Engineering with Computers最新文献

In this study, we propose a new numerical scheme for physics-informed neural networks (PINNs) that enables precise and inexpensive solutions for partial differential equations (PDEs) in case of arbitrary geometries while strongly enforcing Dirichlet boundary conditions. The proposed approach combines admissible NURBS parametrizations (admissible in the calculus of variations sense, that is, satisfying the boundary conditions) required to define the physical domain and the Dirichlet boundary conditions with a PINN solver. Therefore, the boundary conditions are automatically satisfied in this novel Deep NURBS framework. Furthermore, our sampling is carried out in the parametric space and mapped to the physical domain. This parametric sampling works as an importance sampling scheme since there is a concentration of points in regions where the geometry is more complex. We verified our new approach using two-dimensional elliptic PDEs when considering arbitrary geometries, including non-Lipschitz domains. Compared to the classical PINN solver, the Deep NURBS estimator has a remarkably high accuracy for all the studied problems. Moreover, a desirable accuracy was obtained for most of the studied PDEs using only one hidden layer of neural networks. This novel approach is considered to pave the way for more effective solutions for high-dimensional problems by allowing for a more realistic physics-informed statistical learning framework to solve PDEs.

The analysis of particle size distributions is important to better understand the relation between the microstructure and the heterogenous physical behavior of granular materials, including soils, sands, and concrete. This paper presents a novel analytical model, entitled piecewise linear sieve curve, to accurately reproduce the complicated and wide-ranging particle size distribution of granular materials. The model assumes that the passing percentage varies linearly with aggregate size between two adjacent sieves. The probability density function and cumulative distribution function of the piecewise linear sieve curve can be determined directly once the experimental particle gradation is known. Several types of concrete with different mix designs were taken as numerical examples, and the particle modeling based on piecewise linear sieve curve and the classical Fuller curve were compared. The results show that the piecewise linear sieve curve provides a much better representation of different aggregate particle size distributions than the Fuller curve, and the proposed model achieves the goal to reproduce the experimental aggregate gradation in an efficient and accurate way.

In the capillary underfill packaging process, resin with specific characteristics such as low viscosity, high flowability, fast curing, and high reliability is utilized to fill the gaps between the substrate and the die. This underfill resin serves to reinforce the connections between metal bumps and the substrate, thereby extending the lifespan and enhancing the reliability of FCBGA (Flip-Chip Ball Grid Array) packages. Despite the availability of flow simulation tools, the development of the underfill process remains a significant challenge for engineers due to the multitude of control parameters involved. The objective of this study is to identify the key factors influencing the accuracy of underfill flow simulations and explore potential solutions to these challenges. In this study, it is found that necessary ingredients for accurate underfill simulation need to include the following items: 1. Good flow simulation software 2. Accurately measured material properties 3. Good and fine mesh 4. Right amount of dispensed resin 5. Right timing for resin dispensing. The accuracy of the simulation is particularly affected by factors such as overflowing, resin climbing, non-uniform flow, and air trapping, which are influenced by the amount and timing of resin dispensing. By addressing these factors, this study demonstrates that accurate underfill simulation can be achieved, providing valuable insights into microscale flip-chip underfill physics. This research lays the groundwork for the development of validated models applicable to next-generation high-density flip-chip products.

In this work, we study the effect of the geometry representation in the context of the IsoGeometric-Analysis-based Boundary Element Method (IGABEM) and we propose an algorithm for the construction of a physics-informed geometric representation which leads to approximation results of high accuracy that are comparable to known adaptive refinement schemes. As a model problem, we use a previously studied 2D potential flow problem around a cylinder; see Politis et al. (Proceedings of SIAM/ACM joint conference on geometric and physical modeling, California, pp 349–354, 2009. https://doi.org/10.1145/1629255.1629302L). This study involves a systematic examination of a series of transformations and reparametrizations and their effect on the achieved accuracy and convergence rate of the numerical solution to the problem at hand. Subsequently, a new parametrization is proposed based on a coarse-level approximation of the field-quantity solution, coupling in this way the geometry representation to the physics of the problem. Finally, the performance of our approach is compared against an exact-solution-driven adaptive refinement scheme and a posteriori error estimates for adaptive IGABEM methods. The proposed methodology delivers results of similar quality to the adaptive approaches, but without the computational cost of error estimates evaluation at each refinement step.

This paper introduces an innovative mesh-free computational approach for simulating problems with geometric nonlinearity, focusing on the buckling analysis of thin plates. Addressing significant deformations, the study formulates governing partial differential equations based on Kirchhoff’s plate theory and discretizes them using the Galerkin method. To tackle the complexities of this problem, which demands higher-order continuity in shape functions and accommodates both Dirichlet and Neumann boundary conditions, the research extends the Hermite-type point interpolation method (HPIM). Despite HPIM’s effectiveness, occasional singularities in the moment matrix require enhancement. This work proposes an improved Hermite-type point interpolation method augmented by radial basis functions (Hermite-RPIM) to ensure a well-conditioned moment matrix. The efficacy of the proposed method is validated through detailed numerical examples, including buckling and post-buckling analysis of sandwich functionally graded material (FGM) plates under various loadings, boundary conditions, and material types. These examples highlight the robustness, reliability, and computational efficiency of the enhanced Hermite-RPIM, establishing its potential as a valuable tool for analyzing geometrically nonlinear problems, especially in thin plate buckling analysis.

We propose a novel finite element-based physics-informed operator learning framework that allows for predicting spatiotemporal dynamics governed by partial differential equations (PDEs). The Galerkin discretized weak formulation is employed to incorporate physics into the loss function, termed finite operator learning (FOL), along with the implicit Euler time integration scheme for temporal discretization. A transient thermal conduction problem is considered to benchmark the performance, where FOL takes a temperature field at the current time step as input and predicts a temperature field at the next time step. Upon training, the network successfully predicts the temperature evolution over time for any initial temperature field at high accuracy compared to the solution by the finite element method (FEM) even with a heterogeneous thermal conductivity and arbitrary geometry. The advantages of FOL can be summarized as follows: First, the training is performed in an unsupervised manner, avoiding the need for large data prepared from costly simulations or experiments. Instead, random temperature patterns generated by the Gaussian random process and the Fourier series, combined with constant temperature fields, are used as training data to cover possible temperature cases. Additionally, shape functions and backward difference approximation are exploited for the domain discretization, resulting in a purely algebraic equation. This enhances training efficiency, as one avoids time-consuming automatic differentiation in optimizing weights and biases while accepting possible discretization errors. Finally, thanks to the interpolation power of FEM, any arbitrary geometry with heterogeneous microstructure can be handled with FOL, which is crucial to addressing various engineering application scenarios.

Converting a three-dimensional medical image into a 3D mesh that satisfies both the quality and fidelity constraints of predictive simulations and image-guided surgical procedures remains a critical problem. Presented is an image-to-mesh conversion method called CBC3D. It first discretizes a segmented image by generating an adaptive Body-Centered Cubic mesh of high-quality elements. Next, the tetrahedral mesh is converted into a mixed element mesh of tetrahedra, pentahedra, and hexahedra to decrease element count while maintaining quality. Finally, the mesh surfaces are deformed to their corresponding physical image boundaries, improving the mesh’s fidelity. The deformation scheme builds upon the ITK open-source library and is based on the concept of energy minimization, relying on a multi-material point-based registration. It uses non-connectivity patterns to implicitly control the number of extracted feature points needed for the registration and, thus, adjusts the trade-off between the achieved mesh fidelity and the deformation speed. We compare CBC3D with four widely used and state-of-the-art homegrown image-to-mesh conversion methods from industry and academia. Results indicate that the CBC3D meshes: (1) achieve high fidelity, (2) keep the element count reasonably low, and (3) exhibit good element quality.

This work presents a physics-driven machine learning framework for the simulation of acoustic scattering problems. The proposed framework relies on a physics-informed neural network (PINN) architecture that leverages prior knowledge based on the physics of the scattering problem as well as a tailored network structure that embodies the concept of the superposition principle of linear wave interaction. The framework can also simulate the scattered field due to rigid scatterers having arbitrary shape as well as high-frequency problems. Unlike conventional data-driven neural networks, the PINN is trained by directly enforcing the governing equations describing the underlying physics, hence without relying on any labeled training dataset. Remarkably, the network model has significantly lower discretization dependence and offers simulation capabilities akin to parallel computation. This feature is particularly beneficial to address computational challenges typically associated with conventional mesh-dependent simulation methods. The performance of the network is investigated via a comprehensive numerical study that explores different application scenarios based on acoustic scattering.

Meshfree methods, such as the Reproducing Kernel Particle Method, have been proven advantageous in modeling excessive deformation problems involving material separation, fracture, impact, etc. However, the domain integration in RKPM remains challenging due to instability and sub-optimal convergence for high strain rate events. Although some novel developments alleviate the above issue, they are either computationally expensive or require evaluating the contour integral, which is not straightforward to obtain in contact and material separation problems using meshfree discretization. This work develops a simple and stable integration method based on the extension of modified Simpson’s rule. The method is free from conforming subdomains and can straightforwardly be applied to the meshfree formulation with updated configuration. To model penetration into the earth, a standard viscous boundary is introduced to address the issue of reflecting waves from the truncated computational domain for the ground target. The numerical results are validated with experimental data for various geo-materials and experimental setups.

Digital twin, a concept of establishing mapping linkages between physical and digital areas using digital technology to achieve instantaneous information transfer for monitoring, optimization or decision-making. Digital twins has emerged as a crucial instrument for ensuring structural safety. However, achieving real-time prediction in time series for structural safety monitoring is challenging, as is the dynamic synthesis of heterogeneous data from numerous sources. This study presents a shape-performance coupled digital twin (SPC-DT) model that integrates heterogeneous data from various sources. The model combines structural analysis, reduced-order processing, and artificial intelligence techniques to incorporate geometric, performance, and sensor data. The aim is to enable dynamic monitoring of structural performance. Furthermore, the deployment of physical space and digital space was accomplished by constructing the SPC-DT model of the scissor lift platform as an illustrative example. The model's effectiveness was validated by a comparison of the measured results, the finite element calculation results, and the SPC-DT model prediction findings. Correlation and error analyses were conducted as part of this verification process. The time required for doing a performance study of complex heavy machinery is greatly decreased by the SPC-DT model. For instance, the SPC-DT prediction saves over 255 times the time cost in the structural prediction of a scissor lift when compared to finite element calculation. This creates a new opportunity for mechanical structure and system safety monitoring.