Finite Elements in Analysis and Design最新文献

In this work, we propose the application of the eXtended Finite Element Method (XFEM) in the context of the coupling between three-dimensional and one-dimensional elliptic problems. In particular, we consider the case in which the 3D–1D coupled problem arises from the geometrical model reduction of a fully three-dimensional problem, characterized by thin tubular inclusions embedded in a much wider domain. In the 3D–1D coupling framework, the use of non conforming meshes is widely adopted. However, since the inclusions typically behave as singular sinks or sources for the 3D problem, mesh adaptation near the embedded 1D domains may be necessary to enhance solution accuracy and recover optimal convergence rates. An alternative to mesh adaptation is represented by the XFEM, which we here propose to enhance the approximation capabilities of an optimization-based 3D–1D coupling approach. An effective quadrature strategy is devised to integrate the enrichment functions and numerical tests on single and multiple segments are proposed to demonstrate the effectiveness of the approach.

High-energy particles, including photons (x-ray, γ-ray, bremsstrahlung), electrons, and protons, possess the capability to penetrate materials and deposit energy within them. The degree of absorption depends on both the energy and type of particles, as well as the properties of the materials with which they interact. This energy deposition can manifest either at the material's surface or throughout its volume, potentially resulting in various failure modes.

The primary aim of this paper is to establish a structured analysis methodology for evaluating the structural integrity of beam-intercepting devices when subjected to high-energy particles. The paper also reviews some of the underlying physics, pertinent to the scope of the thermomechanical analysis, potential failure modes, and introduces verification and validation methodologies. Engineers and researchers can utilize the guidelines presented in this paper to effectively plan the development of beam intercepting devices, thereby ensuring their reliability and performance in the presence of high-energy particle exposure.

The present work deals with the numerical resolution of coupled 3D–2D problems arising from the simulation of fluid flow in fractured porous media modeled via the Discrete Fracture and Matrix (DFM) model. According to the DFM model, fractures are represented as planar interfaces immersed in a 3D porous matrix and can behave as preferential flow paths, in the case of conductive fractures, or can actually be a barrier for the flow, when, instead, the permeability in the normal-to-fracture direction is small compared to the permeability of the matrix. Consequently, the pressure solution in a DFM can be discontinuous across a barrier, as a result of the geometrical dimensional reduction operated on the fracture. The present work is aimed at developing a numerical scheme suitable for the simulation of the flow in a DFM with fractures and barriers, using a mesh for the 3D matrix non conforming to the fractures and that is ready for domain decomposition. This is achieved starting from a PDE-constrained optimization method, currently available in literature only for conductive fractures in a DFM. First, a novel formulation of the optimization problem is defined to account for non permeable fractures. These are described by a filtration-like coupling at the interface with the surrounding porous matrix. Also the extended finite element method with discontinuous enrichment functions is used to reproduce the pressure solution in the matrix around a barrier. The method is presented here in its simplest form, for clarity of exposition, i.e. considering the case of a single fracture in a 3D domain, also providing a proof of the well posedness of the resulting discrete problem. Four validation examples are proposed to show the viability and the effectiveness of the method.

Rolling in Directed Energy Deposition (DED) has shown promising improvements in build quality by providing compressive deformations. The rolling dynamics and associated boundary conditions are crucial for how these deformations impact the stress–strain profiles on the deposited part and substrate. This study investigates these impacts by developing a fully coupled dynamic-thermo-mechanical finite-element model in Abaqus for in-situ micro-rolling in DED. Single bead analyses have been done with a 2D heat flux moving ahead of the roller at a fixed offset. Two rolling boundary condition cases with varying friction at the roller-bead interface have been examined: (i) only translation defined with rotation calculated from roller-bead interaction and (ii) translation with a defined rotation corresponding to a no-slip condition. In the first case, analyses have shown that the surface stress–strain conditions and rolling load variation are susceptible to interfacial friction. With increasing friction, the surface conditions deteriorate and variations in rolling load increase. However, beyond the surface, the overall stress–strain profiles remain similar. The surface stress–strain profile and rolling load variation have been smoothened in the second case because of the defined rotation. Further, a comparison has been made between the results of dynamic-explicit analyses and static-implicit analyses to quantify the roller’s inertia effects. The stress–strain profiles predicted by both analyses have marginal differences but with 16 % over-prediction in rolling load by dynamic-explicit analyses. These results imply that the roller’s inertia marginally affects the deposited part’s stress–strain evolution but has a notable role in rolling load. Also, providing an external drive to the roller corresponding to the second case can effectively minimise the deteriorating effects of roller-bead interfacial friction.

The Cauer ladder network (CLN) method, as proposed by Kameari et al. (2018), has been extensively studied to construct a reduced model of magneto-quasistatic (MQS) Finite Element (FE) models. In this case, this method enables the construction of an equivalent electrical circuit based on resistances and inductances as well as a reduced basis where the solution of a reduced problem is sought. In this article, we propose to extend the applicability of the CLN method to the development of reduced models for FE electro-quasistatic (EQS) models. It appears that the derivation of the reduction of an EQS model is not similar to the one of an MQS model. After development, the process of reduction using CLN leads to consider two electrical circuits based on the cascade association of resistances and capacitances. Each circuit is associated with a reduced basis constructed by applying the self-adjoint Lanczos method. The reduced solution to the EQS problem is got by first solving the circuit equations to determine the voltages and the currents at the terminals of the resistances and capacitances. Then, the approximated solution of the FE EQS model is got by a linear combination of the vectors of the two reduced bases weighted by the currents (or the voltages) previously calculated. An error estimator is also derived, enabling to calculate the distance between the reduced solution and the FE solution without solving the FE model. The proposed approach has been applied on an industrial application, a resin-impregnated paper bushing, in order to evaluate the accuracy in function of the size of the reduced bases as well as the efficiency in terms of computation time.

The Node-to-Segment (NTS) method enhanced computational contact mechanics by enabling contact analysis with large deformations with contact location as part of the unknowns. Despite having shortcomings, it is still to this day largely employed by the industry for contact analysis between continuous surfaces due to its low computational cost and scalability, instead of more precise, mathematically sound, but more computationally expensive methods. The method’s persistent relevance inspired attempts at improving its performance, usually for first-order elements. It is well known that NTS is not working well for higher orders due to its topological inconsistency. This work proposes a way of reducing the side-effects of the second order penalty-based Node-to-Segment method without adding complexity to contact detection or formulation. This can be achieved using virtual elements to describe the adjacent continuum, because of a filter effect introduced by the polynomial projection used in stress post-processing, which reduces the stress oscillations resulting from higher order penalty-based Node-to-Segment methods.

Considering the interaction between concrete and steel reinforcement in numerical simulations of reinforced concrete structures is crucial for accurately capturing the concrete cracking process. This is particularly interesting when studying structures fulfilling functions that go beyond their simple mechanical resistance, such as waterproofing functions. While three-dimensional (3D) volumetric finite element modeling offers detailed insights into structural behavior, its computational intensity becomes prohibitive for large-scale structures. In such contexts, adopting beam and plate elements formulations proves computationally more efficient, due to their reduced number of degrees of freedom. This paper presents a kinematic enhancement technique designed to integrate steel-concrete interface behavior into beam and plate finite element formulations. The approach combines classical beam or plate elements representing concrete behavior, conventional beam or truss elements modeling steel reinforcement, and the incorporation of bond stresses at the interface. The paper provides comprehensive explanations of this enhancement technique along with a curated selection of numerical validation and application examples. These examples are supplemented by a comparison with experimental data, illustrating the efficiency of the proposed enhancement approach.

In the Directed Energy Deposition (DED) process, when the mass flow of metal particles is relatively high, the thickness of the layers increases, leading to a more productive process. The higher the mass flow is, the more difficult it becomes to get a stable melt pool. The accumulation of residual heat in the previously consolidated material constitutes a thermal input affecting the balance at the laser-material interaction zone. An accurate control of the temperature of the laser-material interaction zone is critical to maintain the dynamic viscosity of the liquid metal within the narrow margin in which it can be managed in a stable way. The present work introduces a thermal model in which domains with tunable properties are considered to reproduce the growing of the manufactured sample. Concurrently, a virtual closed-loop PID regulator has been implemented in order to calculate suitable values of laser power to compensate the heat accumulated in the material, offering the results from the model as input process parameters to be directly applied in the real process. The levels of laser power proposed by the model have been experimentally applied, leading to a stable process capable of carrying out in reality the desired component.

This work is the second of a two-part research project focused on modeling solid-shell elements using a stabilized two-field finite element formulation. The first part introduces a stabilization technique based on the Variational Multiscale framework, which is proven to effectively address numerical locking in infinitesimal strain problems. The primary objective of the study was to characterize the inherent numerical locking effects of solid-shell elements in order to comprehensively understand their triggers and how stabilized mixed formulations can overcome them. In this current phase of the work, the concept is extended to finite strain solid dynamics involving hyperelastic materials. The aim of introducing this method is to obtain a robust stabilized mixed formulation that enhances the accuracy of the stress field. This improved formulation holds great potential for accurately approximating shell structures undergoing finite deformations. To this end, three techniques based in the Variational Multiscale stabilization framework are presented. These stabilized formulations allow circumventing the compatibility restriction of interpolating spaces of the unknowns inherent to mixed formulations, thus allowing any combination of them. The accuracy of the stress field is successfully enhanced while maintaining the accuracy of the displacement field. These improvements are also inherited to the solid-shell elements, providing locking-free approximation of thin structures.

A comprehensive model has been developed to couple CFD with the population balance equation (PBE) for a flat sheet membrane-assisted antisolvent crystallization (FS-MAAC) process. The model accurately depicts the fluid dynamics, mass transfer, heat transfer and crystal size distribution (CSD) in the FS-MAAC crystallizer. The crystallization system considered was to produce α-form crystals of glycine. The model investigates the effects of different parameters, such as the velocities of the crystallizing and antisolvent solutions, antisolvent composition, temperature, and gravity. A good agreement was observed between the simulation results and experimental data for the α-form crystals of glycine. The simulation results show a steady-state antisolvent concentration profile in the liquid layer and varied only in the z-direction. Regardless of the variations in the velocity of either the antisolvent solution or the crystallizing solution, the CSD remained narrow, with mean crystal sizes ranging from 27 to 40 μm. Furthermore, increasing mass transfer through the antisolvent transmembrane flux leads to a narrower CSD. Slower antisolvent permeation rates at higher temperatures also promote crystal growth. Also, a narrow CSD is maintained regardless of the initial circulation position of the antisolvent solution. In conclusion, membrane antisolvent crystallization provides a reliable and consistent solution for obtaining crystals with desired CSD under optimal operating conditions.