Finite Elements in Analysis and Design最新文献

This study aims to optimize topology of structures at macro and micro scales, simultaneously, by using a level set method in an isogeometric analysis (IGA) framework. To achieve this, equilibrium and homogenization equations in the model are solved by IGA method. The level set functions are defined over a grid in parameter space of associating b-splines of the IGA model. Therefore, control net of the model and level set grid are separated and there is no need to refine the control net for having smooth boundaries. Sensitivity analyses for both scales are performed to calculate the velocity of boundary points and the level set functions are updated by solving reaction-diffusion equations. Finally, several 2D and 3D examples with different geometry and boundary conditions are provided to show performance and efficiency of the method. Obtained results show good agreement with examples in literature in terms of both topology and final value of objective function. Also, by using IGA level set method, smooth boundaries are achieved in the final topology of micro and macro structures.

A novel topology optimization method for the design of coated structures infilled with multiple materials is proposed in this paper, where a novel material interpolation model for the topology description is developed based on the ordered SIMP scheme. With the introduction of two special Heaviside projections into the two-step filtering and projection procedure, the external coating and the substrate region can be well identified by using several modified design variables. Then, the material distribution of the multi-material infilling is obtained by multiplying the infill identification field with the piece-wisely projected design variables and optimized via the mathematical programming algorithm under the ordered SIMP framework. Using an eroded density field and its original field, the uniform thickness of the external coating can be well controlled. The proposed approach for optimizing coated structures with multi-phase infill materials is easy to implement due to its implementation relying on those frequently-used filtering and projection operations. Besides, without introducing any additional design variables, the method developed in this paper inherits the advantages of the ordered SIMP method and has great calculation efficiency and stable iteration performance. With the consideration of several issues such as different coating thicknesses and different design parameters, several 2D numerical examples are studied to demonstrate the effectiveness of the proposed approach, as well as a 3D example. The optimization results illustrate that the method developed in this paper is effective for the design of coated structures infilled with multiple materials and the advantages of considering multiple infill materials is also validated.

Polymeric materials find extensive applications across various engineering sectors. Among these, a particularly critical application for these materials is in the field of roller coasters. The wheels are typically made with an aluminum hub and a dense polyurethane coating, which, being in contact with the track, endures dynamic loads at high speeds. Due to the viscoelastic behavior typical of polymeric materials, these loads induce overheating of the coating leading to rapid degradation of the wheel. This results in machine downtime and a significant waste of time and money. In this manuscript, a methodology for finite element thermal-structural analysis has been developed. This method allows for the rapid evaluation of temperatures reached during operational cycles if compared to classical coupled-field thermal-structural analysis. The proposed methodology proves to be useful in selecting the appropriate type of wheels during the design phase requiring short computational time. The study first involved the development of the methodology, followed by validation through a comparison of analysis results with data obtained from experimental tests conducted by the manufacturer.

This study presents a combination approach of the higher-order shear deformation theory, nonlocal strain gradient theory (NSGT) and isogeometric analysis (IGA) for the free vibration of carbon nanotube-reinforced (CNT) magneto-electro-elastic (MEE) nanoplates. To account size-dependent effects at the nanoscale, the classical theory model is extended with two additional scale parameters. However, this extended model necessitates at least the third derivative of the approximation function, which is incompatible with the standard finite element method. So, IGA with NURBS offers higher-order continuity through its basis functions, making it well-suited for this size-dependent model. To simplify computations, a power-law scheme is employed to represent the material properties. Various distribution types of carbon nanotubes (CNTs) including UD, FG-X, FG-O and FG-V are incorporated to investigate their effects on mechanical behaviors of CNT-MEE nanoplates. The governing equations of motion are derived in their weak form using the principle of extended virtual displacement and then solved by isogeometric analysis (IGA). The impact of the magnetic, electric and elastic fields on the coupling behaviors of CNT-MEE nanoplates are studied. Specially, parametric studies are conducted to analyze the influence of geometrical parameters, CNT distributions, CNT volume fraction, matrix volume fraction, electric voltage, magnetic potential, nonlocal and strain gradient parameters on the natural frequencies of the CNT-MEE nanoplates. Comparisons between the results obtained using NSGT and the classical theory reveal significant findings. The natural frequencies calculated by NSGT exhibit dependence on the relative values of the nonlocal and strain gradient parameters.

Numerical simulations in biomechanics, particularly in bone healing, present a cost-effective option compared to experiments that demand prolonged observations with human or with animal models. However, to define in-silico simulations of the bone healing process requires considering multiple factors, such as the implant design and patient’s characteristics. As a result, the current challenge is integrating different numerical methodologies to simulate bone healing, aiming to facilitate the emergence of innovative clinical treatments and new implant designs.

In this paper, we present a patient-specific numerical methodology to simulate the bone healing process, able to consider patient’s load conditions and bone density distribution provided by CT-scans. The main novelty is the combination of the Cartesian grid Finite Element Method (cgFEM) with a bone callus healing model, complemented by a load-condition optimisation scheme to relate implant materials and load conditions while ensuring successful healing outcome.

This numerical methodology creates a finite element model based on the patient’s medical image, serving as a virtual testing tool for investigating the influence of implant materials on gait pattern requirements to ensure an optimal healing outcome. In practice, a personalised bone fracture model was employed to evaluate four distinct implant materials: two conventional materials (stainless steel and titanium) and two bioabsorbable candidates (polylactic acid plastic (PLA) and magnesium). The results offer personalised optimal load conditions for each studied material, showcasing the potential of in-silico studies in minimising uncertainties associated with exploring new clinical treatments.

Acoustic metamaterial structures have received extensive attention for sound and vibration engineering applications from the scientific community in recent years. However, the real-life application of conventional acoustic metamaterial structures is frequently limited by fixed frequency bands and increased structural thicknesses in low-frequency noise reduction. In this study, we introduce an origami-based acoustic metamaterial structure that consists of a Miura-ori foldcore, along with a perforated and an unperforated panel. The proposed Miura-ori foldcore sandwich acoustic metastructure (MOF-SAM) exhibits adjustable low-frequency sound absorption capacities due to the foldability of the origami foldcore. Moreover, we employ numerical methods to investigate the sound absorption properties of the MOF-SAM, quantified by the sound absorption coefficient. The results indicate that the structure has a single absorption peak which is superior to that of acoustic structures composed of conventional honeycomb cores. The dissipation of acoustic energy is due to the structural vibrations of the metastructure and the losses in the folding process of the origami foldcore. The numerical results of this study show that the proposed sound absorption mechanism enables tunable low-frequency sound absorption. The geometric design and periodicity of the origami unit fragments offer multiple distinct absorption peaks and thus tunable acoustic performance. These findings of this study are expected to inspire novel designs for next-generation acoustic devices.

The Hilbert spaces $H\left(\mathrm{curl}\right)$ and $H\left(\mathrm{div}\right)$ are employed in various variational problems formulated in the context of the de Rham complex in order to guarantee well-posedness. Seeing as the well-posedness follows automatically from the continuous setting to the discrete setting in the presence of commuting interpolants as per Fortin’s criterion, the construction of conforming subspaces becomes a crucial step in the formulation of stable numerical schemes. This work aims to introduce a novel, simple method of directly constructing semi-continuous vectorial base functions on the reference element via template vectors associated with the geometric polytopes of the element and an underlying $H^1$-conforming polynomial subspace. The base functions are then mapped from the reference element to the element in the physical domain via consistent Piola transformations. The method is defined in such a way, that the underlying $H^1$-conforming subspace can be chosen independently, thus allowing for constructions of arbitrary polynomial order. We prove a linearly independent construction of Nédélec elements of the first and second type, Brezzi–Douglas–Marini elements, and Raviart–Thomas elements on triangulations and tetrahedralizations. The application of the method is demonstrated with two examples in the relaxed micromorphic model.

This paper presents results and convergence study of the Global–Local Iterative Coupling through the implementation in the commercial software Abaqus making use of the co-simulation engine. A hierarchical modeling and simulation approach is often required to alleviate modeling burdens. Particular focus has been devoted here on convergence acceleration and performance optimization. Two applications in statics with nonlinear material behavior and geometrically nonlinear formulation are considered here: first a holed curved plate under traction with elastic–plastic material, then a pre-stressed bolted joint connecting two plates between each other and subjected to traction load. Three different convergence acceleration techniques are compared in terms of convergence performance and accuracy. An inexact solver strategy is proposed to improve computing time performance. The results show promising results for the coupling technology and constitute a step forward in the availability of non-intrusive multi-scale modeling capabilities for complex structures and assemblies.

This study investigates the numerical simulation of fracture behaviour in quasi-brittle materials like magnesia spinel refractories using the Gradient-Enhanced Damage (GED) model. It focuses on the complex modelling of these materials non-linear responses and compares conventional and variant GED models through a wedge splitting test. The results demonstrate that all GED models show a good fit to experimental data. However, the conventional GED model falls short in accurately depicting the fracture process zone. In contrast, the localizing GED model more accurately represents the fracture process zone, limiting spurious damage distribution, but requires finer meshing, elevating computational demands. The stress-based variant reduces spurious damage but is less effective comparatively. The study also assesses the role of heterogeneous strength distribution in replicating realistic crack patterns as observed in experiments.

In the present study, an elastoplastic phase-field model of quasi-static fracture in ductile materials is proposed in the variational framework for J₂ plasticity with isotropic hardening, which is suitable to describe the quasi-static behavior of metals as investigated in the performed experiments. These contributions include: (1) the free energy functions for coupling elastic response, plastic yielding and damage evolution are established. (2) The new elastic and plastic energy degradation functions are constructed to quantitatively describe the relationship between energy release and phase-field evolution of elastoplastic materials. (3) Damage evolution and plastic yielding criteria are derived. (4) From a numerical point of view, we derive the governing equations and the corresponding weak forms and the overall solution procedure for the phase-field model is given via the use of a return-mapping algorithm. This phase-field model was validated by a series of tensile experiments on Inconel 718 nickel-based super-alloys standard specimens. In order to compare the simulation results with the experimental results more comprehensively, the digital image correlation (DIC) technique is applied to experimentally investigate the specimen deformation information. In addition, to verify the potential of the model to capture complex cracks, we performed Nooru-Mohamed tests. The numerical simulation results are in good agreements with the results of previous experimental work.