Two-step Finite Element Research Articles

Analytical investigation of hygrothermal effects on failure mechanisms of adhesively bonded corrugated sandwich structures under three-point bending

This research paper presents an analytical mechanics model for studying the degraded failure mechanics of an adhesively bonded corrugated sandwich structure (ABCSS) subjected to three-point bending and hygrothermal ageing loads. The model incorporates a detailed stress state model that considers the stress distribution of the adhesive layer, including the adhesive fillet, to more accurately reflect the failure mechanics of ABCSS. The Fickian Diffusion model and a degradation coefficient are used to describe the characteristics of water diffusion and hygrothermal mechanical degradation for the adhesive joint in ABCSS. The hygrothermal ageing experiments are conducted by immersing the ABCSS into deionized water and 5 wt% NaCl water, followed by three-point bending tests after hygrothermal ageing. The proposed two-step finite element (FE) method is developed to simulate both moisture diffusion and three-point bending test. The presented FE method is validated through comparison with corresponding experimental results, then it is utilized to demonstrate that the proposed analytical model is accurate enough in initial failure modes and initial failure loads predictions. At last, the hygrothermal effects on degraded stress distribution and degraded failure performance are investigated through analytical method, and the degraded failure mechanics maps are constructed to further visually demonstrate failure mechanics with the aid of the analytical model.

On the Dirichlet BVP of fractional diffusion advection reaction equation in bounded interval: Structure of solution, integral equation and approximation

We revisit a Dirichlet boundary value problem that involves a fractional diffusion, advection, and reaction differential equation in a one-dimensional bounded domain. By utilizing a variational formulation, we establish the existence of a weak solution to this problem. A procedure that involves raising regularity is employed to transform the variational formulation solution into the classical one. Furthermore, we demonstrate that such a solution has a closed-form expression, which is decomposable into two components: a completely known non-smooth part and a smooth part expressed as an integral of an unknown function. Availability of this decomposition allows for the development of a numerical approximation of the solution indirectly via an approximation of the aforementioned unknown function. This function satisfies a type of Volterra–Fredholm integral equation. We propose a two-step finite element method that transforms the integral equation into solving two decoupled Volterra integral equations of the second kind. Once this is in place, an approximate solution to the boundary value problem is gathered from the previously mentioned closed-form. The performance of the proposed method is substantiated by a convergence analysis and a set of numerical experiments.

Soybean-inspired nanomaterial-based broadband piezoelectric energy harvester with local bistability

Bistable nonlinear energy harvesters are effective structures for scavenging broadband energy from frequency-varying vibration sources. The bistable characteristic of such structures is typically induced by introducing magnetic fields, prestress, and nonuniform geometries or fixtures. However, the complicated structures or single deformation modes of these structures limit their practical application. Inspired by the structure of soybean pods, a bionic metallic nanomaterial-based bistable piezoelectric energy harvester is developed in this study. The nanoplate substrate with a local bistable region mimics the configuration of a soybean pod. To the best of the authors’ knowledge, the local bistable configuration represents a novel energy harvesting strategy. The local bistable nanoplate is fabricated using a mature surface mechanical attrition treatment technique that generates a gradient nanostructure to enhance the mechanical properties of the bistable structure. The energy harvesting performance and nonlinear dynamic characteristics of the energy harvester are evaluated through frequency-sweep and fixed-frequency vibration tests and numerical simulations with a new two-step finite element (FE) model. The harvester characteristics in three vibration modes (single-well vibration (SV), intermittent cross-well vibration (ICV), and continuous cross-well vibration (CCV)) are discussed. The experimental and numerical results demonstrate that the voltage output and working bandwidth of the proposed harvester increase by five times in the ICV and CCV modes when the excitation acceleration increases from 0.5 g to 3.0 g. The bionic nanomaterial-based bistable piezoelectric energy harvester can be potentially used in various applications such as vehicle suspension systems, tires, and vehicle-bridge systems.

Two-Step Finite Element Model Tuning Strategy of a Bridge Subjected to Mining-Triggered Tremors of Various Intensities Based on Experimental Modal Identification

In this paper, a two-step tuning strategy of a finite element (FE) model of a bridge with pot bearings exposed to mining-triggered tremors of various intensities is proposed. In the study, a reinforced concrete bridge 160 m long is considered. Once the modal identification of the bridge was experimentally carried out based on low-energy ambient vibrations, the FE model was tuned by replacing the free-bearing sliding with a Coulomb friction-regularized model. This model of friction split the tangential relative displacement rates between contacting surfaces into a reversible elastic part and irreversible sliding. The elastic microslip (spring-like behavior) prior to macrosliding can be explained by the deformation of asperities (roughness of contacting surfaces on the microscopic scale). The proposed model allows for accurate sliding bearing performance simulation under both low-energy and high-energy mining-induced tremors. In the first step of the FE model tuning strategy, the elastic microslip constant was experimentally estimated based on the modal identification. In the second step, the macro-sliding friction parameter was implemented to address the realistic behavior of the bridge under mining-induced shocks. Finally, the dynamic responses of the bridge to mining-triggered tremors of various intensities were calculated and assessed using the untuned and tuned FE models. The analysis proved that the untuned model was not suitable for dynamic bridge assessment in the case of low-intensity tremors. The stresses obtained for this model turned out to be strongly underestimated. For shocks of higher intensity, frictionless sliding at the bearings gives a relatively good global estimation of the structure performance but undervalues its local response. The analysis also reveals that the tuned Coulomb friction-regularized model allows for the accurate simulation of sliding bearings under both low and high-energy mining-induced tremors.

Anti-symmetric Plane Anti-symmetric Arch Cable-stayed Bridge abutment Joint Stress Analysis based on Finite Element Method

As an example by two step finite element analysis method, North Central Bridge of Taiyuan is calculated with the three abutment joint in static and dynamic conditions of the calculation results. Steel arch mainly produces bending, torsion, compression deformation and dynamic combination of working conditions is significantly higher than that of the dynamic combination of conditions. The overall stress level is not high can be appropriately increased the proportion of steel arch. The two-step finite element analysis method is used to establish the finite element model of the whole bridge by MIDAS / Civil, and the local finite element model of the arch abutment joint is established by using ANSYS. The results of the finite element model of the whole bridge are loaded into the local finite element model in the form of medium force and concentrated couple through the main node of rigid area. The result (absolute value) of dynamic combination condition is obviously higher than that of static combination condition, which indicates the importance of considering dynamic load combination in design. Whether the maximum stress of steel plate or the maximum first principal stress and the minimum third principal stress of concrete are within the reasonable range.

Transverse impact behavior and residual axial compression characteristics of braided composite tubes: Experimental and numerical study

In this study, transverse low-velocity impact response and residual axial compression behavior of braided composite tube with different ply number was investigated by experimental and numerical methods. The transverse low-velocity impact tests with 5.6 J energy were conducted on the composite tubes. The quasi-static axial compression performance of intact and pre-impacted tubes was compared to evaluate the effect of impact damage. A two-step finite element (FE) model was also established to reveal damage mechanisms of braided tube under impact loading and following axial compression. It was found that the wall thickness had a significant influence on the impact response. Obvious structural deformation occurred in 2-ply tube when subjected to impact loading, resulting in a large projected delamination area. In following axial compression process, the delamination failure significantly reduced the local compression stiffness and caused a structural instability, which led to a buckling failure mode. In contrast, increasing bending stiffness of 3 or 4-ply tube suppressed its structural deformation during impact, leading to a confined projected delamination area and therefore the buckling of tube wall was prevented effectively when subjected to axial compression. For all impacted tubes, the transition of failure mode from progressive folding mode in intact tube led to a lower energy absorption capacity per composite ply, especially for 2-ply tube.

New finite element based method for thermal analysis of axial flux interior rotor permanent magnet synchronous machine

A new method for computing convection heat transfer coefficients in axial flux permanent magnet synchronous machines (AF-PMSMs) is introduced. The method is based on a two-step finite element analysis (FEA). In the first step, a simple 2D model is introduced and fluid flow and temperature fields are studied using computational fluid dynamic (CFD) technique. Convective heat transfer coefficients for all heat transfer surfaces of the model are extracted from CFD analysis and are then used as inputs to a 3D thermal finite element model. Two case studies are considered to check the accuracy of the abovementioned two-step method. One of the case studies is an air-cooled AF-PMSM that has air inlet and outlet on its enclosure and the other case is a totally enclosed AF-PMSM. The correctness of the mentioned method is verified by practical measurements on the second case. In addition, an experimental set-up is conducted to measure the temperature of different parts of the second case. It is observed that the results of the two-step CFD-FEA model are in good agreement with the experimental data. In the other case, the effect of inlet air velocity on heat transfer coefficients, as well as the thermal behaviour of the machine are explored.

Parametric Formulae for Elastic Stress Concentration Factor at the Weld Toe of Distorted Butt-Welded Joints.

The evaluation of the stress concentration factor (SCF) at the notches of welds is of importance, especially for butt-welded joints that are widespread in the industry. Some empirical formulae can be found in the literature to estimate the SCF at the weld toes of butt-welded joints, while few solutions are available for the distorted joints under tensile fatigue test conditions. In the present study, the existing SCF formulae for butt-welded joints loaded in tension are examined and discussed. The influence of the weld width on SCF, which is commonly ignored or misestimated by existing solutions, is investigated comprehensively based on a large set of two-dimensional (2D) finite element analyses. Consequently, a new precise parametric formula for the elastic SCF at the weld toe of geometrically symmetric butt-welded joints under tension is proposed, together with a wide application range. Moreover, the analysis is also extended to consider joints with angular distortion. A two-step finite element analysis is employed to simulate the clamping and loading procedures in the fatigue test. Similarly, the parametric formulae for the assessment of clamping-induced stress and SCF caused by angular distortion are carried out as well based on the results from finite element analyses. The formulae proposed by this paper are finally tested and proved to be valid and precise.

Parallel two-step finite element algorithm based on fully overlapping domain decomposition for the time-dependent natural convection problem

Purpose This paper aims to propose two parallel two-step finite element algorithms based on fully overlapping domain decomposition for solving the 2D/3D time-dependent natural convection problem. Design/methodology/approach The first-order implicit Euler formula and second-order Crank–Nicolson formula are used to time discretization respectively. Each processor of the algorithms computes a stabilized solution in its own global composite mesh in parallel. These algorithms compute a nonlinear system for the velocity, pressure and temperature based on a lower-order element pair (P1b-P1-P1) and solve a linear approximation based on a higher-order element pair (P2-P1-P2) on the same mesh, which shows that the new algorithms have the same convergence rate as the two-step finite element methods. What is more, the stability analysis of the proposed algorithms is derived. Finally, numerical experiments are presented to demonstrate the efficacy and accuracy of the proposed algorithms. Findings Finally, numerical experiments are presented to demonstrate the efficacy and accuracy of the proposed algorithms. Originality/value The novel parallel two-step algorithms for incompressible natural convection problem are proposed. The rigorous analysis of the stability is given for the proposed parallel two-step algorithms. Extensive 2D/3D numerical tests demonstrate that the parallel two-step algorithms can deal with the incompressible natural convection problem for high Rayleigh number well.

Parallel two-step finite element algorithm for the stationary incompressible magnetohydrodynamic equations

Purpose The purpose of this paper is to propose a local parallel finite element algorithm based on fully overlapping domain decomposition technique to solve the incompressible magnetohydrodynamic equations. Design/methodology/approach The algorithm uses a lower-order element pair to compute an initial approximation by the Oseen-type iteration and uses a higher-order element pair to solve a linear system in each processor. Findings Besides, the convergence analysis of local parallel finite element algorithm is given. Finally, numerical experiments are presented to verify the efficiency of the proposed algorithm. Originality/value Compared with the numerical solution of the common two-step method, this method is easy to realize and can produce a more accurate solution. And, this approach is executed in parallel, so it saves a lot of computational time.

Dry Generating Gear Grinding: Hierarchical Two-Step Finite Element Model for Process Optimization

Recent developments in the automotive industry have led to more stringent requirements for transmission gear quality. This aspect, combined with a massive increase in the number of gears produced per year, has seen generating grinding become the finishing method of choice for mass production of gears. Due to the intrinsic nature of grinding, this process remains the only manufacturing phase that still requires the widespread use of lubricant. With the aim of improving the environmental sustainability of this process chain, recent attempts at performing dry grinding without lubricant have highlighted the critical aspect of thermal damage produced under these conditions. In the present work, a two-step finite element modeling approach is presented for predicting thermal damage during dry generating gear grinding. Grinding forces and thermal energy generated by the interaction of a single grain with the workpiece are first calculated based on real grain geometry acquired via computed tomography. Results of this single-grain model are then applied at a gear tooth level together with process kinematics to determine the temperature distribution during dry generating grinding. Single-grain and generating grinding tests are performed to verify the predicted onset of thermal damage and the ability to optimize process parameters using the proposed hierarchical modeling approach.

Distortion Prediction of Welded Thin Plate Lap Joints by Finite Element Analysis and Experiment

Welding process is an efficient joining process of metals that is achieved by gas metal arc welding (GMAW) process. Localized heating during welding process can result in distortion of the welded plate. The estimation of magnitude and distribution of distortion are important to maintain the quality of products. Finite element method is implemented to investigate the distortions behavior of thin steel plate, cold rolled (SPCC) material in lap joint using GMAW process. A three-dimensional, two-step thermomechanical finite element model study was applied to analyze and evaluate distortion behavior in lap joint. The result of distortion from finite element analysis (FEA) was compared to experimental data to validate the accuracy of the method.

A novel parallel two-step algorithm based on finite element discretization for the incompressible flow problem

Based on a two-step finite element method and fully overlapping domain decomposition technique, a parallel two-step algorithm for the incompressible flow problem is introduced and analyzed. In the new algorithm, all of the computations are performed in parallel on global composite meshes which are fine around the subdomain that we concentrate on but coarse elsewhere. Each processor first solves an original problem based on the P1–P1 stabilized finite element method and then solves a generalized Stokes problem based on the P2–P2 stabilized finite element method on a global composite mesh. The proposed algorithm is easy to implement. What’s more, the new algorithm can yield more accurate solutions compared with the numerical solution obtained by the common two-step method. Numerical tests are presented to verify the efficiency and validity of the proposed algorithm.

Lattice materials composed by curved struts exhibit adjustable macroscopic stress-strain curves

In this paper, a mechanism called buckling-dominated is proposed for the deformation of lattice materials. To investigate this mechanism and its utilization potentiality, sandwich panels with lattice cores composed by curved struts which follow a two-parameter trigonometric function were put forward. A two-step finite element method (FEM) were carried out to find the two parameters. Specimens with the two parameters were prepared and tested by quasi-static compression. The results indicate the macroscopic compressive stress-strain curves of them are adjustable by changing the struts curvatures. When this feature is utilized to design materials for energy-absorption, more favorable stress-strain curves can be obtained, i.e., the specific energy-absorbing of the designed materials are 39%–74% higher and energy-absorption efficiency are 32%–42% higher than common lattice materials with similar density, at 0.6 reference strain.

Numerical Study on Mechanical Properties of Discontinuously Reinforced Titanium Matrix Composite with Network Reinforcement Architecture

A two-step finite element modeling method is adopted to predict the elastic properties and reveal the strengthening mechanisms of discontinuously reinforced titanium matrix composites (DRTMCs) with network reinforcement architecture. The microstructure of the composite consists of reinforcement-rich phase (Phase I) and reinforcement-lean phase (Phase II). In the first step, the mechanical properties of Phase I with varying whisker reinforcement content are calculated. In the second step, the calculated mechanical properties are used as input parameters for the homogenized Phase I in the representative volume elements (RVEs) of the composites. In addition, a direct procedure is adopted to generate the exact RVE to validate the two-step method. The predicted elastic moduli obtained by the two-step procedure agree well with those from experiments. Following the same procedure, the strength increase of the composites contributed by the two mechanisms, i.e., load-transfer by the reinforcement and matrix strengthening caused by grain refinement, solution strengthening, etc., can be determined from the simulations separately, which shows that the strength enhancement of the DRTMCs with the addition of TiB whiskers by in situ reaction is primarily due to the matrix strengthening rather than the load-transfer mechanism.

A hybrid two-step finite element method for flux approximation:a prioriestimates

We present a new two–step method based on the hybridization of mesh sizes in the traditional mixed finite element method. On a coarse mesh, the primary variable is approximated by a standard Galerkin method, whose computational cost is very low. Then, on a fine mesh, an H (div) projection of the dual variable is sought as an accurate approximation for the flux variable. Our method does not rely on the framework of traditional mixed formulations, the choice of pair of finite element spaces is, therefore, free from the requirement of inf-sup stability condition. More precisely, our method is formulated in a fully decoupled manner, still achieving an optimal error convergence order. This leads to a computational strategy much easier and wider to implement than the mixed finite element method. Additionally, the independently posed solution strategy allows to use different meshes as well as different discretization schemes in the calculation of the primary and flux variables. We show that the finer mesh size h can be taken as the square of the coarse mesh size H , or a higher order power with a proper choice of parameter δ . This means that the computational cost for the coarse-grid solution is negligible compared to that for the fine-grid solution. In fact, numerical experiments show an advantage of using our strategy compared to the mixed finite element method. Some guidelines to choose an optimal parameter δ are also given. In addition, our approach is shown to provide an asymptotically exact a posteriori error estimator for the primary variable p in H 1 norm.

Simulation and experiment analysis on thermal deformation of tool system in single-point diamond turning of aluminum alloy

The aim of this work is to simulate thermal deformation of tool system and investigate the influence of cutting parameters on it in single-point diamond turning (SPDT) of aluminum alloy. The experiments with various cutting parameters were conducted. Cutting temperature was measured by FLIR A315 infrared thermal imager. Tool wear was measured by scanning electron microscope (SEM). The numerical model of heat flux considering tool wear generated in cutting zone was established. Then two-step finite element method (FEM) simulations matching the experimental conditions were carried out to simulate the thermal deformation. In addition, the tests of deformation of tool system were performed to verify previous simulation results. And then the influence of cutting parameters on thermal deformation was investigated. The results show that the temperature and thermal deformation from simulations agree well with the results from experiments in the same conditions. The maximum thermal deformation of tool reaches to 7 μm. The average flank wear width and cutting speed are the dominant factors affecting thermal deformation, and the effective way to decrease the thermal deformation of tool is to control the tool wear and the cutting speed.

The effect of microscale residual stress from thermal cooldown on the nanoindentation properties of fibre-reinforced composites

A two-step finite element framework is presented that examines the effect of microscale thermal residual stress on the nanoindentation properties of fibre-reinforced composites. Firstly, micromechanical modelling is used to determine the residual stress state following thermal cooldown of a carbon-fibre composite material from cure temperature. A three-dimensional finite element nanoindentation model is then used to characterise the effects of residual stress on material properties determined by nanoindentation theory. The results show that the hardness of the matrix pockets decreases following thermal cooldown due to the existence of equibiaxial tensile residual stresses. The hardness property is also found to decrease for the majority of interfacial region stress states, while the microstructural areas where the effects of the residual stress are nullified are determined. The indentation modulus property is relatively insensitive to the microstructural residual stress, and thus is the recommended indentation property to be determined when carrying out a comparative parametric analysis between microstructural regions. The property changes are shown to be insensitive to any errors associated with contact area estimation using the Oliver and Pharr method.

A Method of Modeling Fabric Shear using Finite Element Analysis

Fabric modeling may be attempted by modeling fibres or yarns or small fabric units. The first is computationally intensive while the third does not allow relationships between the fabric’s structure and its mechanical properties to be predicted. The second approach has been the most widely used so far. Out of the various ways in which this has been attempted, the finite element approach offers high flexibility while allowing the procedure to be relatively simple because of the availability of user-friendly softwares. This work explores a two-step finite element approach for modeling in-plane fabric shear. A major innovation of the modeling process was that the path of yarns in the fabric was allowed to evolve through the modeling process rather than being pre-defined. The relationship between shear angle and shear stress predicted by this model was compared with that obtained from a picture frame shear experiment. It was found that modeling the yarn with a set of anisotropic properties, gave very good correlation with experimental results.

A Form-finding Technique for Three-dimensional Spatial Structures

A form-finding technique is proposed for three-dimensional spatial structures. Two-step discrete finite element (FE) mesh generator based on computer aided geometric design (CAGD) is introduced and used to control the shape of three-dimensional spatial structures. Mathematical programming technique is adopted to search new forms (or shapes) of spatial structures. For this purpose, the strain energy is introduced as the objective function to be minimized and the initial volume (or the initial weight) is considered as constraint function. Numerical examples are carried out to test the capability of the proposed form-finding techniques and provided as benchmark tests.