International Journal for Numerical Methods in Engineering最新文献

The microlayer framework is an innovative and powerful approach for the numerical simulation of heterogeneous materials, such as aggregate-matrix composites across multiple scales. In this study, the microlayer framework is extended for the first time to account for viscoelastic-elastoplastic material behavior. The kinematics of the representative volume element (RVE) at the microscale are designed to accurately capture the behavior of typical composites, such as asphalt or concrete. The constitutive equations at the microscale are developed independently of the macroscale, ensuring the necessary conditions for proper computational homogenization. The thermodynamically motivated scale transition is carried out using the principle of multiscale virtual power (PMVP). In numerical studies, it is shown by embedding classical material models at the micro level that homogenization leads to physically meaningful triaxial mechanical behavior at the macro level. It is demonstrated that with a suitable choice of microlayer geometry, the tensile-compressive anomaly of the stress-strain behavior observed in aggregate-matrix composites can be modeled without modifying the material model. Finally, the quality of the microlayer framework is shown by validating a triaxial test of an asphalt specimen with a complex cyclic harmonic axial and radial loading regime.

The multiresolution finite wavelet domain method has been meticulously studied in numerous wave propagation simulations, showing excellent convergence properties and very fast computing times. The multiresolution procedure always starts with the coarse solution, and then finer solutions can be superimposed on the coarse solution until convergence is achieved. Based on repetitive observations on the multiple resolution components of the method, two indices have been developed: a residual-based convergence indicator that reveals convergence at the coarse solution and a displacement-based convergence metric that indicates convergence on the next step of the multiresolution process. Those convergence metrics are both rapidly applicable and straightforward, and can also divulge the spatial and temporal domains in which the already obtained solution needs to be enhanced, using quantitative and robust threshold parameters. In this way, targeted and automatic adaptive refinement techniques are proposed for the specific localized enrichment of the solution, only in the specific grid points and timesteps that refinement is actually needed. This is feasible due to the multiresolution equations of motion that permit the partial computation of the fine solutions. Numerical case studies regarding wave propagation in rods and beams manifest the effectiveness and accuracy of the proposed refinement techniques, as well as the excellent performance of the suggested convergence indicators.

Model reduction is an active research field to construct low-dimensional surrogate models of high fidelity to accelerate engineering design cycles. In this work, we investigate model reduction for linear structured systems using dominant reachable and observable subspaces. When the training set—containing all possible interpolation points—is large, these subspaces can be determined by solving many large-scale linear systems. However, for high-dimensional models, this easily becomes computationally intractable. To circumvent this issue, in this work, we propose an active sampling strategy to sample only a few points from the given training set, which can allow us to estimate those subspaces accurately. To this end, we formulate the identification of the subspaces as the solution of the generalized Sylvester equations, guiding us to select the most relevant samples from the training set to achieve our goals. Consequently, we construct solutions of the matrix equations in low-rank forms, which encode subspace information. We extensively discuss computational aspects and efficient usage of the low-rank factors in the process of obtaining reduced-order models. We illustrate the proposed active sampling scheme to obtain reduced-order models via dominant reachable and observable subspaces and present its comparison with the method where all the points from the training set are taken into account. It is shown that the active sample strategy can provide us a speed-up by one order of magnitude without sacrificing any noticeable accuracy.

Steering a system towards a desired target in a very short amount of time is a challenging task from a computational standpoint. Indeed, the intrinsically iterative nature of optimal control problems requires multiple simulations of the state of the physical system to be controlled. Moreover, the control action needs to be updated whenever the underlying scenario undergoes variations, as it often happens in applications. Full-order models based on, for example, the Finite Element Method, do not meet these requirements due to the computational burden they usually entail. On the other hand, conventional reduced order modeling techniques, such as the Reduced Basis method, despite their rigorous construction, are intrusive, rely on a linear superimposition of modes, and lack efficiency when addressing nonlinear time-dependent dynamics. In this work, we propose a non-intrusive Deep Learning-based Reduced Order Modeling (DL-ROM) technique for the rapid control of systems described in terms of parametrized PDEs in multiple scenarios. In particular, optimal full-order snapshots are generated and properly reduced by either Proper Orthogonal Decomposition or deep autoencoders (or a combination thereof) while feedforward neural networks are exploited to learn the map from scenario parameters to reduced optimal solutions. Nonlinear dimensionality reduction, therefore, allows us to consider state variables and control actions that are both low-dimensional and distributed. After (i) data generation, (ii) dimensionality reduction, and (iii) neural networks training in the offline phase, optimal control strategies can be rapidly retrieved in an online phase for any scenario of interest. The computational speedup and the extremely high accuracy obtained with the proposed approach are finally assessed on different PDE-constrained optimization problems, ranging from the minimization of energy dissipation in incompressible Navier–Stokes flows to the thermal active cooling in heat transfer.

Parametric model order reduction by matrix interpolation allows for efficient prediction of the behavior of dynamic systems without requiring knowledge about the underlying parametric dependency. Within this approach, reduced models are first sampled and then made consistent with each other by transforming the underlying reduced bases. Finally, the transformed reduced operators can be interpolated to predict reduced models for queried parameter points. However, the accuracy of the predicted reduced model strongly depends on the similarity of the sampled reduced bases. If the local reduced bases change significantly over the parameter space, inconsistencies are introduced in the training data for the matrix interpolation. These strong changes in the reduced bases can occur due to the model order reduction method used, a change of the system's dynamics with a change of the parameters, and mode switching and truncation. In this paper, individual approaches for removing these inconsistencies are extended and combined into one general framework to simultaneously treat multiple sources of inconsistency. For that, modal truncation is used for the reduction, an adaptive sampling of the parameter space is performed, and eventually, the parameter space is partitioned into regions in which all local reduced bases are consistent with those of their neighboring samples within the same region. The proposed framework is applied to a cantilever Timoshenko beam and the Kelvin cell for one- to three-dimensional parameter spaces. Compared to the original version of parametric model order reduction by matrix interpolation and an existing method for inconsistency removal, the proposed framework leads to parametric reduced models with significantly smaller errors.

This paper introduces an unprecedented unified approach for developing structural theories with an arbitrary kinematic variable over the beam cross-section. Each of the three displacement variables can be analyzed using an independent expansion function. Both the order of the expansion and the number of terms in each field can be any. That is, the same order does not necessarily correspond to the same number of unknown variables. This method permits starting from a general model and write classical and known higher-order beam theories without any restrain. In this paper, the structural theories are built by using the polynomial expansion of the cross-sectional variables. The Carrera unified formulation (CUF) is employed to describe the cross-sectional kinematics. The finite element method (FEM) is employed to discretize the structure along the beam axis, utilizing Lagrange-based elements. The governing equations and related FE arrays for linear analysis are derived using the principle of virtual displacements. Both compact and thin-walled beams are examined to highlight the importance of each term of the three considered expansions. Various loading conditions, including bending, torsion, torsion-bending, and different beam slenderness ratios, are considered. The selected case studies are drawn from existing literature. The accuracy of the models presented is assessed for both displacements and stress components. The results demonstrate that the choice of the most suitable model closely depends on the specific parameters of the individual problem. That is, each structural problem has its own “best” computational models in terms of accuracy versus degree of freedom.

We present a second-order computational multiscale model for heterogeneous porous media, which allows for the scale bridging of transient fluid-flow processes through porous materials with non-separated scales. The formulation connects a homogenized macroscopic scale described by a local theory of grade two with heterogeneous microstructures described by a local theory of grade one. At the macroscale, this leads to $��{�C�}^{�1�}�$-continuity requirements on the macroscopic solution field; at the microscale, we need to take account of constraints on fluctuation fields that require $��H�\left(�\text{div}�\right)�\cap �H�\left(�\text{grad}�\right)�$-conformity of microscopic solutions. Both these challenges are addressed through the development of mixed Hu–Washizu formulations that result in a variationally consistent homogenization framework with minimization structure across scales. We validate the second-order multiscale model by means of fully resolved, direct numerical simulations and provide comparisons with results of first-order FE² simulations. By considering linear Darcy and nonlinear Darcy–Forchheimer flow through two- and three-dimensional porous microstructures, we provide further insights into the framework and associated length-scale effects.