LaCàN  Laboratori de Càlcul Numèric
http://hdl.handle.net/2117/2072
Mon, 16 Oct 2017 22:10:56 GMT
20171016T22:10:56Z
LaCàN  Laboratori de Càlcul Numèric
http://upcommons.upc.edu/bitstream/id/22442/logoLaCaN128.gif
http://hdl.handle.net/2117/2072

Coexistence of wrinkles and blisters in supported graphene
http://hdl.handle.net/2117/108583
Coexistence of wrinkles and blisters in supported graphene
Zang, Kuan; Arroyo Balaguer, Marino
Blisters induced by gas trapped in the interstitial space between supported graphene and the substrate are commonly observed. These blisters are often quasispherical with a circular rim, but polygonal blisters are also common and coexist with wrinkles emanating from their vertices. Here, we show that these different blister morphologies can be understood mechanically in terms of free energy minimization of the supported graphene sheet for a given mass of trapped gas and for a given lateral strain. Using a nonlinear continuum model for supported graphene closely reproducing experimental images of blisters, we build a morphological diagram as a function of strain and trapped mass. We show that the transition from quasispherical to polygonal of blisters as compressive strain is increased is a process of stretching energy relaxation and focusing, as many other crumpling events in thin sheets. Furthermore, to characterize this transition, we theoretically examine the onset of nucleation of short wrinkles in the periphery of a quasispherical blister. Our results are experimentally testable and provide a framework to control complex outofplane motifs in supported graphene combining blisters and wrinkles for strain engineering of graphene.
Tue, 10 Oct 2017 10:43:11 GMT
http://hdl.handle.net/2117/108583
20171010T10:43:11Z
Zang, Kuan
Arroyo Balaguer, Marino
Blisters induced by gas trapped in the interstitial space between supported graphene and the substrate are commonly observed. These blisters are often quasispherical with a circular rim, but polygonal blisters are also common and coexist with wrinkles emanating from their vertices. Here, we show that these different blister morphologies can be understood mechanically in terms of free energy minimization of the supported graphene sheet for a given mass of trapped gas and for a given lateral strain. Using a nonlinear continuum model for supported graphene closely reproducing experimental images of blisters, we build a morphological diagram as a function of strain and trapped mass. We show that the transition from quasispherical to polygonal of blisters as compressive strain is increased is a process of stretching energy relaxation and focusing, as many other crumpling events in thin sheets. Furthermore, to characterize this transition, we theoretically examine the onset of nucleation of short wrinkles in the periphery of a quasispherical blister. Our results are experimentally testable and provide a framework to control complex outofplane motifs in supported graphene combining blisters and wrinkles for strain engineering of graphene.

Radaptivity in limit analysis
http://hdl.handle.net/2117/108434
Radaptivity in limit analysis
Muñoz Romero, José; Hambleton, James; Sloan, Scott
Direct methods aim to find the maximum load factor that a domain made of a plastic material can sustain before undergoing full collapse. Its analytical solution may be posed as a constrained maximisation problem, which is computationally solved by resorting to appropriate discretisation of the relevant fields such as the stress or velocity fields. The actual discrete solution is though strongly dependent on such discretisation, which is defined by a set of nodes, elements, and the type of interpolation.
We here resort to an adaptive strategy that aims to perturb the positions of the nodes in order to improve the solution of the discrete maximisation problem. When the positions of the nodes are taken into account, the optimisation problem becomes highly nonlinear. We approximate this problem as two staggered linear problems, one written in terms of the stress variable (lower bound problem) or velocity variables (upper bound problem), and another with respect to the nodal positions. In this manner, we show that for some simple problems, the computed load factor may be further improved while keeping a constant number of elements.
Fri, 06 Oct 2017 09:34:09 GMT
http://hdl.handle.net/2117/108434
20171006T09:34:09Z
Muñoz Romero, José
Hambleton, James
Sloan, Scott
Direct methods aim to find the maximum load factor that a domain made of a plastic material can sustain before undergoing full collapse. Its analytical solution may be posed as a constrained maximisation problem, which is computationally solved by resorting to appropriate discretisation of the relevant fields such as the stress or velocity fields. The actual discrete solution is though strongly dependent on such discretisation, which is defined by a set of nodes, elements, and the type of interpolation.
We here resort to an adaptive strategy that aims to perturb the positions of the nodes in order to improve the solution of the discrete maximisation problem. When the positions of the nodes are taken into account, the optimisation problem becomes highly nonlinear. We approximate this problem as two staggered linear problems, one written in terms of the stress variable (lower bound problem) or velocity variables (upper bound problem), and another with respect to the nodal positions. In this manner, we show that for some simple problems, the computed load factor may be further improved while keeping a constant number of elements.

Numerical modeling of erosion using an improvement of the extended finite element method
http://hdl.handle.net/2117/108059
Numerical modeling of erosion using an improvement of the extended finite element method
Cottereau, Régis; Díez, Pedro
We present in this paper a numerical model of the erosion of a soil that accounts for both the flow in the open fluid and the flow of fluid through the porous soil. The interface between the open fluid and the soil is represented using a levelset function, and the erosion is controlled by the shear stress vector. The evaluation of the approximate value of this gradient is particularly focused on, and an improved method, called XFE+ method, is presented. Numerical results in 2D and 3D illustrate the accuracy and the potentiality of this method.
This is an Accepted Manuscript of an article published by Taylor & Francis Group in "European journal of environmental and civil engineering" on 2011, available online at: http://www.tandfonline.com/doi/abs/10.1080/19648189.2011.9714848
Wed, 27 Sep 2017 09:09:01 GMT
http://hdl.handle.net/2117/108059
20170927T09:09:01Z
Cottereau, Régis
Díez, Pedro
We present in this paper a numerical model of the erosion of a soil that accounts for both the flow in the open fluid and the flow of fluid through the porous soil. The interface between the open fluid and the soil is represented using a levelset function, and the erosion is controlled by the shear stress vector. The evaluation of the approximate value of this gradient is particularly focused on, and an improved method, called XFE+ method, is presented. Numerical results in 2D and 3D illustrate the accuracy and the potentiality of this method.

The main factors and rules of stress shadow of perpendicular cracks
http://hdl.handle.net/2117/108040
The main factors and rules of stress shadow of perpendicular cracks
Wang, Daobing; Zhou, Fujian; Ge, Hongkui; Zlotnik, Sergio; Yang, Xiangtong; Peng, Jinlong
Based on elasticity theory, we use numerical Galerkin finite element discretization method and implement Matlab finite element code to simulate “stress shadow” distributions of mutual orthogonal fractures. The principal stress and principal distributions have the symmetry characteristic on the intersection (coordinate origin). The relationships between stress shadow and flow pressure ratio, pore pressure, fluid pressure and horizontal stress contract are analyzed, respectively. By these techniques of variable displacement construction, changing the viscosity of the fracturing fluid, exploitation of oil and gas wells changing pump rate and fracturing fluid viscosity, reducing pore pressure and increasing the injection volume, taking the advantages of shadow effect, it is likely to produce a complex fracture network.
Tue, 26 Sep 2017 16:58:22 GMT
http://hdl.handle.net/2117/108040
20170926T16:58:22Z
Wang, Daobing
Zhou, Fujian
Ge, Hongkui
Zlotnik, Sergio
Yang, Xiangtong
Peng, Jinlong
Based on elasticity theory, we use numerical Galerkin finite element discretization method and implement Matlab finite element code to simulate “stress shadow” distributions of mutual orthogonal fractures. The principal stress and principal distributions have the symmetry characteristic on the intersection (coordinate origin). The relationships between stress shadow and flow pressure ratio, pore pressure, fluid pressure and horizontal stress contract are analyzed, respectively. By these techniques of variable displacement construction, changing the viscosity of the fracturing fluid, exploitation of oil and gas wells changing pump rate and fracturing fluid viscosity, reducing pore pressure and increasing the injection volume, taking the advantages of shadow effect, it is likely to produce a complex fracture network.

Monitoring a PGD solver for parametric power flow problems with goaloriented error assessment
http://hdl.handle.net/2117/107471
Monitoring a PGD solver for parametric power flow problems with goaloriented error assessment
García Blanco, Raquel; Borzacchiello, Domenico; Chinesta, Francisco; Díez, Pedro
The parametric analysis of electric grids requires carrying out a large number of Power Flow computations. The different parameters describe loading conditions and grid properties. In this framework, the Proper Generalized Decomposition (PGD) provides a numerical solution explicitly accounting for the parametric dependence. Once the PGD solution is available, exploring the multidimensional parametric space is computationally inexpensive. The aim of this paper is to provide tools to monitor the error associated with this significant computational gain and to guarantee the quality of the PGD solution. In this case, the PGD algorithm consists in three nested loops that correspond to 1) iterating algebraic solver, 2) number of terms in the separable greedy expansion and 3) the alternated directions for each term. In the proposed approach, the three loops are controlled by stopping criteria based on residual goaloriented error estimates. This allows one for using only the computational resources necessary to achieve the accuracy prescribed by the end user. The paper discusses how to compute the goaloriented error estimates. This requires linearizing the error equation and the Quantity of Interest to derive an efficient error representation based on an adjoint problem. The efficiency of the proposed approach is demonstrated on benchmark problems.
This is the peer reviewed version of the following article: [GarcíaBlanco, R., Borzacchiello, D., Chinesta, F., and Diez, P. (2017) Monitoring a PGD solver for parametric power flow problems with goaloriented error assessment. Int. J. Numer. Meth. Engng, 111: 529–552. doi: 10.1002/nme.5470], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.5470/full. This article may be used for noncommercial purposes in accordance with Wiley Terms and Conditions for SelfArchiving.
Wed, 06 Sep 2017 17:48:16 GMT
http://hdl.handle.net/2117/107471
20170906T17:48:16Z
García Blanco, Raquel
Borzacchiello, Domenico
Chinesta, Francisco
Díez, Pedro
The parametric analysis of electric grids requires carrying out a large number of Power Flow computations. The different parameters describe loading conditions and grid properties. In this framework, the Proper Generalized Decomposition (PGD) provides a numerical solution explicitly accounting for the parametric dependence. Once the PGD solution is available, exploring the multidimensional parametric space is computationally inexpensive. The aim of this paper is to provide tools to monitor the error associated with this significant computational gain and to guarantee the quality of the PGD solution. In this case, the PGD algorithm consists in three nested loops that correspond to 1) iterating algebraic solver, 2) number of terms in the separable greedy expansion and 3) the alternated directions for each term. In the proposed approach, the three loops are controlled by stopping criteria based on residual goaloriented error estimates. This allows one for using only the computational resources necessary to achieve the accuracy prescribed by the end user. The paper discusses how to compute the goaloriented error estimates. This requires linearizing the error equation and the Quantity of Interest to derive an efficient error representation based on an adjoint problem. The efficiency of the proposed approach is demonstrated on benchmark problems.

A semianalytical scheme for highly oscillatory integrals over tetrahedra
http://hdl.handle.net/2117/107470
A semianalytical scheme for highly oscillatory integrals over tetrahedra
Hospital Bravo, Raúl; Sarrate Ramos, Josep; Díez, Pedro
This paper details a semianalytical procedure to efficiently integrate the product of a smooth function and a complex exponential over tetrahedral elements. These highly oscillatory integrals appear at the core of different numerical techniques. Here, the Partition of Unity Method (PUM) enriched with plane waves is used as motivation. The high computational cost or the lack of accuracy in computing these integrals is a bottleneck for their application to engineering problems of industrial interest. In this integration rule, the nonoscillatory function is expanded into a set of Lagrange polynomials. In addition, Lagrange polynomials are expressed as a linear combination of the appropriate set of monomials, whose product with the complex exponentials is analytically integrated, leading to 16 specific cases that are developed in detail. Finally, we present several numerical examples to assess the accuracy and the computational efficiency of the proposed method, compared to standard GaussLegendre quadratures.
This is the peer reviewed version of the following article: [HospitalBravo, R., Sarrate, J., and Díez, P. (2017) A semianalytical scheme for highly oscillatory integrals over tetrahedra. Int. J. Numer. Meth. Engng, 111: 703–723. doi: 10.1002/nme.5474], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.5474/full. This article may be used for noncommercial purposes in accordance with Wiley Terms and Conditions for SelfArchiving.
Wed, 06 Sep 2017 17:36:23 GMT
http://hdl.handle.net/2117/107470
20170906T17:36:23Z
Hospital Bravo, Raúl
Sarrate Ramos, Josep
Díez, Pedro
This paper details a semianalytical procedure to efficiently integrate the product of a smooth function and a complex exponential over tetrahedral elements. These highly oscillatory integrals appear at the core of different numerical techniques. Here, the Partition of Unity Method (PUM) enriched with plane waves is used as motivation. The high computational cost or the lack of accuracy in computing these integrals is a bottleneck for their application to engineering problems of industrial interest. In this integration rule, the nonoscillatory function is expanded into a set of Lagrange polynomials. In addition, Lagrange polynomials are expressed as a linear combination of the appropriate set of monomials, whose product with the complex exponentials is analytically integrated, leading to 16 specific cases that are developed in detail. Finally, we present several numerical examples to assess the accuracy and the computational efficiency of the proposed method, compared to standard GaussLegendre quadratures.

Experimental numerical correlation of subsystem contributions in the advanced transfer path analysis framework
http://hdl.handle.net/2117/107407
Experimental numerical correlation of subsystem contributions in the advanced transfer path analysis framework
Magrans Fontrodona, Francesc Xavier; Arcas, Kevin; Vicens Rodríguez, Pere; PobletPuig, Jordi; Rodríguez Ferran, Antonio
In a complex vibroacoustic system the overall noise or vibration in a given location is the sum of multiple subsystem contributions. From an experimental perspective, the total noise can be directly measured but not the contributions. Methods based in transmissivity measurements, as ATPA, allow to find these contributions experimentally and understand the system behaviour through the path concept. Two different contributions to the ATPA method are included here. On the one hand, a numerical model that simulates a simple vibroacoustic problem is shown. This is a closed cuboidshaped box with air cavity inside. The ATPA experimental procedure is reproduced numerically in order to gain knowledge on some aspects of the method. On the other hand, a technique for the auto matic identification of the subsystems which is based on the path concept and transfer matrices is applied to the acoustic problem of coupled rooms. The proper definition of subsystems influences very much the reliability of ATPA results.
Tue, 05 Sep 2017 13:49:22 GMT
http://hdl.handle.net/2117/107407
20170905T13:49:22Z
Magrans Fontrodona, Francesc Xavier
Arcas, Kevin
Vicens Rodríguez, Pere
PobletPuig, Jordi
Rodríguez Ferran, Antonio
In a complex vibroacoustic system the overall noise or vibration in a given location is the sum of multiple subsystem contributions. From an experimental perspective, the total noise can be directly measured but not the contributions. Methods based in transmissivity measurements, as ATPA, allow to find these contributions experimentally and understand the system behaviour through the path concept. Two different contributions to the ATPA method are included here. On the one hand, a numerical model that simulates a simple vibroacoustic problem is shown. This is a closed cuboidshaped box with air cavity inside. The ATPA experimental procedure is reproduced numerically in order to gain knowledge on some aspects of the method. On the other hand, a technique for the auto matic identification of the subsystems which is based on the path concept and transfer matrices is applied to the acoustic problem of coupled rooms. The proper definition of subsystems influences very much the reliability of ATPA results.

Discrete mesomodeling of steel fiber reinforced concrete: simulation of flexural behavior
http://hdl.handle.net/2117/107371
Discrete mesomodeling of steel fiber reinforced concrete: simulation of flexural behavior
Pros Parés, Alba; Díez, Pedro; Molins i Borrell, Climent
Concrete provides with a variety of innovative designs, but two characteristics have limited its use: it is brittle and weak under tension. One way to overcome this problem is to add steel fibers into the concrete matrix, a technique introduced in the 70's called Steel Fiber Reinforced Concrete (SFRC). Fibers shape, length and slenderness
characterize its behavior. It is also necessary to take into account the orientation and the distribution of the fibers in the concrete matrix. Different flexural tests are reproduced considering SFRC in order to characterize and analyze the influence of the fibers. Inthe present work, a numerical tool for including fibers into plain concrete is presented. The numerical approach considered is based on the idea of the Immersed Boundary (IB) methods which were designed for solving problems of a solid structure immersed on a fluid. Herein, the IB method is applied for SFRC considering the concrete accounting
for fluid and the steel fibers playing the role of the solid structure. Thus, the philosophy of the IB methodology is used to couple the behavior of the two systems, the concrete bulk and the fiber cloud, precluding the need of matching finite element meshes. Note that, considering the different size scales and the intricate geometry of the fiber cloud,
the conformal matching of the meshes would be a restriction resulting in a practically unaffordable mesh. Concrete is modeled considering a nonlinear model and to take into account the whole process between fibers and concrete, the constitutive equations of the fibers are based on analytical expressions available in the literature describing the pullout test behavior. The constitutive expressions depend on (1) the angle between each fiber and the crack of the concrete specimen and (2) the shape of the fiber.
Mon, 04 Sep 2017 13:51:20 GMT
http://hdl.handle.net/2117/107371
20170904T13:51:20Z
Pros Parés, Alba
Díez, Pedro
Molins i Borrell, Climent
Concrete provides with a variety of innovative designs, but two characteristics have limited its use: it is brittle and weak under tension. One way to overcome this problem is to add steel fibers into the concrete matrix, a technique introduced in the 70's called Steel Fiber Reinforced Concrete (SFRC). Fibers shape, length and slenderness
characterize its behavior. It is also necessary to take into account the orientation and the distribution of the fibers in the concrete matrix. Different flexural tests are reproduced considering SFRC in order to characterize and analyze the influence of the fibers. Inthe present work, a numerical tool for including fibers into plain concrete is presented. The numerical approach considered is based on the idea of the Immersed Boundary (IB) methods which were designed for solving problems of a solid structure immersed on a fluid. Herein, the IB method is applied for SFRC considering the concrete accounting
for fluid and the steel fibers playing the role of the solid structure. Thus, the philosophy of the IB methodology is used to couple the behavior of the two systems, the concrete bulk and the fiber cloud, precluding the need of matching finite element meshes. Note that, considering the different size scales and the intricate geometry of the fiber cloud,
the conformal matching of the meshes would be a restriction resulting in a practically unaffordable mesh. Concrete is modeled considering a nonlinear model and to take into account the whole process between fibers and concrete, the constitutive equations of the fibers are based on analytical expressions available in the literature describing the pullout test behavior. The constitutive expressions depend on (1) the angle between each fiber and the crack of the concrete specimen and (2) the shape of the fiber.

A subsystem identification method based on the path concept with coupling strength estimation
http://hdl.handle.net/2117/107082
A subsystem identification method based on the path concept with coupling strength estimation
Magrans Fontrodona, Francesc Xavier; PobletPuig, Jordi; Rodríguez Ferran, Antonio
For complex geometries, the definition of the subsystems is not a straightforward task. We present here a subsystem identification method based on the direct transfer matrix, which represents the firstorder paths. The key ingredient is a cluster analysis of the rows of the powers of the transfer matrix. These powers represent highorder paths in the system and are more affected than loworder paths by damping.
Once subsystems are identified, the proposed approach also provides a quantification of the degree of coupling between subsystems. This information is relevant to decide whether a subsystem may be analysed in a computer model or measured in the laboratory independently of the rest or subsystems or not. The two features (subsystem identification and quantification of the degree of coupling) are illustrated by means of numerical examples: plates coupled by means of springs and rooms connected by means of a cavity.
Tue, 22 Aug 2017 10:10:36 GMT
http://hdl.handle.net/2117/107082
20170822T10:10:36Z
Magrans Fontrodona, Francesc Xavier
PobletPuig, Jordi
Rodríguez Ferran, Antonio
For complex geometries, the definition of the subsystems is not a straightforward task. We present here a subsystem identification method based on the direct transfer matrix, which represents the firstorder paths. The key ingredient is a cluster analysis of the rows of the powers of the transfer matrix. These powers represent highorder paths in the system and are more affected than loworder paths by damping.
Once subsystems are identified, the proposed approach also provides a quantification of the degree of coupling between subsystems. This information is relevant to decide whether a subsystem may be analysed in a computer model or measured in the laboratory independently of the rest or subsystems or not. The two features (subsystem identification and quantification of the degree of coupling) are illustrated by means of numerical examples: plates coupled by means of springs and rooms connected by means of a cavity.

Catalogue of vibration reduction index formulas for heavy junctions based on numerical simulations
http://hdl.handle.net/2117/106840
Catalogue of vibration reduction index formulas for heavy junctions based on numerical simulations
PobletPuig, Jordi; GuigouCarter, Catherine
The vibration reduction index (Kij) is a key parameter in the prediction of flanking transmissions according to the EN12354 standard. Formulas for the evaluation of Kij in L, T and X junctions that depend on the mass ratio are available in the Annex E. Junctions of straight elements with different thickness or thin elastic layers are also included. However, other junction types that are important for building industry are not considered: Hshaped junctions, L or T junctions not forming a right angle, asymmetrical Tjunctions , Xjunctions where only one of the parts is different (thickness or material) from the other two/three. In the current research, expressions for these noncovered junctions are provided. They are obtained by means of numerical simulations based on the spectral finite element method. Kij is predicted for a large population of junctions, considering usual thicknesses and heavy material combinations (no lightweight frame systems have been considered). Statistical analysis is carried out to obtain relatively simple formulae that could be used in acoustic design projects without the need for timeconsuming computations with finite element software.
© (2017) S. Hirzel Verlag/European Acoustics Association.
The definitive publisherauthenticated version is available online at http://www.ingentaconnect.com/contentone/dav/aaua/2017/00000103/00000004/art00011 and http//dx.doi.org/10.3813/AAA.919091.
Readers must contact the publisher for reprint or permission to use the material in any form.
Tue, 25 Jul 2017 14:29:02 GMT
http://hdl.handle.net/2117/106840
20170725T14:29:02Z
PobletPuig, Jordi
GuigouCarter, Catherine
The vibration reduction index (Kij) is a key parameter in the prediction of flanking transmissions according to the EN12354 standard. Formulas for the evaluation of Kij in L, T and X junctions that depend on the mass ratio are available in the Annex E. Junctions of straight elements with different thickness or thin elastic layers are also included. However, other junction types that are important for building industry are not considered: Hshaped junctions, L or T junctions not forming a right angle, asymmetrical Tjunctions , Xjunctions where only one of the parts is different (thickness or material) from the other two/three. In the current research, expressions for these noncovered junctions are provided. They are obtained by means of numerical simulations based on the spectral finite element method. Kij is predicted for a large population of junctions, considering usual thicknesses and heavy material combinations (no lightweight frame systems have been considered). Statistical analysis is carried out to obtain relatively simple formulae that could be used in acoustic design projects without the need for timeconsuming computations with finite element software.