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See detailStable 3D extended finite elements with higher order enrichment for accurate non planar fracture
Agathos, Konstantinos; Chatzi, Eleni; Bordas, Stéphane UL

in Computer Methods in Applied Mechanics & Engineering (2015)

We present an extended finite element method (XFEM) for 3D nonplanar linear elastic fracture. The new approach not only provides optimal convergence using geometrical enrichment but also enables to ... [more ▼]

We present an extended finite element method (XFEM) for 3D nonplanar linear elastic fracture. The new approach not only provides optimal convergence using geometrical enrichment but also enables to contain the increase in conditioning number characteristic of enriched finite element formulations: the number of iterations to convergence of the conjugate gradient solver scales similarly to and converges faster than the topologically-enriched version of the standard XFEM. This has two advantages: (1) the residual can be driven to zero to machine precision for at least 50% fewer iterations than the standard version of XFEM; (2) additional enrichment functions can be added without significant deterioration of the conditioning. Numerical examples also show that our new approach is up to 40% more accurate in terms of stress intensity factors, than the standard XFEM. [less ▲]

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See detailStable 3D XFEM/vector-level sets for non-planar 3D crack propagation and comparison of enrichment schemes
Agathos, Konstantinos UL; Ventura, Giulio; Chatzi, Eleni et al

in International Journal for Numerical Methods in Engineering (2017)

We present a three-dimensional (3D) vector level set method coupled to a recently developed stable extended finite element method (XFEM). We further investigate a new enrichment approach for XFEM adopting ... [more ▼]

We present a three-dimensional (3D) vector level set method coupled to a recently developed stable extended finite element method (XFEM). We further investigate a new enrichment approach for XFEM adopting discontinuous linear enrichment functions in place of the asymptotic near-tip functions. Through the vector level set method, level set values for propagating cracks are obtained via simple geometrical operations, eliminating the need for solution of differential evolution equations. The first XFEM variant ensures optimal convergence rates by means of geometrical enrichment, i.e., the use of enriched elements in a fixed volume around the crack front, without giving rise to conditioning problems. The linear enrichment approach significantly simplifies implementation and reduces the computational cost associated with numerical integration. The two dicretization schemes are tested for different benchmark problems, and their combination to the vector level set method is verified for non-planar crack propagation problems. [less ▲]

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See detailStable extended finite element method: Convergence, Accuracy, Properties and Diffpack implementation
Paladim, Daniel; Natarajan, Sundarajan; Bordas, Stéphane UL et al

in International Conference on Extended Finite Element Methods - XFEM 2013, September 11 – 13, 2013, Lyon, France (2013)

Problems involving singularities and moving boundaries, especially when they involve discontinuities, create difficulties for the finite element method. On another, albeit related, front, two diametrally ... [more ▼]

Problems involving singularities and moving boundaries, especially when they involve discontinuities, create difficulties for the finite element method. On another, albeit related, front, two diametrally opposed approaches are attempting to simplify the CAD to Analysis pipeline: isogeometric methods on the one hand [1] aim at coupling the geometry and field approximations, whilst implicit boundary definition-based methods attempt to decouple them [3,4,5]. We examine in this paper one instance of the latter approach, and rely on partition of unity enrichment of the field variable to capture discontinuities along material interface or domain boundaries. We study in particular the stable generalized finite element method of Babuˇka and Banerjee [6] for higher order approximations in two and three dimensions and propose a generic implementation within the C++ library Diffpack from inuTech GmbH [7]. In a companion paper, the implementation of enrichment within Diffpack is presented in more detail. We will present results obtained with our 3D implementation of partition of unity enrichment within Diffpack. This implementation represents the interfaces through level-sets and palliates blending problems using various approaches. We study here the stabilisation approach proposed in [6] in more detail and pay particular attention to the global convergence rate of the approach and to the stability and the local flux converence close to the interfaces. [less ▲]

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See detailThe stable GFEM. Convergence, accuracy and Diffpack implementation
Alves Paladim, Daniel; Natarajan, Sundarajan; Bordas, Stéphane UL et al

Presentation (2015, May 12)

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See detailA staggered cell-centered finite element method for compressible and nearly-incompressible linear elasticity on general meshes
Ong, Thanh Hai; Hoang, Thi Thao Phuong; Bordas, Stéphane UL et al

in SIAM Journal on Numerical Analysis (2015), 53(4), 2051-2073

We propose a new numerical method, namely, the staggered cell-centered finite element method for compressible and nearly incompressible linear elasticity problems. By building a dual mesh and its ... [more ▼]

We propose a new numerical method, namely, the staggered cell-centered finite element method for compressible and nearly incompressible linear elasticity problems. By building a dual mesh and its triangular submesh, the scheme can be constructed from a general mesh in which the displacement is approximated by piecewise linear (P1) functions on the dual submesh and, in the case of nearly incompressible problems, the pressure is approximated by piecewise constant (P0) functions on the dual mesh. The scheme is cell centered in the sense that the solution can be computed by cell unknowns of the primal mesh (for the displacement) and of the dual mesh (for the pressure). The method is presented within a rigorous theoretical framework to show stability and convergence. In particular, for the nearly incompressible case, stability is proved by using the macroelement technique. Numerical results show that the method, compared with other methods, is effective in terms of accuracy and computational cost. [less ▲]

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See detailStatic and fatigue strength of a novel anatomically contoured implant compared to five current open-wedge high tibial osteotomy plates
Diffo Kaze, Arnaud UL; Maas, Stefan UL; Belsey, James et al

in Journal of Experimental Orthopaedics (2017), 4(39),

Abstract Background The purpose of the present study was to compare the mechanical static and fatigue strength of the size 2 osteotomy plate “Activmotion” with the following five other common implants for ... [more ▼]

Abstract Background The purpose of the present study was to compare the mechanical static and fatigue strength of the size 2 osteotomy plate “Activmotion” with the following five other common implants for the treatment of medial knee joint osteoarthritis: the TomoFix small stature, the TomoFix standard, the Contour Lock, the iBalance and the second generation PEEKPower. Methods Six fourth-generation tibial bone composites underwent a medial open-wedge high tibial osteotomy (HTO), according to standard techniques, using size 2 Activmotion osteotomy plates. All bone-implant constructs were subjected to static compression load to failure and load-controlled cyclic fatigue failure testing, according to a previously defined testing protocol. The mechanical stability was investigated by considering different criteria and parameters: maximum forces, the maximum number of loading cycles, stiffness, the permanent plastic deformation of the specimens during the cyclic fatigue tests, and the maximum displacement range in the hysteresis loops of the cyclic loading responses. Results In each test, all bone-implant constructs with the size 2 Activmotion plate failed with a fracture of the lateral cortex, like with the other five previously tested implants. For the static compression tests the failure occurred in each tested implant above the physiological loading of slow walking (> 2400 N). The load at failure for the Activmotion group was the highest (8200 N). In terms of maximum load and number of cycles performed prior to failure, the size 2 Activmotion plate showed higher results than all the other tested implants except the ContourLock plate. The iBalance implant offered the highest stiffness (3.1 kN/mm) for static loading on the lateral side, while the size 2 Activmotion showed the highest stiffness (4.8 kN/mm) in cyclic loading. Conclusions Overall, regarding all of the analysed strength parameters, the size 2 Activmotion plate provided equivalent or higher mechanical stability compared to the previously tested implant. Implants with a metaphyseal slope adapted to the tibia anatomy, and positioned more anteriorly on the proximal medial side of the tibia, should provide good mechanical stability. [less ▲]

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See detailStatistical extraction of process zones and representative subspaces in fracture of random composites
Kerfriden, P.; Schmidt, K. M.; Rabczuk, T. et al

in International Journal for Multiscale Computational Engineering (2013), 11(3), 253-287

We propose to identify process zones in heterogeneous materials by tailored statistical tools. The process zone is redefined as the part of the structure where the random process cannot be correctly ... [more ▼]

We propose to identify process zones in heterogeneous materials by tailored statistical tools. The process zone is redefined as the part of the structure where the random process cannot be correctly approximated in a low-dimensional deterministic space. Such a low-dimensional space is obtained by a spectral analysis performed on precomputed solution samples. A greedy algorithm is proposed to identify both process zone and low-dimensional representative subspace for the solution in the complementary region. In addition to the novelty of the tools proposed in this paper for the analysis of localized phenomena, we show that the reduced space generated by the method is a valid basis for the construction of a reduced-order model. © 2013 by Begell House, Inc. [less ▲]

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See detailA Step Beyond to Overcome Design Fixation: A Design-by-Analogy Approach
Moreno Grandas, Diana Paola UL; Yang, Maria C.; Hernandez, Alberto A. et al

in Gero, John; Hanna, Sean (Eds.) Design Computing and Cognition’14 (2014, June)

Design fixation is a phenomenon that negatively impacts design outcomes, especially when it occurs during the ideation stage of a design process. This study expands our understanding of design fixation by ... [more ▼]

Design fixation is a phenomenon that negatively impacts design outcomes, especially when it occurs during the ideation stage of a design process. This study expands our understanding of design fixation by presenting a review of de-fixation approaches, as well as metrics employed to understand and account for design fixation. The study then explores the relevant ideation approach of Design-by-Analogy (DbA) to overcome design fixation, with a fixation experiment of 73 knowledge-domain experts. The study provides a design fixation framework and constitutes a genuine contribution to effectively identify approaches to mitigate design fixation in a wide range of design problems. [less ▲]

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See detailA stochastic Galerkin cell-based smoothed finite element method (SGCS-FEM)
Mathew, Tittu; Beex, Lars UL; Bordas, Stéphane UL et al

in International Journal of Computational Methods (in press)

In this paper, the cell based smoothed finite element method is extended to solve stochastic partial diff erential equations with uncertain input parameters. The spatial field of Young's moduli and the ... [more ▼]

In this paper, the cell based smoothed finite element method is extended to solve stochastic partial diff erential equations with uncertain input parameters. The spatial field of Young's moduli and the corresponding stochastic results are represented by Karhunen-Lo eve expansion and polynomial chaos expansion, respectively. The Young's Modulus of structure is considered to be random for stochastic static as well as free vibration problems. Mathematical expressions and the solution procedure are articulated in detail to evaluate the statistical characteristics of responses in terms of static displacements and free vibration frequencies. The feasibility and eff ectiveness of the proposed SGCS-FEM method in terms of accuracy and lower requirement on the mesh size in the solution domain over that of conventional FEM for stochastic problems are demonstrated by carefully chosen numerical examples. From the numerical study, it is inferred that the proposed framework is computationally less demanding without compromising accuracy. [less ▲]

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See detailStochastic Model Predictive Control for Eco-Driving Assistance Systems in Electric Vehicles
Sajadi Alamdari, Seyed Amin UL

Doctoral thesis (2018)

Electric vehicles are expected to become one of the key elements of future sustainable transportation systems. The first generation of electric cars are already commercially available but still, suffer ... [more ▼]

Electric vehicles are expected to become one of the key elements of future sustainable transportation systems. The first generation of electric cars are already commercially available but still, suffer from problems and constraints that have to be solved before a mass market might be created. Key aspects that will play an important role in modern electric vehicles are range extension, energy efficiency, safety, comfort as well as communication. An overall solution approach to integrating all these aspects is the development of advanced driver assistance systems to make electric vehicles more intelligent. Driver assistance systems are based on the integration of suitable sensors and actuators as well as electronic devices and software-enabled control functionality to automatically support the human driver. Driver assistance for electric vehicles will differ from the already used systems in fuel-powered cars such as electronic stability programs, adaptive cruise control etc. in a way that they must support energy efficiency while the system itself must also have a low power consumption. In this work, an eco-driving functionality as the first step towards those new driver assistance systems for electric vehicles will be investigated. Using information about the internal state of the car, navigation information as well as advanced information about the environment coming from sensors and network connections, an algorithm will be developed that will adapt the speed of the vehicle automatically to minimize energy consumption. From an algorithmic point of view, a stochastic model predictive control approach will be applied and adapted to the special constraints of the problem. Finally, the solution will be tested in simulations as well as in first experiments with a commercial electric vehicle in the SnT Automation & Robotics Research Group (SnT ARG). [less ▲]

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See detailStochastic modelling of clay/epoxy nanocomposites
Silani, Mohammad; Talebi, Hossein; Ziaei-Rad, Saeed et al

in Composite Structures (2014), 118

This paper presents a numerical investigation of the mechanical properties of exfoliated clay/epoxy nanocomposites. The large scatter in the material properties and distribution of the inclusions and ... [more ▼]

This paper presents a numerical investigation of the mechanical properties of exfoliated clay/epoxy nanocomposites. The large scatter in the material properties and distribution of the inclusions and matrix is taken into account by introducing an appropriate stochastic damage modelling at the nano scale. Then, the overall properties of the nanocomposite are upscaled using computational homogenisation. Two mechanical properties are investigated: the random distribution of the homogenised Young’s modulus and the overall loss of stiffness observed in the case of extreme loading. The results obtained in the former case are in good agreement with experimental results from the literature. In the second case, we show that exfoliation does not significantly affect the overall strength of the nanocomposite. [less ▲]

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See detailStochastic Optimum Energy Management for Advanced Transportation Network
Sajadi Alamdari, Seyed Amin UL; Voos, Holger UL; Darouach, Mohamed

in 15th IFAC Symposium on Control in Transportation Systems CTS 2018 (2018, July 19)

Smart and optimal energy consumption in electric vehicles has high potential to improve the limited cruising range on a single battery charge. The proposed concept is a semi-autonomous ecological advanced ... [more ▼]

Smart and optimal energy consumption in electric vehicles has high potential to improve the limited cruising range on a single battery charge. The proposed concept is a semi-autonomous ecological advanced driver assistance system which predictively plans for a safe and energy-efficient cruising velocity profile autonomously for battery electric vehicles. However, high entropy in transportation network leads to a challenging task to derive a computationally efficient and tractable model to predict the traffic flow. Stochastic optimal control has been developed to systematically find an optimal decision with the aim of performance improvement. However, most of the developed methods are not real-time algorithms. Moreover, they are mainly risk-neutral for safety-critical systems. This paper investigates on the real-time risk-sensitive nonlinear optimal control design subject to safety and ecological constraints. This system improves the efficiency of the transportation network at the microscopic level. Obtained results demonstrate the effectiveness of the proposed method in terms of states regulation and constraints satisfaction. [less ▲]

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See detailStrain smoothing in FEM and XFEM
Bordas, Stéphane UL; Rabczuk, T.; Hung, N.-X. et al

in Computers & Structures (2010), 88(23-24), 1419-1443

We present in this paper recent achievements realised on the application of strain smoothing in finite elements and propose suitable extensions to problems with discontinuities and singularities. The ... [more ▼]

We present in this paper recent achievements realised on the application of strain smoothing in finite elements and propose suitable extensions to problems with discontinuities and singularities. The numerical results indicate that for 2D and 3D continuum, locking can be avoided. New plate and shell formulations that avoid both shear and membrane locking are also briefly reviewed. The principle is then extended to partition of unity enrichment to simplify numerical integration of discontinuous approximations in the extended finite element method. Examples are presented to test the new elements for problems involving cracks in linear elastic continua and cracked plates. In the latter case, the proposed formulation suppresses locking and yields elements which behave very well, even in the thin plate limit. Two important features of the set of elements presented are their insensitivity to mesh distortion and a lower computational cost than standard finite elements for the same accuracy. These elements are easily implemented in existing codes since they only require the modification of the discretized gradient operator, B. © 2008 Elsevier Ltd. All rights reserved. [less ▲]

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See detailStress analysis without meshing: isogeometric boundary element method
Lian, Haojie; Simpson, Robert; Bordas, Stéphane UL

in Proceedings of the ICE - Engineering and Computational Mechanics (2013), 166(2), 8899

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See detailStress analysis without meshing: Isogeometric boundary-element method
Lian, H.; Simpson, R. N.; Bordas, Stéphane UL

in Proceedings of the Institution of Civil Engineers: Engineering and Computational Mechanics (2013), 166(2), 88-99

The focus of this paper is the description and numerical validation of a computational method where stress analysis can be performed directly from computer-aided design data without mesh generation. The ... [more ▼]

The focus of this paper is the description and numerical validation of a computational method where stress analysis can be performed directly from computer-aided design data without mesh generation. The clear benefit of the approach is that no mesh needs to be generated prior to running the analysis. This is achieved by utilising the isogeometric concept whereby computer-aided design data are used to construct not only the geometry discretisation but also the displacement and traction approximations. In this manner, significant savings can be made in the engineering design and analysis process. This paper also demonstrates that, compared with a standard boundary-element method implementation using quadratic Lagrangian shape functions, superior accuracy is achieved using the present approach for the same number of degrees of freedom. It further illustrates practical applications of the method, comparing against results obtained with a standard boundary-element method and finite-element method for verification. In addition, a propeller is analysed as a sample to show the ability of the present method to handle complex three-dimensional geometries. [less ▲]

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See detailStress analysis, damage tolerance assessment and shape optimisation without meshing
Hale, Jack UL; Bordas, Stéphane UL; Peng, Xuan et al

Poster (2014, June 24)

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See detailStrongly-coupled modelling and analysis of energy harvesting devices
Zilian, Andreas UL; Ravi, Srivathsan UL

in Applied Mathematics and Mechanics (2016), 16

A monolithic approach is proposed that provides simultaneous modelling and analysis of the harvester, which involves surface- coupled fluid-structure interaction, volume-coupled electro- mechanics and a ... [more ▼]

A monolithic approach is proposed that provides simultaneous modelling and analysis of the harvester, which involves surface- coupled fluid-structure interaction, volume-coupled electro- mechanics and a controlling energy harvesting circuit for applica- tions in energy harvesting. A space-time finite element approximation is used for numerical solution of the weighted residual form of the governing equations of the flow-driven piezoelectric energy harvesting device. This method enables time-domain investigation of different types of structures (plate, shells) subject to exterior/interior flow with varying cross sections, material compositions, and attached electrical circuits with respect to the electrical power output generated. [less ▲]

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See detailStructural health monitoring based on static measurements with temperature compensation
Nguyen, Viet Ha UL; Schommer, Sebastian UL; Zürbes, Arno et al

in QUALITY SPECIFICATIONS FOR ROADWAY BRIDGES, STANDARDIZATION AT A EUROPEAN LEVEL (2016)

The paper presents the main results from static tests in a prestressed concrete beam taken out from a real bridge. The tests were achieved during about one month with several scenarios of damage that ... [more ▼]

The paper presents the main results from static tests in a prestressed concrete beam taken out from a real bridge. The tests were achieved during about one month with several scenarios of damage that loaded and unloaded states were monitored for each scenario. Damages in 4 levels were simulated by cutting prestressed tendons. There were 8 transducers distributed along the length’s beam to measure displacements. Deflection lines resulted from the static measurements from every state allow discovering the location of damages. Moreover, the calculation of slope and curvature lines leads also to very interesting issues for damage localization. [less ▲]

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