LaCàN - Laboratori de Càlcul Numèric
http://hdl.handle.net/2117/2072
2017-10-20T12:18:34ZAAR-based decomposition method for lower bound limit analysis
http://hdl.handle.net/2117/108908
AAR-based decomposition method for lower bound limit analysis
Muñoz Romero, José; Rabiei, Nima
Despite the recent progress in optimisation techniques, finite-element stability analysis of realistic three-dimensional problems is still hampered by the size of the resulting optimisation problem. Current solvers may take a prohibitive computational time, if they give a solution at all. The possible remedies to this are the design of adaptive de-remeshing techniques, decomposition of the system of equations or of the optimisation problem. This paper concentrates on the last approach, and presents an algorithm especially suited for limit analysis. Optimisation problems in limit analysis are in general convex but non-linear. This fact renders the design of decomposition techniques specially challenging. The efficiency of general approaches such as Benders or Dantzig–Wolfe is not always satisfactory, and strongly depends on the structure of the optimisation problem. This work presents a new method that is based on rewriting the feasibility region of the global optimisation problem as the intersection of two subsets. By resorting to the averaged alternating reflections (AAR) method in order to find the distance between the sets, the optimisation problem is successfully solved in a decomposed manner. Some representative examples illustrate the application of the method and its efficiency with respect to other well-known decomposition algorithms.
2017-10-20T10:53:50ZMuñoz Romero, JoséRabiei, NimaDespite the recent progress in optimisation techniques, finite-element stability analysis of realistic three-dimensional problems is still hampered by the size of the resulting optimisation problem. Current solvers may take a prohibitive computational time, if they give a solution at all. The possible remedies to this are the design of adaptive de-remeshing techniques, decomposition of the system of equations or of the optimisation problem. This paper concentrates on the last approach, and presents an algorithm especially suited for limit analysis. Optimisation problems in limit analysis are in general convex but non-linear. This fact renders the design of decomposition techniques specially challenging. The efficiency of general approaches such as Benders or Dantzig–Wolfe is not always satisfactory, and strongly depends on the structure of the optimisation problem. This work presents a new method that is based on rewriting the feasibility region of the global optimisation problem as the intersection of two subsets. By resorting to the averaged alternating reflections (AAR) method in order to find the distance between the sets, the optimisation problem is successfully solved in a decomposed manner. Some representative examples illustrate the application of the method and its efficiency with respect to other well-known decomposition algorithms.Ferroelectrics as smart mechanical materials
http://hdl.handle.net/2117/108844
Ferroelectrics as smart mechanical materials
Cordero Edwards, Kumara; Domingo Marimon, Neus; Abdollahi Hosnijeh, Amir; Sort Viñas, Jordi; Catalan, Gustau
The mechanical properties of materials are insensitive to space inversion, even when they are crystallographically asymmetric. In practice, this means that turning a piezoelectric crystal upside down or switching the polarization of a ferroelectric should not change its mechanical response. Strain gradients, however, introduce an additional source of asymmetry that has mechanical consequences. Using nanoindentation and contact-resonance force microscopy, this study demonstrates that the mechanical response to indentation of a uniaxial ferroelectric (LiNbO3) does change when its polarity is switched, and use this mechanical asymmetry both to quantify its flexoelectricity and to mechanically read the sign of its ferroelectric domains.
This is the peer reviewed version of the following article: Cordero, K., Domingo Marimon, Neus, Abdollahi, A., Sort Viñas, Jordi, Catalan, G. Ferroelectrics as smart mechanical materials. "Advanced materials", 21 Juliol 2017, vol. 29, núm. 37, p. 1-6, which has been published in final form at DOI: 10.1002/adma.201702210. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
2017-10-19T08:43:20ZCordero Edwards, KumaraDomingo Marimon, NeusAbdollahi Hosnijeh, AmirSort Viñas, JordiCatalan, GustauThe mechanical properties of materials are insensitive to space inversion, even when they are crystallographically asymmetric. In practice, this means that turning a piezoelectric crystal upside down or switching the polarization of a ferroelectric should not change its mechanical response. Strain gradients, however, introduce an additional source of asymmetry that has mechanical consequences. Using nanoindentation and contact-resonance force microscopy, this study demonstrates that the mechanical response to indentation of a uniaxial ferroelectric (LiNbO3) does change when its polarity is switched, and use this mechanical asymmetry both to quantify its flexoelectricity and to mechanically read the sign of its ferroelectric domains.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 quasi-spherical 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 quasi-spherical 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 quasi-spherical blister. Our results are experimentally testable and provide a framework to control complex out-of-plane motifs in supported graphene combining blisters and wrinkles for strain engineering of graphene.
2017-10-10T10:43:11ZZang, KuanArroyo Balaguer, MarinoBlisters induced by gas trapped in the interstitial space between supported graphene and the substrate are commonly observed. These blisters are often quasi-spherical 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 quasi-spherical 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 quasi-spherical blister. Our results are experimentally testable and provide a framework to control complex out-of-plane motifs in supported graphene combining blisters and wrinkles for strain engineering of graphene.R-adaptivity in limit analysis
http://hdl.handle.net/2117/108434
R-adaptivity 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 non-linear. 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.
2017-10-06T09:34:09ZMuñoz Romero, JoséHambleton, JamesSloan, ScottDirect 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 non-linear. 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 level-set 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
2017-09-27T09:09:01ZCottereau, RégisDíez, PedroWe 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 level-set 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.
2017-09-26T16:58:22ZWang, DaobingZhou, FujianGe, HongkuiZlotnik, SergioYang, XiangtongPeng, JinlongBased 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 goal-oriented error assessment
http://hdl.handle.net/2117/107471
Monitoring a PGD solver for parametric power flow problems with goal-oriented 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 goal-oriented 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 goal-oriented 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: [García-Blanco, R., Borzacchiello, D., Chinesta, F., and Diez, P. (2017) Monitoring a PGD solver for parametric power flow problems with goal-oriented 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 non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
2017-09-06T17:48:16ZGarcía Blanco, RaquelBorzacchiello, DomenicoChinesta, FranciscoDíez, PedroThe 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 goal-oriented 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 goal-oriented 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 semi-analytical scheme for highly oscillatory integrals over tetrahedra
http://hdl.handle.net/2117/107470
A semi-analytical scheme for highly oscillatory integrals over tetrahedra
Hospital Bravo, Raúl; Sarrate Ramos, Josep; Díez, Pedro
This paper details a semi-analytical 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 non-oscillatory 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 Gauss-Legendre quadratures.
This is the peer reviewed version of the following article: [Hospital-Bravo, R., Sarrate, J., and Díez, P. (2017) A semi-analytical 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 non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
2017-09-06T17:36:23ZHospital Bravo, RaúlSarrate Ramos, JosepDíez, PedroThis paper details a semi-analytical 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 non-oscillatory 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 Gauss-Legendre 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; Poblet-Puig, 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 cuboid-shaped 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.
2017-09-05T13:49:22ZMagrans Fontrodona, Francesc XavierArcas, KevinVicens Rodríguez, PerePoblet-Puig, JordiRodríguez Ferran, AntonioIn 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 cuboid-shaped 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 meso-modeling of steel fiber reinforced concrete: simulation of flexural behavior
http://hdl.handle.net/2117/107371
Discrete meso-modeling 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.
2017-09-04T13:51:20ZPros Parés, AlbaDíez, PedroMolins i Borrell, ClimentConcrete 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.