Finite Element Method Research Articles

Numerical investigation of surface and volume thermal imaging of nickel-graphene foam sheets by finite element method

The detailed theoretical analysis of heat equations is applied to Nickel foam specimens with various pore-size coated graphene thin film of 200 nm thickness under laser excitation. 2D and 3D thermal numerical models were proposed by applying the finite element method. To explain the proposed numerical model, the influence of discretization parameters and the heat diffusion length were studied. The proposed model accurately predicts the thermal spreading in the specimens. The numerical model showed the sensitivity of the model for the structure variation to achieve an accurate thermal imaging when the used laser is of radius value is within of specimen pore size and modulated at low frequency.

Exploring the optimal mechanical properties of triply periodic minimal surface structures for biomedical applications: A Numerical analysis

Currently, cutting-edge Additive Manufacturing techniques, such as Selective Laser Melting (SLM) and Electron Beam Melting (EBM), offer manufacturers a valuable avenue, especially in biomedical devices. These techniques produce intricate porous structures that draw inspiration from nature, boast biocompatibility, and effectively counter the adverse issues tied to solid implants, including stress shielding, cortical hypertrophy, and micromotions. Within the domain of such porous structures, Triply Periodic Minimal Surface (TPMS) configurations, specifically the Gyroid, Diamond, and Primitive designs, exhibit exceptional performance due to their bioinspired forms and remarkable mechanical and fatigue properties, outshining other porous counterparts. Consequently, they emerge as strong contenders for biomedical implants. However, assessing the mechanical properties and manufacturability of TPMS structures within the appropriate ranges of pore size, unit cell size, and porosity tailored for biomedical applications remains paramount. This study aims to scrutinize the mechanical behavior of Gyroid, Diamond, and Primitive structures in solid and sheet network iterations within the morphological parameter ranges suitable for tasks like cell seeding, vascularization, and osseointegration. A comparison with the mechanical characteristics of host bones is also undertaken. The methodology revolves around Finite Element Method (FEM) analysis. The six structures are originally modeled with unit cell sizes of 1, 1.5, 2, and 2.5 mm, and porosity levels ranging from 50% to 85%. Subsequently, mechanical properties, such as elasticity modulus and yield strength, are quantified through numerical analysis. The results underscore that implementing TPMS designs enables unit cell sizes between 1 and 2.5 mm, facilitating pore sizes within the suitable range of approximately 300–1500 μm for biomedical implants. Elasticity modulus spans from 1.5 to 33.8 GPa, while yield strength ranges around 20–304.5 MPa across the 50%–85% porosity spectrum. Generally, altering the unit cell size exhibits minimal impact on mechanical properties within the range above; however, it's noteworthy that smaller porosities correspond to heightened defects in additively manufactured structures. Thus, for an acceptable pore size range of 500–1000 μm and a minimum wall thickness of 150 μm, a prudent choice would involve adopting a 2.5 mm unit cell size.

Vibration suppression of a meta-structure with hybridization of Kresling origami and Yoshimura origami

In recent years, the deployment and vibration suppression capabilities of spacecraft have become one of the prominent research topics. Considerable effort has been dedicated to studying the deployability and vibration suppression performance of origami structures. However, traditional origami types severely limit their application in aerospace engineering due to their unique deployment behavior. This study introduces a novel meta-structure with hybridization of Kresling origami and Yoshimura origami (MHKYO), designed to suppress low-frequency vibrations. The band structure and transmission rate of the proposed metastructure were studied to evaluate its vibration suppression performance. The adjustment of the bandgap of the metastructure was achieved through geometric parameter variation. Quasi-static compression experiments and transmission rate experiments were carried out, and the results obtained were almost consistent with those obtained by finite element methods. During the compression process, the origami metastructure exhibited quasi-zero-stiffness (QZS) behavior. The influence of the metastructure’s stiffness on the band structure was analyzed. It is also proved that the hybrid origami metastructure improves the vibration suppression performance of the traditional origami metastructure. This work proposes a new origami-inspired metastructure, providing a certain theoretical basis for the application of origami technology in aerospace engineering.

Free Vibration of Graphene Nanoplatelet-Reinforced Porous Double-Curved Shells of Revolution with a General Radius of Curvature Based on a Semi-Analytical Method

Based on domain decomposition, a semi-analytical method (SAM) is applied to analyze the free vibration of double-curved shells of revolution with a general curvature radius made from graphene nanoplatelet (GPL)-reinforced porous composites. The mechanical properties of the GPL-reinforced composition are assessed with the Halpin–Tsai model. The double-curvature shell of revolution is broken down into segments along its axis in accordance with first-order shear deformation theory (FSDT) and the multi-segment partitioning technique, to derive the shell’s functional energy. At the same time, interfacial potential is used to ensure the continuity of the contact surface between neighboring segments. By applying the least-squares weighted residual method (LWRM) and modified variational principle (MVP) to relax and achieve interface compatibility conditions, a theoretical framework for analyzing vibrations is developed. The displacements and rotations are described through Fourier series and Chebyshev polynomials, accordingly, converting a two-dimensional issue into a suite of decoupled one-dimensional problems. The obtained solutions are contrasted with those achieved using the finite element method (FEM) and other existing results, and the current formulation’s validity and precision are confirmed. Example cases are presented to demonstrate the free vibration of GPL-reinforced porous composite double-curved paraboloidal, elliptical, and hyperbolical shells of revolution. The findings demonstrate that the natural frequency of the shell is related to pore coefficients, porosity, the mass fraction of the GPLs, and the distribution patterns of the GPLs.

Design and Failure Analysis of Piston Using Ansys

A piston is a component of reciprocating engines. The purpose of piston is to transfer force from expanding gas in the cylinder to the crankshaft via a piston rod and a connecting rod. It is one of the most complex components of an automobile. In This project we are describes the Thermal analysis by using finite element method (FEM). The specifications used for designing the piston belong to four stroke single cylinder engine of piston. Modeling of piston is done using SOLID EDGE v20. static structural, Thermal and fatigue analysis is performed by using ANSYS WORKBENCH 2022 R1. The parameters used for the simulation are operating gas pressure, material properties of piston. The results predict the maximum stress and strain on pistons using FEA. The best material is selected based on static structural, thermal and fatigue analysis. The analysis results are used to optimize piston geometry of best two Materials

A Simplified Calibration Procedure for DEM Simulations of Granular Material Flow

The discrete element method (DEM) has emerged as an essential computational tool in geotechnical engineering for the simulation of granular materials, offering significant advantages over traditional continuum-based methods such as the finite element method (FEM) and the finite difference method (FDM). The DEM’s ability to model particle-level interactions, including contact forces, rotations, and particle breakage, allows for a more precise understanding of granular media behavior under various loading conditions. However, accurate DEM simulations require meticulous calibration of input parameters, such as particle density, stiffness, and friction, to effectively replicate real-world behavior. This study proposes a simplified calibration procedure, intended to be conducted prior to any granular material flow DEM modeling, based on three fundamental physical tests: bulk density, surface friction, and angle of repose. The ability of these tests, conducted on dry quartz sand, to accurately determine DEM micromechanical parameters, was validated through numerical simulation of cylinder tests with varying height-to-radius ratios. The results demonstrated that this calibration approach effectively reduced computational complexity while maintaining high accuracy, with validation errors of 0% to 12%. This research underscores the efficacy of simplified DEM calibration methods in enhancing the predictive reliability of simulations, particularly for sand modeling in geotechnical applications.

A study on the influence of material gradient index on bending and stress responses of FGM rectangular plates using the Finite Element Method

Functionally graded materials (FGMs) are advanced materials designed to achieve specific property gradients. The unique characteristic of these materials—variations in spatial dimensions—allows for integrating the advantages of different materials within a single component, where a combination of properties, such as mechanical strength, thermal resistance, and others, is needed. This paper utilizes finite element analysis to examine the deflection and stress responses of FGM rectangular plates with different material gradient profiles. Various boundary conditions, including clamped, simply supported, and free edges in different configurations, are considered. The plates are subjected to uniformly distributed, sinusoidally distributed, and concentrated loads. The study investigates the effects of boundary and loading conditions, along with the impact of the material gradient, on the deflections and stress responses of FGM rectangular plates. The results indicate variations in deflection and stress values for different material gradients, under varying boundary and loading conditions.

Advanced Computational Methods for Simulating and Optimizing Stochastic Fracture: A Systematic Literature Review

Stochastic fracture processes, pervasive in diverse natural and engineered systems, pose intricate challenges for accurate simulation and optimization. This systematic literature review surveys the landscape of advanced computational methodologies to unravel and optimize stochastic fracture phenomena. Grounded in multidisciplinary perspectives spanning engineering, physics, and applied mathematics, the review navigates through the intricacies of simulation techniques and optimizations methods. From Finite Element Method (FEM) to Molecular Dynamics (MD) simulations, the review delineates the evolution and application of computational frameworks. It scrutinizes optimization strategies ranging from evolutionary algorithms to surrogate-assisted techniques, illuminating their efficacy in optimizing fracture properties amidst stochasticity. Drawing from applications in geological formations, engineered materials, and biomechanics, the review elucidates the diverse realms where advanced computational methods find resonance. Despite strides in computational prowess, challenges loom large, including computational complexity, validation dilemmas, and interdisciplinary communication barriers. Looking ahead, the review prognosticates on the integration of machine learning, novel algorithmic developments, and standardization endeavor’s to propel the frontier of stochastic fracture simulations towards unprecedented realms of understanding and optimization. Through synthesis and critique, this review engenders a roadmap for future research and underscores the transformative potential of advanced computational methods in deciphering stochastic fracture phenomena.

Local resonance metamaterial-based integrated design for suppressing longitudinal and transverse waves in fluid-conveying pipes

To solve the problem of low broadband multi-directional vibration control of fluid-conveying pipes, a novel metamaterial periodic structure with multi-directional wide bandgaps is proposed. First, an integrated design method is proposed for the longitudinal and transverse wave control of fluid-conveying pipes, and a novel periodic structure unit model is constructed for vibration reduction. Based on the bandgap vibration reduction mechanism of the acoustic metamaterial periodic structure, the material parameters, structural parameters, and the arrangement interval of the periodic structure unit are optimized. The finite element method (FEM) is used to predict the vibration transmission characteristics of the fluid-conveying pipe installed with the vibration reduction periodic structure. Then, the wave/spectrum element method (WSEM) and experimental test are used to verify the calculated results above. Lastly, the vibration attenuation characteristics of the structure under different conditions, such as rubber material parameters, mass ring material, and fluid-structure coupling effect, are analyzed. The results show that the structure can produce a complete bandgap of 46 Hz–75 Hz in the low-frequency band below 100 Hz, which can effectively suppress the low broadband vibration of the fluid-conveying pipe. In addition, a high damping rubber material is used in the design of the periodic structure unit, which realizes the effective suppression of each formant peak of the pipe, and improves the vibration reduction effect of the fluid-conveying pipe. Meanwhile, the structure has the effect of suppressing both bending vibration and longitudinal vibration, and effectively inhibits the transmission of transverse waves and longitudinal waves in the pipe. The research results provide a reference for the application of acoustic metamaterials in the multi-directional vibration control of fluid-conveying pipes.

Elastic wave insulation and propagation control based on the programmable curved-beam periodic structure

AbstractCurved-beams can be used to design modular multistable metamaterials (MMMs) with reprogrammable material properties, i.e., programmable curved-beam periodic structure (PCBPS), which is promising for controlling the elastic wave propagation. The PCBPS is theoretically equivalent to a spring-oscillator system to investigate the mechanism of bandgap, analyze the wave propagation mechanisms, and further form its geometrical and physical criteria for tuning the elastic wave propagation. With the equivalent model, we calculate the analytical solutions of the dispersion relations to demonstrate its adjustability, and investigate the wave propagation characteristics through the PCBPS. To validate the equivalent system, the finite element method (FEM) is employed. It is revealed that the bandgaps of the PCBPS can be turned on-and-off and shifted by varying its physical and geometrical characteristics. The findings are highly promising for advancing the practical application of periodic structures in wave insulation and propagation control.

Cumulative effects of cyclic train loading on strains in reinforced soils around tunnels

Metro tunnels often experience uneven settlement of the soil beneath them during operation, a problem that is especially pronounced in soft soil layers such as silt. This uneven settlement negatively affects the operational safety of subways, prompting engineers to use soil reinforcement techniques to mitigate ground deformation. However, there is a lack of research on the cumulative deformation of reinforced soils under cyclic train loading. In this study, dynamic triaxial tests were conducted to obtain the deformation parameters of silty reinforced soils under cyclic loading. The principal dynamic relationship was summarized, and the effect of loading frequency on soil deformation was analyzed. The results indicated that as the loading frequency increased, the cumulative deformation of the soil decreased. Using the dynamic constitutive relationship derived from the tests, the finite element method was employed to model the interaction system between the load, tunnel, and strata, as well as the dynamic modulus attenuation behavior of the reinforced soil layer. This approach was used to investigate the cumulative deformation characteristics of reinforced soils under cyclic loading. The findings indicated that the dynamic modulus of the reinforced soil decayed rapidly at the beginning of the loading period, leading to an accelerated increase in the cumulative deformation. Additionally, the cumulative deformation was measured at different train speeds, revealing that when the speeds exceeded 80 km/h, the cumulative strain of the soil increased gradually with speed.

Theoretical and Numerical Analysis of Singular Perturbation Problems in Ordinary Differential Equations

Background: Singular perturbation troubles in everyday differential equations (ODEs) involve a small parameter ϵ that causes answers to show off behaviors on multiple scales, main to massive challenges in both theoretical and numerical evaluation. Objective: This paper at targets to comprehensively look at the theoretical and numerical techniques for reading and solving singular perturbation troubles in ODEs. Focus is located on know-how the behaviors precipitated through the small parameter and developing strong numerical techniques to accurately seize these behaviors. Methods: Theoretical approaches employed include matched asymptotic expansions and multiple scale analysis. These methods decompose the solution domain into regions with different scales, constructing and matching approximate solutions to ensure smooth transitions. Numerical techniques such as finite difference methods, finite element methods, and spectral methods are utilized, with particular emphasis on adaptive mesh refinement to handle boundary layers effectively Results: Theoretical evaluation demonstrates the effectiveness of matched asymptotic expansions and multiple scale analysis in presenting correct approximations and easy transitions among one of a kind solution regions. Numerical techniques showed high accuracy and performance, particularly whilst blended with adaptive techniques. Finite distinction strategies with non-uniform grids and adaptive mesh refinement, finite detail techniques with adaptive mesh strategies, and spectral strategies with special handling of boundary layers all proved successful. Stability and convergence analyses showed the reliability of those techniques. Conclusions: This comprehensive evaluation highlights the strengths and applicability of each theoretical and numerical strategies in tackling singular perturbation issues in ODEs. The mixed use of these techniques lets in for correct and green answers, presenting treasured equipment for applications in diverse clinical and engineering fields.

Damage Quantification Using Mode Converted Guided Wave Based 1D Damage-Spectral Element

Quantifying the sizes of the damages in structures using guided waves is an emerging technology. It needs a suitable mathematical model that represents the behavior of the guided waves as they travel through the structure. Though finite element based theoretical models can provide insight into the behavior, they are computationally very costly. Spectral element is a promising solution in this regard. Quantifying the damage using a mode-converted wave based spectral element has not been reported yet. In this work, a spectral element that represents the characteristics of wave propagation, scattering and mode conversion caused by asymmetric notch-type damage in an isotropic waveguide is presented. This frequency domain damage-spectral element is formulated through a combination of three structural waveguides by enforcing appropriate force equilibrium conditions. The spectral element is able to represent the wave scattering and mode conversion due to the presence of the damage. This spectral element is employed in analyzing the wave propagation in a beam that has damage and the characteristics obtained are in agreement with the results expected based on time-of-flight calculations and those obtained using the finite element method. The relation between the depth of the damage and the magnitude of the mode-converted wave for notch-type damage is established using this spectral element and compared with the experimental result. Usage of the same spectral element in quantifying the length of the damage based on the reflections of the primary propagating wave from the damage ends is also demonstrated.

The cross-sectional morphology of the proximal femoral diaphysis is defined by the anteversion angle.

Osteoporosis in postmenopausal women is one of the causes of femoral fractures and is prevented by the administration of bisphosphonates. Individual morphologies are considered to increase the risk of atypical fractures associated with long-term administration. To evaluate cortical bone morphology quantitatively, we established a method to measure the distance from the center point of a cross-section to the external and internal borders based on CT images. Using this method, 44 sides of a female femoral skeleton specimen were examined and areas of protrusion and thickening in the medial anterior and lateral posterior regions just below the lesser trochanter were identified. These positions strongly correlated with the anteversion angle, suggesting the involvement of the distribution of the load received from body weight defined by the angle. The finite element method was used to examine the relationships between the positions of these areas with compressive and tensile stress distribution areas in the one-legged standing condition. The medial anterior region and lateral posterior region protruded and thickened in response to compressive and tensile stress, respectively. In addition, a hierarchical relationship was observed between the anteversion angle, tensile stress distribution, protrusion, and thickening in femurs with thinning of cortical bone, indicating that morphogenesis occurs adaptively to loading. The present results demonstrate the usefulness of this method in considering the formation mechanism and function of the femoral diaphysis and suggest that bone remodeling is necessary to maintain adaptability.

Low-frequency bandgap and vibration suppression mechanism of a novel square hierarchical honeycomb metamaterial

AbstractThe suppression of low-frequency vibration and noise has always been an important issue in a wide range of engineering applications. To address this concern, a novel square hierarchical honeycomb metamaterial capable of reducing low-frequency noise has been developed. By combining Bloch’s theorem with the finite element method, the band structure is calculated. Numerical results indicate that this metamaterial can produce multiple low-frequency bandgaps within 500 Hz, with a bandgap ratio exceeding 50%. The first bandgap spans from 169.57 Hz to 216.42 Hz. To reveal the formation mechanism of the bandgap, a vibrational mode analysis is performed. Numerical analysis demonstrates that the bandgap is attributed to the suppression of elastic wave propagation by the vibrations of the structure’s two protruding corners and overall expansion vibrations. Additionally, detailed parametric analyses are conducted to investigate the effect of θ, i.e., the angle between the protruding corner of the structure and the horizontal direction, on the band structures and the total effective bandgap width. It is found that reducing θ is conducive to obtaining lower frequency bandgaps. The propagation characteristics of elastic waves in the structure are explored by the group velocity, phase velocity, and wave propagation direction. Finally, the transmission characteristics of a finite periodic structure are investigated experimentally. The results indicate significant acceleration amplitude attenuation within the bandgap range, confirming the structure’s excellent low-frequency vibration suppression capability.

Dynamic data-driven multiscale modeling for predicting the degradation of a 316L stainless steel nuclear cladding material

We have developed a long short-term memory stacked ensemble (LSTM-SE) surrogate modeling approach that can provide rapid predictions of microstructural evolution and the resultant mechanical properties of American Iron and Steel Institute (AISI) 316L series stainless steel (SS316L) fuel cladding under conditions of varying temperature and radiation dose rate. To acquire training data, we developed and implemented a kinetic Monte Carlo (KMC) model to simulate precipitation kinetics of M23C6, γ’, and G phases within SS316L cladding. Experimentally reported precipitation kinetics of SS316L in literature were linked to the kinetic parameters of the simulated precipitation in our KMC model. The model was then used to simulate microstructure evolution under synthetically generated treatments of varying temperature and radiation dose rate for periods of up to 3000 h. Changes in volume fraction, number density, and particle size of precipitates were recorded, and particle area fractions were correlated using statistical methods to develop the surrogate model. Simultaneously, the mechanical properties of the simulated microstructures were evaluated using microstructure-based finite element method (FEM) analysis to determine the elastic modulus, yield stress, ultimate tensile strength, and elongation to failure of the aged microstructures. Using this approach, our surrogate model can predict precipitation behavior within 0.25 % volume fraction and mechanical properties within 6 % relative error from the values predicted by the KMC and FEM models using 50 training simulations as input. The trained recurrent neural network-based model can return estimations of precipitation kinetics and mechanical properties ∼1000 times faster than the physics-based codes. This work demonstrates, as a proof of concept, that microstructural evolution under variable conditions can be predicted using a statistics-based model informed by a practicably obtainable dataset. The potential applications of this type of modeling framework are discussed.

Characteristics study of a dual-wavelength polarization filter based on gold-filled square lattice photonic crystal fiber

This study proposes a polarization filter based on gold-filled photonic crystal fiber (PCF) with a square lattice structure. Utilizing the finite element method (FEM), the filtering characteristics of the model were numerically simulated. The dispersion relation and loss characteristics of this structure were analyzed, and the optimal structural parameters were obtained through structural adjustments. Furthermore, the performance of the filter was evaluated under a 2% variation in manufacturing tolerances for gold film thickness (), air hole spacing (), and air hole diameters () and (). Results indicated that at the 1310 nm and 1550 nm communication windows, the confinement losses of the filter were 1354.6 dB/cm and 869.04 dB/cm, respectively, while the losses for the -polarization were merely 16.97 dB/cm and 0.98 dB/cm. When the filter length was set to 0.5 mm, the maximum extinction ratios (ERs) for the two windows reached 588.2 dB and 370.6 dB, and the filter bandwidth extended to 640 nm. Moreover, the characteristics of the filter under manufacturing tolerances were computed, revealing that the filter’s performance remained stable and feasible despite manufacturing errors. The proposed rectangular gold-coated PCF is anticipated to have broad applications in optical fiber communication and optical information processing.

Study of the Sliding Friction Coefficient of Different-Size Elements in Discrete Element Method Based on an Experimental Method

The materials involved in geotechnical engineering are objects of concern in granular mechanics. In order to study the influence of the sliding friction coefficient corresponding to different-sized elements in the discrete element method (DEM) on the simulation results, we establish a two-dimensional DEM model based on the experimental method to analyze a slope example. The correctness of the DEM model is verified by comparing the sliding surface of a finite element method (FEM) model and the DEM slope model. A sliding friction coefficient algorithm based on the experimental method is embedded into the DEM slope model and compared with the original model. The comparison results show that embedding the DEM model into the sliding friction coefficient algorithm leads to an increase in displacement. The reason for this is that the contact information between elements of different sizes has changed, but the displacement trend is the same. Different sliding friction coefficients should be set based on different-sized elements in the DEM, as they can improve simulation accuracy.

A High-Precision Inverse Finite Element Method for Shape Sensing and Structural Health Monitoring

In the contemporary era, the further exploitation of deep-sea resources has led to a significant expansion of the role of ships in numerous domains, such as in oil and gas extraction. However, the harsh marine environments to which ships are frequently subjected can result in structural failures. In order to ensure the safety of the crew and the ship, and to reduce the costs associated with such failures, it is imperative to utilise a structural health monitoring (SHM) system to monitor the ship in real time. Displacement reconstruction is one of the main objectives of SHM, and the inverse finite element method (iFEM) is a powerful SHM method for the full-field displacement reconstruction of plate and shell structures. However, existing inverse shell elements applied to curved shell structures with irregular geometry or large curvature may result in element distortion. This paper proposes a high-precision iFEM for curved shell structures that does not alter the displacement mode of the element or increase the mesh and node quantities. In reality, it just modifies the methods of calculation. This method is based on the establishment of a local coordinate system on the Gaussian integration point and the subsequent alteration of the stiffness integration. The results of numerical examples demonstrate that the high-precision iFEM is capable of effectively reducing the displacement difference resulting from inverse finite element method reconstruction. Furthermore, it performs well in practical engineering applications.

Effect of random variation in input parameter on cracked orthotropic plate using extended isogeometric analysis (XIGA) under thermomechanical loading

Abstract This research introduces the Stochastic Extended Isogeometric Analysis (XIGA) method to investigate fracture behavior of isotropic and orthotropic materials under mechanical, thermal, and thermomechanical loads. Employing knot spans from Isogeometric Analysis (IGA) for domain discretization, the study utilizes identical basis functions for geometry construction and solution discretization. Utilizing Extended Finite Element Method (XFEM) enrichment functions, accurate crack face displacement discontinuity and tip singularity within the stress field are characterized. Additionally, employing a second-order perturbation technique within XIGA framework, the research derives mean and coefficient of variance values for mixed-mode Stress Intensity Factors (SIF). Stochastic variations in material elastic properties, crack length, and crack angle are considered in this computation. Credibility and robustness of the study are confirmed through comparative analyses against available literatures and Monte Carlo Simulations (MCS). The observed exceptional agreement validates the precision and reliability of the proposed stochastic XIGA method for fracture analysis in orthotropic material systems under thermomechanical loading conditions.