Engineering with Computers最新文献

Many natural materials exhibit highly complex, nonlinear, anisotropic, and heterogeneous mechanical properties. Recently, it has been demonstrated that data-driven strain energy functions possess the flexibility to capture the behavior of these complex materials with high accuracy while satisfying physics-based constraints. However, most of these approaches disregard the uncertainty in the estimates and the spatial heterogeneity of these materials. In this work, we leverage recent advances in generative models to address these issues. We use as building block neural ordinary equations (NODE) that—by construction—create polyconvex strain energy functions, a key property of realistic hyperelastic material models. We combine this approach with probabilistic diffusion models to generate new samples of strain energy functions. This technique allows us to sample a vector of Gaussian white noise and translate it to NODE parameters thereby representing plausible strain energy functions. We extend our approach to spatially correlated diffusion resulting in heterogeneous material properties for arbitrary geometries. We extensively test our method with synthetic and experimental data on biological tissues and run finite element simulations with various degrees of spatial heterogeneity. We believe this approach is a major step forward including uncertainty in predictive, data-driven models of hyperelasticity.

Abstract

Imposing local boundary conditions and mitigating the surface effect at free surfaces in peridynamic (PD) models are often desired. The fictitious nodes method (FNM) “extends” the domain with a thin fictitious layer of thickness equal to the PD horizon size, and is a commonly used technique for these purposes. The FNM, however, is limited, in general, to domains with simple geometries. Here we introduce an algorithm for the mirror-based FNM that can be applied to arbitrary domain geometries. The algorithm automatically determines mirror nodes (in the given domain) of all fictitious nodes based on approximating, at each fictitious node, the “generalized” (or nonlocal) normal vector to the domain boundary. We tested the new algorithm for a peridynamic model of a classical diffusion problem with a flux singularity on the boundary. We show that other types of FNMs exhibit “pollution” of the solution far from the singularity point, while the mirror-based FNM does not and, in addition, shows a significantly faster rate of convergence to the classical solution in the limit of the horizon going to zero. The new algorithm is then used for mirror-based FNM solutions of diffusion problems in domains with curvilinear boundaries and with intersecting cracks. The proposed algorithm significantly improves the accuracy near boundaries of domains of arbitrary shapes, including those with corners, notches, and crack tips.

Graphical Abstract

In the context of surrogate-based optimization, the efficient global exploration of the design space strongly relies on the overall accuracy of the surrogate model. For most modeling approaches, significant inaccuracies are often observed at the outlier region of the design space, where very few samples are spotted, known as the “corner error”. Inspired by the Runge effect originating from equidistant samples, a Chebyshev-transformed Orthogonal Latin Hypercube sampling approach is proposed to alleviate corner errors. An initial OLH sample was generated on a unit hyper-sphere, and its radial projection was used as the start of a sequential sampling process. The acquisition function uses the confidence interval of the Kriging predictor, combined with the min–max-distance criterion. To testify the proposed approach, models built with ordinary OLH grids are compared to the models built with Chebyshev-transformed OLH grids. Benchmark tests were performed on a series of multimodal functions, four 2-dimensional functions, and three 6-dimensional functions, both the root mean-squared error and the maximum error were reduced compared with the OLH design for most of the tests. This approach was applied to increase the pressure rise of the engine cooling fan without reducing the efficiency, for which 2.5% higher pressure rise was gained compared to the reference design.

This research seeks to explore the heat shift mechanisms in a rotating system that contains a hybrid nanofluid comprising of graphene oxide and copper particles mixed with pure water, using a novel methodology. The fluid flow in a rotating system is described by mathematical equations that involve nonlinear partial differential equations (PDEs). These equations are simplified by using similarity transformations, resulting in a system of ordinary differential equations. In general, it is not feasible to find a closed-form analytical solution for nonlinear ordinary differential equations (ODEs), which implies that determining an exact mathematical expression that characterizes the behavior of the solution to such ODEs is often challenging or impossible. To that end, we have utilized the controlled learning procedure of machine learning algorithms to predict the solutions for the nonlinear nanofluid problem flowing in the rotating system. The surrogated model are developed for different cases and scenarios, to review the might of differences in various physical parameters on the profiles of the fluid. Furthermore, the solutions are supported by performing an extensive statistical analysis based on different errors. It is concluded that machine learning-based method can potentially provide insights into the underlying physics of nonlinear flow problems, which can aid in the progress of more advanced and accurate models for prognosticating the behavior of nonlinear systems.

Tau tangles in the brain cortex spread along the brain network in distinct patterns among Alzheimer's patients. We aim to simulate their network-based spreading within the cortex, tailored to each individual along the Alzheimer's continuum, without assuming any assumptions about the network architecture. A group-level intrinsic spreading network was constructed to model the pathways for the proximal and distal spreading of tau tangles by optimizing the biophysical model based on a discovery dataset of longitudinal tau positron emission tomography images for 78 amyloid-positive individuals. Group-level spreading parameters were also obtained and subsequently adjusted to produce individuated tau trajectories. By simulating these individuated tau spreading models for every individual in the discovery dataset, we successfully captured proximal and distal tau spreading, allowing reliable inferences about the underlying mechanism of tau spreading. Simulating the models also allowed highly accurate prediction of future tau topography for both discovery and independent validation datasets.

Although deep learning has achieved remarkable success in various scientific machine learning applications, its opaque nature poses concerns regarding interpretability and generalization capabilities beyond the training data. Interpretability is crucial and often desired in modeling physical systems. Moreover, acquiring extensive datasets that encompass the entire range of input features is challenging in many physics-based learning tasks, leading to increased errors when encountering out-of-distribution (OOD) data. In this work, motivated by the field of functional data analysis (FDA), we propose generalized functional linear models as an interpretable surrogate for a trained deep learning model. We demonstrate that our model could be trained either based on a trained neural network (post-hoc interpretation) or directly from training data (interpretable operator learning). A library of generalized functional linear models with different kernel functions is considered and sparse regression is used to discover an interpretable surrogate model that could be analytically presented. We present test cases in solid mechanics, fluid mechanics, and transport. Our results demonstrate that our model can achieve comparable accuracy to deep learning and can improve OOD generalization while providing more transparency and interpretability. Our study underscores the significance of interpretable representation in scientific machine learning and showcases the potential of functional linear models as a tool for interpreting and generalizing deep learning.

The conductive interconnect structure that connects the electrical functional devices is an important micro-nano structure in stretchable electronics. Given the reliance of numerous devices on steady electrical currents for operation, stretchable electronics would benefit from interconnects with minimal resistance variation during deformation. This paper proposes a topology optimization method for the design of stretchable interconnect structures with stable resistance under large deformation. In the proposed method, an equal material method considering geometrically nonlinear and electromechanical coupling effects is developed to evaluate the resistance of a deformed structure. Besides, a new connectivity control method is proposed to ensure the connectivity between the inlet and outlet by making full use of the electrical problem itself. To achieve the design goal of connected interconnect structures with negligible resistance fluctuation during stretching, a topology optimization formulation is established, and the corresponding sensitivity is also analytically derived. Several numerical examples show that the proposed method is capable of computationally and intelligently generating stretchable structures with extremely small variations in resistance during stretching.

In this paper, we develop a semi-implicit partitioned finite element and discontinuous Galerkin method for the non-isothermal non-Newtonian fluid structure interaction (NNFSI) problem within the arbitrary Lagrangian–Eulerian (ALE) framework. The structure is composed of the elastic solid material. The entire mathematical model consists of the governing equations of the non-Newtonian fluid and the structure, as well as the boundary conditions on the contacting interface. The rheological behavior of non-Newtonian fluid is described according to the power law constitutive equation. The whole system is split into several sub-equations and then appropriate finite element method or discontinuous Galerkin method is employed for the spatial discretizations of them. As for the deformation of the structure and the change of the fluid area and computational mesh, we employ the moving mesh technique to handle them. The problem involving a hot flexible rod fixed on the hot bottom of an irregular pipe is fully investigated. The influences of the fluid inlet velocity and the behavior of the fluid on the deformation of the rod and the temperature distribution are all analyzed.

This paper introduces the application of Physics-Informed Neural Network (PINN), a novel class of scientific machine learning techniques, for analyzing the static bending response of nanobeams as essential structural elements in micro/nanoelectromechanical systems, including nanoprobes, atomic force microscope sensors, nanoswitches, nanoactuators, and nanoscale biosensors on a three-parameter nonlinear elastic foundation. The study combines Euler–Bernoulli beam theory and Eringen’s nonlocal continuum theory to derive the governing differential equation using the minimum total potential energy principle. PINN is utilized for approximating the differential equation solution and identifying the nanobeam’s nonlocal parameter through an inverse problem with measurement data. The loss function incorporates terms representing the initial and boundary conditions, along with the differential equation residual at specific points in the domain and boundary. The research demonstrates PINN’s efficacy in analyzing nanobeam behavior on nonlinear elastic foundations, providing valuable insights into responses under different loading and boundary conditions. The proposed approach's accuracy and efficiency are validated through comparisons with existing literature. Additionally, the study investigates the effects of activation functions, collocation points’ number and distribution, nonlocal parameter, foundation stiffness coefficients, loading types, and various boundary conditions on nanobeam bending behavior.

We introduce a novel immersed-like numerical framework that combines isogeometric analysis with smoothed particle hydrodynamics for simulating air-blast–structure interaction. The solid domain is represented by a Lagrangian point cloud, which is immersed into a background Eulerian fluid domain. The smoothed particle hydrodynamics framework is employed to solve the equations of motion of the solid point cloud, whereas isogeometric analysis is used for the fluid mechanics equations on the background domain. The coupling strategy relies on a penalty-based volumetric coupling scheme that penalizes the velocity difference between the two domains, and involves a minimal amount of modification to existing codes, resulting in a straightforward implementation. The immersed nature of the proposed approach, combined with volumetric coupling, eliminates the need for explicit tracking of fluid–structure interfaces and imposes no limitations on solid domain motion and topology. Ample mathematical details are provided, and the proposed method is verified and validated against established numerical tools and experimental studies. The results affirm the method’s accuracy, robustness, and ease with which it seamlessly integrates two distinct computational techniques.