and-a-half dimensional (2.5D) boundary element-finite element (BEM-FEM) coupled formulation to study noise and vibration from underground structures. The proposed model properly represents the soil-structure interaction problem and the radiated noise and vibration. The soil is modelled with the boundary element method, and the Green's function for a fluid-solid formation is taken as the fundamental solution to represent a solid half-space flattened by a fluid medium, which represents the soil and the air above the ground surface. The finite element method is used to represent structures and enclosed air volumes. The problem representation is limited to a soil-structure interface and the ground surface does not need to be discretised. Radiated noise and vibration are determined after the soil-structure interaction problem has been solved. We verify the proposed method by comparing the solution with an analytical solution for the wave propagation in a fluid-solid medium. Three examples are given to illustrate the noise and vibration radiated by tunnels. The results show that the soil-structure interaction influences the sound pressure field above the ground surfaceMinisterio de Economía y Competitividad BIA2013-43085-

Experimental and numerical evaluation of the wind load on the 516 Arouca pedestrian suspension bridge

The present work analyses the wind load effects on the 516 Arouca bridge, the world's longest pedestrian suspension bridge in 2020. Computational fluid dynamics (CFD) was used to model a range of wind angles of attack between −8° and +8°. The simulations were performed by solving the steady-state Reynolds averaged Navier-Stokes (RANS) equations with the k-ω shear stress transport (SST) model. The fluid domain size was analysed by comparing the fluid flow behaviour for three different downstream sizes. It was shown that the downstream flow is not greatly affected by the bridge body due to the high opening surfaces of the bridge. Therefore, the most appropriate domain size considering the computation time was selected. The simulations were carried out for different bridge configurations to determine the influence of the upper guard of the tray deck and the suspended cables on the generated loads. The numerical results were validated by performing different wind tunnel tests using a reduced scale prototype. The predicted aerodynamic characteristics showed good agreement with the experimental results.FITEC – Fundo de Inovaçao, Tecnologia e Economia Circular CIT/2018/23Ministerio de Ciencia, Innovación y Universidades PID 2019-109622RBFEDER Andalucía US-12649

Theoretical and experimental analysis of the quasi-static and dynamic behaviour of the world's longest suspension footbridge in 2020

This work validates the simplified theoretical, analytical and numerical models used in the preliminary design stage of the 516 Arouca footbridge over the River Paiva (Portugal), the world's longest suspension footbridge. The models were used to define the configuration of the bridge under static loading and the eigenfrequencies excited under dynamic loading. The three-dimensional finite element model used in the detailed design of the bridge is briefly described. The paper also presents in situ experimental results. Tests were performed to study the static and dynamic behaviour of the footbridge under service loads and to assess the analytical/numerical modelling assumptions. The structure was subjected to loads generated by the wind and by a group of people crossing the bridge. Global Navigation Satellite System (GNSS) antennas were used to record the displacements of the bridge under quasi-static loadings caused by the people crossing the bridge at a slow pace. The data recorded by a set of seismometers allowed us to identify the natural frequencies and modes of vibration. The agreement between all the analytical/numerical solutions and the experimental data was found to be very good. The data recorded also allowed one to evaluate the damping coefficients of the bridge for the different vibration modes, something that is very difficult to predict in the design stage.Ministerio de Ciencia, Innovación y Universidades PID2019-109622RB-C21FEDER Andalucía 2014-2020 Operational Program (US-126491