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Ibáñez, Rubén; Abisset‐Chavanne, Emmanuelle; Chinesta, Francisco; Huerta, Antonio; Cueto, Elías
doi: 10.1002/nme.6128pmid: N/A
It is well known that model order reduction techniques that project the solution of the problem at hand onto a low‐dimensional subspace present difficulties when this solution lies on a nonlinear manifold. To overcome these difficulties (notably, an undesirable increase in the number of required modes in the solution), several solutions have been suggested. Among them, we can cite the use of nonlinear dimensionality reduction techniques or, alternatively, the employ of linear local reduced order approaches. These last approaches usually present the difficulty of ensuring continuity between these local models. Here, a new method is presented, which ensures this continuity by resorting to the paradigm of the partition of unity while employing proper generalized decompositions at each local patch.
Çakal, Berkay Alp; Temizer, İlker; Terada, Kenjiro; Kato, Junji
doi: 10.1002/nme.6129pmid: N/A
A homogenization‐based topology optimization framework is developed, which can endow hydrodynamically lubricated interfaces with a micro‐texture, to achieve optimal macroscopic responses by addressing both dissipative and nondissipative physics at the interface. With respect to the homogenization aspects of the problem, the thermodynamic consistency of the two‐scale formulation is explicitly analyzed and verified. With respect to the topology optimization aspects, a variational approach to sensitivity analysis is pursued. Subsequently, these are employed in micro‐texture design studies, which address microscopic and macroscopic objectives. The influence of dissipation on the optimization results is demonstrated through extensive numerical investigations, which also highlight the importance of working in a sufficiently flexible design space that can deliver nearly optimal micro‐texture geometries.
Storvik, Erlend; Both, Jakub W.; Kumar, Kundan; Nordbotten, Jan M.; Radu, Florin A.
doi: 10.1002/nme.6130pmid: N/A
In this work, we are interested in efficiently solving the quasi‐static, linear Biot model for poroelasticity. We consider the fixed‐stress splitting scheme, which is a popular method for iteratively solving Biot's equations. It is well known that the convergence properties of the method strongly depend on the applied stabilization/tuning parameter. We show theoretically that, in addition to depending on the mechanical properties of the porous medium and the coupling coefficient, they also depend on the fluid flow and spatial discretization properties. The type of analysis presented in this paper is not restricted to a particular spatial discretization, although it is required to be inf‐sup stable with respect to the displacement‐pressure formulation. Furthermore, we propose a way to optimize this parameter that relies on the mesh independence of the scheme's optimal stabilization parameter. Illustrative numerical examples show that using the optimized stabilization parameter can significantly reduce the number of iterations.
Martínez‐Rey, Miguel; Santos, Carlos; Nieto, Rubén; Losada, Cristina; Espinosa, Felipe
doi: 10.1002/nme.6131pmid: N/A
In state estimation, adjusting the process noise covariance matrix is an important and often difficult task. Well‐known methods use the innovation vector to perform an adaptive adjustment, but when using event‐based sensors, the innovation vector is not available for the estimator. We propose an online method for adjusting the process noise covariance matrix using the expected and observed event rates, which is based on the golden section search optimization algorithm. Simulation results confirm the suitability and efficiency of our proposed method. The process noise covariance parameter converges to the actual covariance iteratively, reducing the sensor transmission rate and the estimation error.
Nguyen‐Thanh, Nhon; Li, Weidong; Huang, Jiazhao; Srikanth, Narasimalu; Zhou, Kun
doi: 10.1002/nme.6132pmid: N/A
A collocation method has been recently developed as a powerful alternative to Galerkin's method in the context of isogeometric analysis, characterized by significantly reduced computational cost, but still guaranteeing higher‐order convergence rates. In this work, we propose a novel adaptive isogeometric analysis meshfree collocation (IGAM‐C) for the two‐dimensional (2D) elasticity and frictional contact problems. The concept of the IGAM‐C method is based upon the correspondence between the isogeometric collocation and reproducing kernel meshfree approach, which facilitates the robust mesh adaptivity in isogeometric collocation. The proposed method reconciles collocation at the Greville points via the discretization of the strong form of the equilibrium equations. The adaptive refinement in collocation is guided by the gradient‐based error estimator. Moreover, the resolution of the nonlinear equations governing the contact problem is derived from a strong form to avoid the disadvantages of numerical integration. Numerical examples are presented to demonstrate the effectiveness, robustness, and straightforward implementation of the present method for adaptive analysis.
Pfefferkorn, Robin; Betsch, Peter
doi: 10.1002/nme.6133pmid: N/A
We summarize several previously published geometrically nonlinear EAS elements and compare their behavior. Various transformations for the compatible and enhanced deformation gradient are examined. Their effect on the patch test is one main concern of the work, and it is shown numerically and with a novel analytic proof that the improved EAS element proposed by Simo et al in 1993 does not fulfill the patch test. We propose a modification to overcome that drawback without losing the favorable locking‐free behavior of that element. Furthermore, a new transformation for the enhanced field is proposed and motivated in a curvilinear coordinate frame. It is shown in numerical tests that this novel approach outperforms all previously introduced transformations.
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