International Journal for Numerical Methods in Engineering最新文献

In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering contexts. This work proposes a multi-stage machine learning strategy that aims to predict an optimal topology and the related stress fields of interest, either in 2D or 3D, without resorting to any iterative analysis and design process. The overall topology optimization is treated as regression task in a low-dimensional latent space, that encodes the variability of the target designs. First, a fully-connected model is employed to surrogate the functional link between the parametric input space characterizing the design problem and the latent space representation of the corresponding optimal topology. The decoder branch of an autoencoder is then exploited to reconstruct the desired optimal topology from its latent representation. The deep learning models are trained on a dataset generated through a standard method of topology optimization implementing the solid isotropic material with penalization, for varying boundary and loading conditions. The underlying hypothesis behind the proposed strategy is that optimal topologies share enough common patterns to be compressed into small latent space representations without significant information loss. Results relevant to a 2D Messerschmitt-Bölkow-Blohm beam and a 3D bridge case demonstrate the capabilities of the proposed framework to provide accurate optimal topology predictions in a fraction of a second.

This article presents an adaptive remeshing strategy between the finite element method (FEM) and the discrete element method (DEM). To achieve this strategy, an edge-to-edge coupling method based on Lagrange multipliers has been set-up to ensure the continuity of velocities at the interface. To switch from a computation initially purely FEM to a FEM-DEM one, a field transfer method was required. In particular, a displacement field transfer method has been set-up. The switching from a FEM subdomain to a DEM one is activated by a transition criterion. Each time a FEM subdomain is substituted by a DEM one, the DEM subdomain microscopic properties are set-up with respect to the subdomain geometry and desired particle refinement. This is performed thanks to the linking to the so-called “Cooker,” a tool distributed along with the GranOO Workbench. Two subdomain remeshing cases were dealt with: that of an initially FEM subdomain that is converted to DEM, and that of DEM subdomains which coalesce. A numerical test case shows that the dynamic remeshing method behaves as expected: FEM subdomains are substituted by DEM ones when the transition criterion is met, and DEM subdomains coalesce when required. The final numerical test case shows a good agreement with a crack propagation experiment of the literature, while a speedup of about 20 was observed when compared to pure DEM computation.

We present a machine learning framework capable of consistently inferring mathematical expressions of hyperelastic energy functionals for incompressible materials from sparse experimental data and physical laws. To achieve this goal, we propose a polyconvex neural additive model (PNAM) that enables us to express the hyperelastic model in a learnable feature space while enforcing polyconvexity. An upshot of this feature space obtained via the PNAM is that (1) it is spanned by a set of univariate basis functions that can be re-parametrized with a more complex mathematical form, and (2) the resultant elasticity model is guaranteed to fulfill the polyconvexity, which ensures that the acoustic tensor remains elliptic for any deformation. To further improve the interpretability, we use genetic programming to convert each univariate basis into a compact mathematical expression. The resultant multi-variable mathematical models obtained from this proposed framework are not only more interpretable but are also proven to fulfill physical laws. By controlling the compactness of the learned symbolic form, the machine learning-generated mathematical model also requires fewer arithmetic operations than its deep neural network counterparts during deployment. This latter attribute is crucial for scaling large-scale simulations where the constitutive responses of every integration point must be updated within each incremental time step. We compare our proposed model discovery framework against other state-of-the-art alternatives to assess the robustness and efficiency of the training algorithms and examine the trade-off between interpretability, accuracy, and precision of the learned symbolic hyperelastic models obtained from different approaches. Our numerical results suggest that our approach extrapolates well outside the training data regime due to the precise incorporation of physics-based knowledge.

Acoustic emission or scattering problems naturally involve uncertainties about the sound sources or boundary conditions. This article initiates the study of time domain boundary elements for such stochastic boundary problems for the acoustic wave equation. We present a space-time stochastic Galerkin boundary element method which is applied to sound-hard, sound-soft and absorbing scatterers. Uncertainties in both the sources and the boundary conditions are considered using a polynomial chaos expansion. The numerical experiments illustrate the performance and convergence of the proposed method in model problems and present an application to a problem from traffic noise.

The virtual element method (VEM) allows discretization of elasticity and plasticity problems with polygons in 2D and polyhedrals in 3D. The polygons (and polyhedrals) can have an arbitrary number of sides and can be concave or convex. These features, among others, are attractive for meshing complex geometries. However, to the author's knowledge axisymmetric virtual elements have not appeared before in the literature. Hence, in this work a novel first order consistent axisymmetric VEM is applied to problems of elasticity and plasticity. The VEM specific implementation details and adjustments needed to solve axisymmetric simulations are presented. Representative benchmark problems including pressure vessels and circular plates are illustrated. Examples also show that problems of near incompressibility are solved successfully. Consequently, this research demonstrates that the axisymmetric VEM formulation successfully solves certain classes of solid mechanics problems. The work concludes with a discussion of results for the current formulation and future research directions.

This article presents an effective computational method based on the orthogonal collocation on finite element for nonlinear pursuit-evasion differential game problems. The original problems are transformed into two dynamic optimization problems at first, so that the difficulty of obtaining the solution is reduced. To improve the convergence rate and the efficiency, the sensitivities describing the influence of control and interval parameters on state are derived through the discretized dynamic equations for the resulting nonlinear programming problem. The convergence speed is introduced to measure the performance in the upper level iteration. The main structure and the algorithm of the method are also given. Two demonstrative differential game problems with different scenarios from practice are studied. Compared with the approach without sensitivity information, the proposed method needs less function evaluations and saves at least 68.4% of the computational time. The research results show the effectiveness of proposed approach.

Dynamic models generating time-dependent model predictions are typically associated with high-dimensional input spaces and high-dimensional output spaces, in particular if time is discretized. It is computationally prohibitive to apply traditional global sensitivity analysis (SA) separately on each time output, as is common in the literature on multivariate SA. As an alternative, we propose a novel method for efficient global SA of dynamic models with high-dimensional inputs by combining a new polynomial chaos expansion (PCE)-driven partial least squares (PLS) algorithm with the analysis of variance. PLS is used to simultaneously reduce the dimensionality of the input and output variables spaces, by identifying the input and output latent variables that account for most of their joint variability. PCE is incorporated into the PLS algorithm to capture the non-linear behavior of the physical system. We derive the sensitivity indices associated with each output latent variable, based on which we propose generalized sensitivity indices that synthesize the influence of each input on the variance of entire output time series. All sensitivities can be computed analytically by post-processing the coefficients of the PLS-PCE representation. Hence, the computational cost of global SA for dynamic models essentially reduces to the cost for estimating these coefficients. We numerically compare the proposed method with existing methods by several dynamic models with high-dimensional inputs. The results show that the PLS-PCE method can obtain accurate sensitivity indices at low computational cost, even for models with strong interaction among the inputs.

In this paper, a novel first- and second-order stabilization-free virtual element method is proposed for two-dimensional elastoplastic problems. In contrast to traditional virtual element methods, the improved method does not require any stabilization, making the solution of nonlinear problems more reliable. The main idea is to modify the virtual element space to allow the computation of the higher-order $��{�L�}_{�2�}�$ projection operator, ensuring that the strain and stress represent the element energy accurately. Considering the flexibility of the stabilization-free virtual element method, the elastoplastic mechanical problems can be solved by radial return methods known from the traditional finite element framework. $��{�J�}_{�2�}�$ plasticity with hardening is considered for modeling the nonlinear response. Several numerical examples are provided to illustrate the capability and accuracy of the stabilization-free virtual element method.

The paper introduces a computational framework using a novel Arbitrary Lagrangian Eulerian (ALE) formalism in the form of a system of first-order conservation laws. In addition to the usual material and spatial configurations, an additional referential (intrinsic) configuration is introduced in order to disassociate material particles from mesh positions. Using isothermal hyperelasticity as a starting point, mass, linear momentum and total energy conservation equations are written and solved with respect to the reference configuration. In addition, with the purpose of guaranteeing equal order of convergence of strains/stresses and velocities/displacements, the computation of the standard deformation gradient tensor (measured from material to spatial configuration) is obtained via its multiplicative decomposition into two auxiliary deformation gradient tensors, both computed via additional first-order conservation laws. Crucially, the new ALE conservative formulation will be shown to degenerate elegantly into alternative mixed systems of conservation laws such as Total Lagrangian, Eulerian and Updated Reference Lagrangian. Hyperbolicity of the system of conservation laws will be shown and the accurate wave speed bounds will be presented, the latter critical to ensure stability of explicit time integrators. For spatial discretisation, a vertex-based Finite Volume method is employed and suitably adapted. To guarantee stability from both the continuum and the semi-discretisation standpoints, an appropriate numerical interface flux (by means of the Rankine–Hugoniot jump conditions) is carefully designed and presented. Stability is demonstrated via the use of the time variation of the Hamiltonian of the system, seeking to ensure the positive production of numerical entropy. A range of three dimensional benchmark problems will be presented in order to demonstrate the robustness and reliability of the framework. Examples will be restricted to the case of isothermal reversible elasticity to demonstrate the potential of the new formulation.

This article investigates the suitability of constrained Gaussian process regression in predicting nonlinear mechanical responses of material systems with notably reduced uncertainties. This study reinforces the conventional Gaussian processes with mechanics-informed prior knowledge observed in various kinematic responses. Stiffening and softening responses of material systems mostly demonstrate at least one of the boundedness, monotonicity and convexity conditions with respect to some kinematic variables. These relationships or impositions in turn are encoded into a constrained Gaussian process for prediction, uncertainty quantification and extrapolation. Using numerous examples and comparative studies, this article evidently proves that the use of constrained Gaussian processes is data-efficient, highly accurate, yields low uncertainties, recovers model overfitting and extrapolates very well compared to unconstrained or conventional Gaussian processes. Moreover, the usability of the proposed numerical method across various engineering modelling domains such as multiscale homogenisation, experimentation, structural optimisation, material constitutive modelling and structural idealisation is demonstrated.