International Journal for Numerical Methods in Engineering最新文献

The design of continuum structures often presents challenges related to stress concentration, which can cause significant structural damage. To address this issue, the current study presents a new stress minimization method that utilizes the Windowed Evolutionary Structural Optimization (WESO) framework. The method aims to improve algorithm stability by optimizing design variables with an intermediate density. The use of a P-norm stress aggregation method improves the assessment of global stress levels and enhances computational efficiency. Furthermore, a stable element sensitivity formulation, derived from the adjoint sensitivity analysis of the global stress measure, effectively handles the nonlinear stress behavior. Mesh filtering techniques are utilized to convert sensitivity from elements to nodes, and the structural topological solution is represented using the level set function (LSF) based on element-node sensitivity. This method addresses the singularity issue commonly found in density-based optimization methods and facilitates the achievement of smooth topological solutions. Through 2D and 3D benchmark designs, the proposed method's feasibility, stability, and superiority are thoroughly demonstrated. A parametric study is conducted to identify the optimal parameter range for the algorithm, leading to the development of a rational method for parameter selection. The optimized topology, with its smooth boundaries, can guide the design of structures without the need for redesign or post-processing, helping to drive innovation and development in engineering.

This article proposes two contributions to the calculation of free-surface flows using the particle finite element method (PFEM). The PFEM is based upon a Lagrangian approach: a set of particles defines the fluid and each particle is associated with a velocity vector. Then, unlike a pure Lagrangian method, all the particles are connected by a triangular mesh. The difficulty lies in locating the free surface from this mesh. It is a matter of deciding which of the elements in the mesh are part of the fluid domain, and to define a boundary—the free surface. Then, the incompressible Navier–Stokes equations are solved on the fluid domain and the particle position is updated using the velocity vector from the finite element solver. Our first contribution is to propose an approach to adapt the mesh with theoretical guarantees of quality: the mesh generation community has acquired a lot of experience and understanding about mesh adaptation approaches with guarantees of quality on the final mesh. The approach we use here is based on a Delaunay refinement strategy, allowing to insert and remove nodes while gradually improving mesh quality. We show that what is proposed allows to create stable and smooth free surface geometries. One characteristic of the PFEM is that only one fluid domain is modeled, even if its shape and topology change. It is nevertheless necessary to apply conditions on the domain boundaries. When a boundary is a free surface, the flow on the other side is not modeled, it is represented by an external pressure. On the external free surface boundary, atmospheric pressure can be imposed. Nevertheless, there may be internal free surfaces: the fluid can fully encapsulate cavities to form bubbles. The pressure required to maintain the volume of those bubbles is a priori unknown. For example, the atmospheric pressure would not be sufficient to prevent the bubbles from deflating and eventually disappearing. Our second contribution is to propose a multi-point constraint approach to enforce global incompressibility of those empty bubbles. We show that this approach allows to accurately model bubbly flows that involve two fluids with large density differences, for instance water and air, while only modeling the heavier fluid.

In this article, we study an update of the traditional subchannel approximation utilizing local reduced order bases. Through employing the symmetries and periodicity of a 7-pin bundle, the global domain is decomposed into numerous repeating subdomains following several dividing strategies. We locally study the reduced basis generated by proper orthogonal decomposition. We analyze the similarities, assessing the truncation error and the distance between the linear subspaces spanned by the reduced bases. We focus on the first stage of building a reduced order model, the generation of the reduced subspace, which is usually not regarded in detail in our application problem. Our assessment related to flow blockage in liquid metal-cooled nuclear reactors, a postulated high-risk accident that results in potential fuel damage.

As a common smart hydrogel, thermo-sensitive hydrogel exhibits significant potential applications in the field of biological engineering due to its unique property of undergoing a substantial volume transition in response to temperature changes. For numerical implementation of thermo-sensitive hydrogel, many approaches have been developed to simulate the transient deformation during fluid diffusion or heat conduction process. However, the numerical approach for the transient deformation during both fluid diffusion and heat conduction processes is still lacking. To this end, we develop a three-field coupled finite element framework that can be used to simulate the transient deformation behavior of thermo-sensitive hydrogel involving large deformation, fluid diffusion, and heat conduction. In the proposed framework, there exist three processes that deal with displacement, concentration, and temperature fields, separately. To realize the coupling of three fields, the separated solving processes are assembled together by using a two-way coupled approach. Based on the developed finite element framework, the coupling effects between the concentration and temperature can be realized by defining a body flux and a temperature-dependent diffusion coefficient without solving the complex coupling equations. The finite element framework is implemented in ABAQUS by utilizing several user subroutines. The numerical implementation is validated by comparing the numerical results of a hydrogel disk with experimental results. Furthermore, various numerical examples are simulated to investigate the applicability of the proposed finite element framework under different multi-field coupling conditions. The proposed finite element scheme is proved to be an efficient and stable tool for numerically simulating the transient behavior of thermo-sensitive hydrogel incorporating the phase transition effect.

The solution approximation for partial differential equations (PDEs) can be substantially improved using smooth basis functions. The recently introduced mollified basis functions are constructed through mollification, or convolution, of cell-wise defined piecewise polynomials with a smooth mollifier of certain characteristics. The properties of the mollified basis functions are governed by the order of the piecewise functions and the smoothness of the mollifier. In this work, we exploit the high-order and high-smoothness properties of the mollified basis functions for solving PDEs through the point collocation method. The basis functions are evaluated at a set of collocation points in the domain. In addition, boundary conditions are imposed at a set of boundary collocation points distributed over the domain boundaries. To ensure the stability of the resulting linear system of equations, the number of collocation points is set larger than the total number of basis functions. The resulting linear system is overdetermined and is solved using the least square technique. The presented numerical examples confirm the convergence of the proposed approximation scheme for Poisson, linear elasticity, and biharmonic problems. We study in particular the influence of the mollifier and the spatial distribution of the collocation points.

Reduced order models (ROMs) are often coupled with concurrent multiscale simulations to mitigate the computational cost of nonlinear computational homogenization methods. Construction (or training) of ROMs typically requires evaluation of a series of linear or nonlinear equilibrium problems, which itself could be a computationally very expensive process. In the eigenstrain-based reduced order homogenization method (EHM), a series of linear elastic microscale equilibrium problems are solved to compute the localization and interaction tensors that are in turn used in the evaluation of the reduced order multiscale system. These microscale equilibrium problems are typically solved using either the finite element method or semi-analytical methods. In the present study, a reduced order variational spectral method is developed for efficient computation of the localization and interaction tensors. The proposed method leads to a small stiffness matrix that scales with the order of the reduced basis rather than the number of degrees of freedom in the finite element mesh. The reduced order variational spectral method maintains high accuracy in the computed response fields. A speedup higher than an order of magnitude can be achieved compared to the finite element method in polycrystalline microstructures. The accuracy and scalability of the method for large polycrystals and increasing phase property contrast are investigated.

A computational homogenization framework is proposed for solving transient wave propagation in the linear regime in heterogeneous poroelastic media that may exhibit local resonances due to microstructural heterogeneities. The microscale fluid-structure interaction problem and the macroscale are coupled through an extended version of the Hill-Mandel principle, leading to a variationally consistent averaging scheme of the microscale fields. The effective macroscopic constitutive relations are obtained by expressing the microscale problem with a reduced-order model that contains the longwave basis and the so-called local resonance basis, yielding the closed-form expressions for the homogenized material properties. The resulting macroscopic model is an enriched porous continuum with internal variables that represent the microscale dynamics at the macroscale, whereby the Biot model is recovered as a special case. Numerical examples demonstrate the framework's validity in modeling wave transmission through a porous layer.

The hybrid finite element-peridynamic (FEM-PD) models have been evidenced for their exceptional ability to address hydro-mechanical coupled problems involving cracks. Nevertheless, the non-local characteristics of the PD equations and the required inversion operations when solving fluid equations result in prohibitively high computational costs. In this paper, a fast explicit solution scheme for FEM-PD models based on matrix operation is introduced, where the graphics processing units (GPUs) are used to accelerate the computation. An in-house software is developed in MATLAB in both CPU and GPU versions. We first solve a problem related to pore pressure distribution in a single crack, demonstrating the accuracy of the proposed method by a comparison of FEM-PD solutions with those of PD-only models and analytical solutions. Subsequently, several examples are solved, including a one-dimensional dynamic consolidation problem and the fluid-driven hydraulic fracture propagation problems in both 2D and 3D cases, to comprehensively validate the effectiveness of the proposed methods in simulating deformation and fracture in saturated porous media under the influence of hydro-mechanical coupling. In the presented numerical results, some typical strong dynamic phenomena, such as stepwise crack advancement, crack branching, and pressure oscillations, are observed. In addition, we compare the wall times of all the cases executed on both the GPU and CPU, highlighting the substantial acceleration performance of the GPU, particularly when tackling problems with a significant computational workload.

The paper develops a systematic procedure for formulating finite elements on manifolds. The theoretical developments give rise to a modular computational framework for composing coordinate transformations and manifold parameterizations. The procedure is demonstrated with the Cosserat rod model furnishing a novel finite element formulation that rectifies the lack of objectivity of existing finite elements without violating the director constraints or compromising the symmetry of the tangent stiffness at equilibrium. The framework is element-independent, allowing its implementation as a wrapper to existing element libraries without modification of the element state determination procedures.

We present an efficient approach to quantify the uncertainties associated with the numerical simulations of the laser-based powder bed fusion of metals processes. Our study focuses on a thermomechanical model of an Inconel 625 cantilever beam, based on the AMBench2018-01 benchmark proposed by the National Institute of Standards and Technology (NIST). The proposed approach consists of a forward uncertainty quantification analysis of the residual strains of the cantilever beam given the uncertainty in some of the parameters of the numerical simulation, namely the powder convection coefficient and the activation temperature. The uncertainty on such parameters is modelled by a data-informed probability density function obtained by a Bayesian inversion procedure, based on the displacement experimental data provided by NIST. To overcome the computational challenges of both the Bayesian inversion and the forward uncertainty quantification analysis we employ a multi-fidelity surrogate modelling technique, specifically the multi-index stochastic collocation method. The proposed approach allows us to achieve a 33% reduction in the uncertainties on the prediction of residual strains compared with what we would get basing the forward UQ analysis on a-priori ranges for the uncertain parameters, and in particular the mode of the probability density function of such quantities (i.e., its “most likely value”, roughly speaking) results to be in good agreement with the experimental data provided by NIST, even though only displacement data were used for the Bayesian inversion procedure.