Engineering with Computers最新文献

A variational approach is developed with a meshless discretization to enable accurate and robust numerical simulation of partial differential equations for meshes that are of poor quality. Traditional finite element methods use the mesh to both discretize the geometric domain and to define the finite element shape functions. The latter creates a dependence between the quality of the mesh and the properties of the finite element basis that may adversely affect the accuracy of the discretized problem. We propose a new approach for defining finite element shape functions that breaks this dependence and separates mesh quality from the discretization quality, which we call discontinuous piecewise polynomial generalized moving least squares (DPP-GMLS). At the core of the approach is a meshless definition of the shape functions, which limits the purpose of the mesh to representing the geometric domain and integrating the basis functions without having any role in their approximation quality. The resulting non-conforming space can be utilized within a standard discontinuous Galerkin framework, providing a rigorous foundation for solving partial differential equations on low-quality meshes. We present a collection of numerical experiments demonstrating our approach in a wide range of settings: strongly coercive elliptic problems, linear elasticity in the compressible regime, and the stationary Stokes problem. We demonstrate convergence for all problems and stability for element pairs for problems which usually require inf-sup compatibility for conforming methods, also referring to a minor modification possible through the symmetric interior penalty Galerkin framework for stabilizing element pairs that would otherwise be traditionally unstable. Mesh robustness is particularly critical for elasticity, and we provide an example that our approach provides a greater than 5(times) improvement in accuracy and allows for taking an 8(times) larger stable timestep for a highly deformed mesh, compared to the continuous Galerkin finite element method.

Extraction of quadrilateral layouts of surfaces is essential for surface rebuilding using splines, semi-structured bilinear quadrilateral mesh extraction, and texture mapping. Layout generation using integer grid based techniques on triangulated meshes have received particular attention for generation of well-structured layouts. In this work, we reiterate a generalization of integer grid parameterizations in which only topological constraints between singularities are necessary to ensure a valid quadrilateral parameterization (and specifically, the integral curves emanating from singularities are of finite length). This generalized representation is motivated by carefully discussing pros and cons of both integer grid and topologically constrained parameterization methods. A computational framework for extracting a quadrilateral layout from a valid input immersion is then presented, which will work for any parameterization that induces a valid quadrilateral layout. Results demonstrate the validity and the potential of the proposed computational framework on a variety of geometries. The proposed extraction framework is ultimately used to reconstruct the body-in-white of a 1996 Dodge Neon as a set of analysis-suitable bicubic B-splines, which are then used in the first known body-in-white crash analysis using boundary-conforming splines, demonstrating that the reconstruction method is viable for industrial use.

An interface-modified reproducing kernel particle method (IM-RKPM) is introduced in this work to allow for a direct model construction from image pixels of heterogeneous polycrystalline Li-ion battery microstructures. The interface-modified reproducing kernel (IM-RK) approximation is constructed through scaling of a kernel function by a regularized distance function in conjunction with strategic placement of interface node locations. This leads to RK shape functions with either weak or strong discontinuities across material interfaces, suitable for modeling various interface mechanics. With the placement of a triple junction node and distance-based scaling of kernel functions, the resulting IM-RK shape function also possesses proper discontinuities at the triple junctions. This IM-RK approximation effectively remedies the well-known Gibb’s oscillation in the smooth approximation of discontinuities. Different from the conventional meshfree approaches for interface discontinuities, this IM-RK approach is done without additional degrees of freedom associated with the enrichment functions, and it is formulated with the standard procedures in the RK shape function construction. This work focuses on identifying the accuracy and convergence properties of IM-RKPM for modeling the coupled electro-chemo-mechanical system. A linear patch test is formulated and numerically tested for the electro-chemo-mechanical coupled problem with a Butler–Volmer boundary condition representing the physical conditions in Li-ion battery microstructures. This is followed by verification of the optimal rates of convergence of IM-RKPM for solving the coupled problem with higher order solutions. The image-based modeling of Li-ion battery microstructures in the numerical examples demonstrates the applicability of the proposed method to realistic Li-ion battery materials modeling.

Computational fluid dynamics (CFD) has widespread application in research and industry. The quality of the mesh, particularly in the boundary layer, significantly influences the CFD accuracy. Despite its importance, the mesh generation process remains manual and time intensive, with the introduction of potential errors and inconsistencies. The limitations of traditional methods have prompted the recent exploration of deep reinforcement learning (DRL) for mesh generation. Although some studies have demonstrated the applicability of DRL in mesh generation, they have limitations in utilizing existing tools, thereby falling short of fully leveraging the potential of DRL. This study proposes a new boundary mesh generation method using DRL, namely an agent-based mesh generator. The nodes on the surface act as agents and optimize the paths into space to create high-quality meshes. Mesh generation is naturally suited to DRL owing to its computational nature and deterministic execution. However, challenges also arise, including training numerous agents simultaneously and managing their interdependencies in a vast state space. In this study, these challenges are addressed along with an investigation of the optimal learning conditions after formulating grid generation as a DRL task: defining states, agents, actions, and rewards. The derived optimal conditions are applied to generate two dimensional airfoil grids to validate the feasibility of the proposed approach.

Given the small wavelengths and wide range of frequencies of the acoustic waves involved in Aeroacoustics problems, the use of very accurate, low-dissipative numerical schemes is the only valid option to accurately capture these phenomena. However, as the order of the scheme increases, the computational time also increases. In this work, we propose a new high-order flux reconstruction in the framework of finite volume (FV) schemes for linear problems. In particular, it is applied to solve the Linearized Euler Equations, which are widely used in the field of Computational Aeroacoustics. This new reconstruction is very efficient and well suited in the context of very high-order FV schemes, where the computation of high-order flux integrals are needed at cell edges/faces. Different benchmark test cases are carried out to analyze the accuracy and the efficiency of the proposed flux reconstruction. The proposed methodology preserves the accuracy while the computational time relatively reduces drastically as the order increases.

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.