Engineering with Computers最新文献

Isogeometric analysis has brought a paradigm shift in integrating computational simulations with geometric designs across engineering disciplines. This technique necessitates analysis-suitable parameterization of physical domains to fully harness the synergy between Computer-Aided Design and Computer-Aided Engineering analyses. Existing methods often fix boundary parameters, leading to challenges in elongated geometries such as fluid channels and tubular reactors. This paper presents an innovative solution for the boundary parameter matching problem, specifically designed for analysis-suitable parameterizations. We employ a sophisticated Schwarz–Christoffel mapping technique, which is instrumental in computing boundary correspondences. A refined boundary curve reparameterization process complements this. Our dual-strategy approach maintains the geometric exactness and continuity of input physical domains, overcoming limitations often encountered with the existing reparameterization techniques. By employing our proposed boundary parameter matching method, we show that even a simple linear interpolation approach can effectively construct a satisfactory analysis-suitable parameterization. Our methodology offers significant improvements over traditional practices, enabling the generation of analysis-suitable and geometrically precise models, which is crucial for ensuring accurate simulation results. Numerical experiments show the capacity of the proposed method to enhance the quality and reliability of isogeometric analysis workflows.

3D Traction Force Microscopy (3DTFM) constitutes a powerful methodology that enables the computation of realistic forces exerted by cells on the surrounding extracellular matrix (ECM). The ECM is characterized by its highly dynamic structure, which is constantly remodeled in order to regulate most basic cellular functions and processes. Certain pathological processes, such as cancer and metastasis, alter the way the ECM is remodeled. In particular, cancer cells are able to invade its surrounding tissue by the secretion of metalloproteinases that degrade the extracellular matrix to move and migrate towards different tissues, inducing ECM heterogeneity. Typically, 3DTFM studies neglect such heterogeneity and assume homogeneous ECM properties, which can lead to inaccuracies in traction reconstruction. Some studies have implemented ECM degradation models into 3DTFM, but the associated degradation maps are defined in an ad hoc manner. In this paper, we present a novel multiphysics approach to 3DTFM with evolving mechanical properties of the ECM. Our modeling considers a system of partial differential equations based on the mechanisms of activation of diffusive metalloproteinase MMP2 by membrane-bound metalloproteinase MT1-MMP. The obtained ECM density maps in an ECM-mimicking hydrogel are then used to compute the heterogeneous mechanical properties of the hydrogel through a multiscale approach. We perform forward and inverse TFM simulations both accounting for and omitting degradation, and results are compared to ground truth reference solutions in which degradation is considered. The main conclusions resulting from the study are: (i) the inverse methodology yields results that are significantly more accurate than those provided by the forward methodology; (ii) ignoring ECM degradation results in a considerable overestimation of tractions and non negligible errors in all analyzed cases.

We present a numerical framework for solving partial differential equations within an isogeometric context using T-splines in two and three space dimensions. Within this paper, we explain the data structures used for the implementation of deal.t (deal.II with T-splines) and main differences when using deal.t in contrast to deal.II. The authors present numerical experiments with error-based refinement (2D) and a priori refinement (3D) for scalar-valued problems. A full tutorial is given in the appendix. Since the new framework is based on deal.II, T-splines may be applied to various different PDEs.

This article presents a new algorithm designed to create a dynamic r-adaptive mesh within the framework of isogeometric analysis. The approach is based on the simultaneous computation of adaptive meshes using a nonlinear parabolic Monge–Ampere equation with a resolution of partial differential equations in multidimensional spaces. The technique ensures the absence of geometric boundary errors and is simple to implement, requiring the solution of only one Laplace scalar equation at each time step. It utilizes a fast diagonalization method that can be adapted to any dimension. Various numerical experiments were conducted to validate an original parabolic Monge–Ampere solver. The solver was respectively applied to Burgers, Allen–Cahn, and Cahn–Hilliard problems to demonstrate the efficiency of the new approach.

This study proposes a generalized nth-order perturbation method based on (isogeometric) boundary element methods for uncertainty analysis in 3D acoustic scattering problems. In this paper, for the first time, we derive nth-order Taylor expansions of 3D acoustic boundary integral equations, taking incident wave frequency as a random input variable. In addition, subdivision surface basis functions used in geometric modeling are employed to discretize the generalized nth-order derivative boundary integral equations, in order to avoid cumbersome meshing procedure and retain geometric accuracy. Moreover, the fast multipole method is introduced to accelerate the stochastic perturbation analysis with boundary element methods. Numerical examples are given to demonstrate the accuracy and efficiency of the proposed uncertainty quantification algorithm.

We solve acoustic scattering problems by means of the isogeometric boundary integral equation method. In order to avoid spurious modes, we apply the combined field integral equations for either sound-hard scatterers or sound-soft scatterers. These integral equations are discretized by Galerkin’s method, which especially enables the mathematically correct regularization of the hypersingular integral operator. In order to circumvent densely populated system matrices, we employ the isogeometric embedded fast multipole method, which is based on interpolation of the kernel function under consideration on the reference domain, rather than in space. To overcome the prohibitive cost of the potential evaluation in case of many evaluation points, we also accelerate the potential evaluation by a fast multipole method which interpolates in space. The result is a frequency stable algorithm that scales essentially linear in the number of degrees of freedom and potential points. Numerical experiments are performed which show the feasibility and the performance of the approach.

Heart valves play a critical role in maintaining proper cardiovascular function in the human heart; however, valve diseases can lead to improper valvular function and reduced cardiovascular performance. Depending on the extent and severity of the valvular disease, replacement operations are often required to ensure that the heart continues to operate properly in the cardiac system. Transcatheter aortic valve replacement (TAVR) procedures have recently emerged as a promising alternative to surgical replacement approaches because the percutaneous methods used in these implant operations are significantly less invasive than open heart surgery. Despite the advantages of transcatheter devices, the precise deployment, proper valve sizing, and stable anchoring required to securely place these valves in the aorta remain challenging even in successful TAVR procedures. This work proposes a parametric modeling approach for transcatheter heart valves (THVs) that enables flexible valvular development and sizing to effectively generate existing and novel valve designs. This study showcases two THV configurations that are analyzed using an immersogeometric fluid–structure interaction (IMGA FSI) framework to demonstrate the influence of geometric changes on THV performance. The proposed modeling framework illustrates the impact of these features on THV behavior and indicates the effectiveness of parametric modeling approaches for enhancing THV performance and efficacy in the future.

Physics-informed neural networks (PINNs) have recently become a powerful tool for solving partial differential equations (PDEs). However, finding a set of neural network parameters that fulfill a PDE at the boundary and within the domain of interest can be challenging and non-unique due to the complexity of the loss landscape that needs to be traversed. Although a variety of multi-task learning and transfer learning approaches have been proposed to overcome these issues, no incremental training procedure has been proposed for PINNs. As demonstrated herein, by developing incremental PINNs (iPINNs) we can effectively mitigate such training challenges and learn multiple tasks (equations) sequentially without additional parameters for new tasks. Interestingly, we show that this also improves performance for every equation in the sequence. Our approach learns multiple PDEs starting from the simplest one by creating its own subnetwork for each PDE and allowing each subnetwork to overlap with previously learned subnetworks. We demonstrate that previous subnetworks are a good initialization for a new equation if PDEs share similarities. We also show that iPINNs achieve lower prediction error than regular PINNs for two different scenarios: (1) learning a family of equations (e.g., 1-D convection PDE); and (2) learning PDEs resulting from a combination of processes (e.g., 1-D reaction–diffusion PDE). The ability to learn all problems with a single network together with learning more complex PDEs with better generalization than regular PINNs will open new avenues in this field.

It is necessary to determine the input features and output results when constructing a surrogate model within the data-driven neural network. Since the law of features would be restrained when the surrogate mechanical model is employed, it is still a challenge to build a set of natural features to accurately describe the failure process of materials and structures within the traditional continuum mechanics framework. To address this challenge, a robust approach for constructing a surrogate model within the peridynamic-deep learning framework is proposed in this study, which is capable of representing material deformation and failure explicitly. The presented surrogate model integrates both reference and current configuration data to refine input features, enhancing model training. We incorporate a batch-normalization layer before the activation function to mitigate common issues such as slow convergence, low prediction accuracy, and overfitting due to the large numerical differences in the damage dataset. Additionally, numerical analyses on several typical examples are performed to validate the effectiveness and generality of the present model and methodology. The results demonstrate high accuracy in the training set as well as the testing set, confirming the model’s excellent generalization ability and significant potential for material failure analysis. According to this work, more peridynamic expressions can be further derived in the machine-learning-based peridynamic surrogate model by considering the reinforcement learning and symbol space, to potentially broaden its applicability to a wider range of mechanical issues.

Efficient and distributed adaptive mesh construction and editing pose several challenges, including selecting the appropriate distributed data structure, choosing strategies for distributing computational load, and managing inter-processor communication. Distributed Combinatorial Maps permit the representation and editing of distributed 3D meshes. This paper addresses computation load and expands communication aspects through volume transfer operation and repartitioning strategies. This work is the first one defining such transfer for cells of any topology. We demonstrate the benefits of our method by presenting a parallel adaptive hexahedral subdivision operation, involving fully generic volumes, in a process including a conversion to conformal mesh and surface fitting. Our experiments compare different strategies using multithreading and MPI implementations to highlight the benefits of volume transfer. Special attention has been paid to generic aspects and adaptability of the framework.