For Finite Element Research Articles

Investigating the effect of helix angle and pressure angle on bending stress in helical gear under dynamic state

PurposeThe aim of this paper is to study the effect of pressure angle and helix angle on bending stress at the root of helical gear tooth under dynamic state. Gear design is a highly complex process. The consistent demand to build low-cost, quieter and efficient machinery has resulted in a gradual change in gear design. Gear parameters such as pressure angle, helix angle, etc. affect the load-carrying capacity of gear teeth. Adequate load-carrying capacity of a gear is a prime requirement. The failure at the critical section because of bending stress is an unavoidable phenomenon. Besides this fact, the extent of these failures can be reduced by a proper gear design. The stresses produced under dynamic loading conditions in machine member differ considerably from those produced under static loading.Design/methodology/approachThe present work is intended to study the effect of pressure angle and helix angle on the bending stress at the root of helical gear tooth under dynamic state. The photostress method has been used as experimental methods. Theoretical analysis was carried out by velocity factor method and Spott’s equation. LS DYNA has been used for finite element (FE) analysis.FindingsThe results show that experimental method gives a bending stress value that is closer to the true value, and bending stress varies with pressure angle and helix angle. The photostress technique gives clear knowledge of stress pattern at root of tooth.Originality/valueThe outcomes of this work help the designer use optimum weight-to-torque ratio of gear; this is ultimately going to reduce the total bulk of the gear box.

Predicting the Effect of Field Shaper in Electromagnetic Welding Using FEM

The research work presents a 3D numerical simulation to predict the distribution of magnetic field and pressure in the desired region of the tubular jobs using coils with and without field shapers in electromagnetic welding (EMW). For finite element (FE) simulation, single-turn (ST) and multi-turn (MT) (disk type) coils are considered to analyze the effects of field shapers with varying material combinations in ANSYS MAXWELL environment. The change in magnetic field distribution on the outer peripheral region of the flyer tube along axial direction with and without field shaper is graphically shown and compared. Also, variation of magnetic pressure on the flyer tube with respect to increasing voltage and time is compared individually for various material combinations of ST/MT coil and field shaper. Results show that in welding simulation (FE) using single-turn Cu and SS coils with field shapers of Be, Nb and Ta, the magnetic pressure increases by 34, 12 and 11% and 35, 12 and 11%, respectively, as compared to the coil with no field shaper. In case of multi-turn SS coil with Cu and Be field shapers, the magnetic pressure increases by 16 and 10%, respectively. The novelty of the work is the proper guideline to select the material combinations for ST/MT coils and field shapers and positioning of work pieces inside the coil in order to achieve maximum utilization of input energy in EMW system.

A Nonlinear Viscoelastic Model for Adipose Tissue Representing Tissue Response at a Wide Range of Strain Rates and High Strain Levels.

Finite element human body models (FEHBMs) are nowadays commonly used to simulate pre- and in-crash occupant response in order to develop advanced safety systems. In this study, a biofidelic model for adipose tissue is developed for this application. It is a nonlinear viscoelastic model based on the Reese et al.'s formulation. The model is formulated in a large strain framework and applied for finite element (FE) simulation of two types of experiments: rheological experiments and ramped-displacement experiments. The adipose tissue behavior in both experiments is represented well by this model. It indicates the capability of the model to be used in large deformation and wide range of strain rates for application in human body models.

Characterization and modeling of the fatigue behavior of TPU

A comprehensive determination of the material properties is of major importance for the development of an adequate material model for finite element (FE) calculations and further lifetime estimations. As a preparation for the FE simulations, the time-, rate-, temperature- and hysteresis dependency of TPUs is determined and translated into proper hyperelastic material models. The time dependency and the viscoelastic properties were determined with DTMA tests. The methodology of fatigue testing, particularly the determination of local strain bases Wöhler curve (LSWC) for TPUs on Diabolo specimens is covered. As a validation of the whole methodology, the lifetime of a simplified model of a rubber engine mount is calculated.

Finite Element Model Updating in Bridge Structures Using Kriging Model and Latin Hypercube Sampling Method

Computational cost reduction and best model updating method seeking are the key issues during model updating for different kinds of bridges. This paper presents a combined method, Kriging model and Latin hypercube sampling method, for finite element (FE) model updating. For FE model updating, the Kriging model is serving as a surrogate model, and it is a linear unbiased minimum variance estimation to the known data in a region which have similar features. To predict the relationship between the structural parameters and responses, samples are preselected, and then Latin hypercube sampling (LHS) method is applied. To verify the proposed algorithm, a truss bridge and an arch bridge are analyzed. Compared to the predicted results obtained by using a genetic algorithm, the proposed method can reduce the computational time without losing the accuracy.

직접구조강도 평가를 위한 선체 국부구조 상세요소분할모델 자동생성

Under the circumstances of Common Structure Rules for Bulk Carrier and Oil Tanker (CSR-H; Harmonized Common Structure Rules) which is on effective from July 2015, the modeling area for finite element (FE) has been extended to forward and afterward cargo hold regions of a ship, more design man-hours are required in the FE modeling than that of previous rules. In addition, it is mandatorily required to generate the fine-mesh model for hot spot zones, but the target area has been extended so extensively, more design man-hours are required for fine-mesh modeling than that of coarse mesh modeling. Moreover, the local area for fatigue analysis should be modeled with very fine-mesh. However, these kinds of FE modeling for different level of detail and different purpose of analysis are time consuming and repetitive works. In this research, we would like to introduce the auto fine mesh modeling functionality that can generate fine-mesh and very-fine mesh model from the coarse mesh model, and retrieve and restore them to coarse mesh for certain purpose by re-mesh functionality. Through this process, FE model can be managed and reused with a consistent FE model from the initial design stage to detailed design stage of a ship.

Comparison of experimental testing and finite element modelling of a replica of a section of the Vasa warship to identify the behaviour of structural joints

Abstract Modelling in design of new support systems necessitates the joint stiffness of the existing wooden structures. In valuable structures, e.g. in cultural heritage, or structures with inaccessible joints, these stiffness values must be estimated, e.g. by testing joints in tailored replicas of the original parts. Although a simplified structure, the replica, can call for finite element (FE) modelling to capture the stiffness parameters. The first step in such a process is to compare FE predictions with experimental tests, for validation purposes. The reasons for unavoidable differences in load-displacement behaviour between model predictions and experimental test should be identified, and then possibly remedied by an improved model. Underlying causes like the complex shape of joints, geometrical uncertainties, contact mechanisms and material nonlinearity are generally too computationally expensive to be included in a full-scale model. It is therefore convenient to collect such effects in the contact penalty stiffness in the joint contact areas where stresses are high, which influences the resulting joint stiffness. A procedure for this is here illustrated for the case of the 17th century Vasa shipwreck. A replica of a section of the ship has been constructed, and its joints were tested in bending-compression, in-plane shear and rotation. The FE simulations showed stiffer behaviour than the experimental results. Therefore, a normal penalty stiffness in contact surfaces of the joint were introduced, and used as a calibration parameter to account for the simplifying assumptions or indeliberate imprecision in the model, e.g. concerning boundary conditions, material properties and geometrical detail. The difference between numerical predictions and experimental results could then be significantly reduced, with a suitable normal penalty stiffness value. Once an acceptable finite element model has been obtained, it is shown how this can be used to identify stiffness values for joints in the physical structure with compensation for degradation of material properties due to aging and conservation treatment.

Homogenization Method Based on Model Order Reduction for FE Analysis of Multi-Turn Coils

This paper presents a homogenization method based on the model order reduction (MOR) for finite element (FE) analysis of multi-turn coils. The multi-turn coils are replaced by a homogenous material with the complex permeability that is expressed by a rational polynomial of frequency. After the MOR process, the complex permeability can readily be computed at any frequency. It is shown that the present method can drastically reduce the computational time without loss of accuracy.

Statistical factorial analysis approach for parameter calibration on material nonlinearity of intervertebral disc finite element model

In the biomechanics field, material parameters calibration is significant for finite element (FE) model to ensure a legit estimation of biomechanical response. Determining an appropriate combination of calibration factors is challenging as each constitutive component responds differently. This study proposes a statistical factorial analysis approach using L16(45) orthogonal array to evaluate material nonlinearity and applicable calibration factor of the intervertebral disc FE model in pure moment. The calibrated model exhibits improved agreement to the experimental findings for all directions. Appropriate combination of calibration parameter reduces the estimation gap to the experimental findings, ensuring agreeable biomechanical responses.

A Fourier transformation-based temporal integration scheme for viscoplastic solids subjected to fatigue deterioration

Using continuum damage mechanics (CDM) for lifetime prediction requires numerical integration of evolving damage until the onset of failure. The primary challenge for the simulation of structural fatigue failure is caused by the enormous computational costs due to cycle-by-cycle temporal integration throughout the whole loading history, which is in the order of 103–107 cycles. As a consequence, most approaches circumvent this problem and use empirical methods such as Wöhler curves. They are well suited for approximating the lifetime, but they are not capable to capture a realistic degradation of the material including redistribution of stresses. The main objective of the paper is to provide a technique for finite element (FE) simulations of structures under fatigue loading while reducing computational costs.A Fourier transformation-based temporal integration (FTTI) scheme is proposed, which adapts the conventional FE method for modeling the viscoplastic deterioration in a structure subjected to cyclic loading. The response fields are represented by a Fourier series which assumes a temporal scale separation: a microchronological (short time) scale arises from the oscillatory loading and a macrochronological (long time) scale is due to the slow material relaxation resulting from yielding and damage evolution. The original dynamic boundary value problem (BVP) is approximated by the stationary BVP on the microchronological scale. Alternation of the displacement field on the macrochronological scale is correlated with evolution of the history variables by means of a high order adaptive cycle jump method. Performance and significant acceleration of the FE simulations is demonstrated at different loading scenarios for a constitutive damage model where the progressive damage accumulation is driven by viscoplastic yielding.

A Benchmark Study of Finite Element Codes for Forming Simulation of Thermoplastic UD-Tapes

For Finite Element (FE) simulation of composite thermoforming processes, either commercially available codes or multi-purpose FE solvers can be applied. In this work, the commercially available codes AniForm and PAM-FORM, as well as two approaches implemented in the multi-purpose FE solvers LS-Dyna and Abaqus are benchmarked in a comparative study. For this purpose, the final outer contour, as well as wrinkling behavior is analyzed in experimental forming studies and compared to the virtual predictions. It turns out, that FE forming simulation is capable to predict manufacturing defects. However, the capabilities and quality of the prediction of the considered tools differ.

Shear buckling analysis of laminated plates on tensionless elastic foundations

The current study addresses the local buckling analysis of an infinite thin rectangular symmetrically laminated composite plate restrained by a tensionless Winkler foundation and subjected to uniform in-plane shear loading. An analytic method (i.e., one-dimensional mathematical method) is used to achieve the analytical solution estimate of the contact buckling coefficient. In addition, to study the effect of ply angle and foundation stiffness on the critical buckling coefficients for the laminated composite plates, the parametric studies are implemented. Moreover, the convergence for finite element (FE) mesh is analysed, and then the examples in the parametric study are validated by the FE analysis. The results show that the FE analysis has a good agreement with the analytical solutions. Finally, an example with the analytical solution and FE analysis is presented to demonstrate the availability and feasibility of the presented analytical method.

The boundary conditions for simulations of a shake-table experiment on the seismic response of 3D slope

Boundary conditions can significantly affect a slope’s behavior under strong earthquakes. To evaluate the importance of boundary conditions for finite element (FE) simulations of a shake-table experiment on the slope response, a validated three-dimensional (3D) nonlinear FE model is presented, and the numerical and experimental results are compared. For that purpose, the robust graphical user-interface “SlopeSAR”, based on the open-source computational platform OpenSees, is employed, which simplifies the effort-intensive pre- and post-processing phases. The mesh resolution effect is also addressed. A parametric study is performed to evaluate the influence of boundary conditions on the FE model involving the boundary extent and three types of boundary conditions at the end faces. Generally, variations in the boundary extent produce inconsistent slope deformations. For the two end faces, fixing the y-direction displacement is not appropriate to simulate the shake-table experiment, in which the end walls are rigid and rough. In addition, the influence of the length of the 3D slope’s top face and the width of the slope play an important role in the difference between two types of boundary conditions at the end faces (fixing the y-direction displacement and fixing the (y, z) direction displacement). Overall, this study highlights that the assessment of a comparison between a simulation and an experimental result should be performed with due consideration to the effect of the boundary conditions.

Finite Element Analysis of Bend Test of Sandwich Structures Using Strain Energy Based Homogenization Method

The purpose of this article is to present a simplified methodology for analysis of sandwich structures using the homogenization method. This methodology is based upon the strain energy criterion. Normally, sandwich structures are composed of hexagonal core and face sheets and a complete and complex hexagonal core is modeled for finite element (FE) structural analysis. In the present work, the hexagonal core is replaced by a simple equivalent volume for FE analysis. The properties of an equivalent volume were calculated by taking a single representative cell for the entire core structure and the analysis was performed to determine the effective elastic orthotropic modulus of the equivalent volume. Since each elemental cell of the hexagonal core repeats itself within the in-plane direction, periodic boundary conditions were applied to the single cell to obtain the more realistic values of effective modulus. A sandwich beam was then modeled using determined effective properties. 3D FE analysis of Three- and Four-Point Bend Tests (3PBT and 4PBT) for sandwich structures having an equivalent polypropylene honeycomb core and Glass Fiber Reinforced Plastic (GFRP) composite face sheets are performed in the present study. The authenticity of the proposed methodology has been verified by comparing the simulation results with the experimental bend test results on hexagonal core sandwich beams.

Analysis of RC Continuous Beams Strengthened with FRP Plates: A Finite Element Model

Strengthening of reinforced concrete (RC) beams with externally bonded fibre reinforced polymer (FRP) plates/sheets technique has become widespread in the last two decades. Although a great deal of research has been conducted on simply supported RC beams, a few studies have been carried out on continuous beams strengthened with FRP composites. This paper presents a simple uniaxial nonlinear finite-element model (UNFEM) that is able to accurately estimate the load-carrying capacity and the behaviour of RC continuous beams flexurally strengthened with externally bonded FRP plates on both of the upper and lower fibres. A 21-degree of freedom element is proposed with layer-discretization of the cross-sections for finite element (FE) modelling. Realistic nonlinear constitutive relations are employed to describe the stress-strain behaviour of each component of the strengthened beam. The FE model is based on nonlinear fracture mechanics. The interfacial shear and normal stresses in the adhesive layer are presented using an analytical uncoupled cohesive zone model with a mixed-mode fracture criterion. The results of the proposed FE model are verified by comparison with various selected experimental measurements available in the literature. The numerical results of the plated beams (beams strengthened with FRP plates) agreed very well with the experimental results. The use of FRP increased the ultimate load capacity up to 100 % compared with the non-strengthened beams as occurred in series (S). The major objective of the current model is to help engineers’ model FRP-strengthened RC continuous beams in a simple manner.

Modeling of thermal expansion behavior of densely packed Al/SiC composites

In this paper the approach for finite element (FE) modeling and analysis of thermal expansion behavior of densely packed Al/SiC composites is proposed. The coefficient of linear thermal expansion (CTE) is predicted from 50°C to 500°C by considering temperature dependent linear elastic and elastoplastic matrix material behavior. Three dimensional representative volume elements (RVEs) are generated to model the composite's microstructures. In order to study the effect of thermal residual stresses, first the RVEs are simulated for cooling process from processing temperature to room temperature and thermal residual stresses are estimated by considering different mechanical behaviors of Al matrix. Next, the thermal expansion behavior is examined with existing residual stresses. The presence of thermal residual stresses is observed to influence the effective CTE in the initial temperature range (25 °C–100 °C) of heating. The contact state of reinforced particles significantly influences the thermal expansion behavior. It is observed that the effective CTE of composites with non-interpenetrating microstructure is higher than that of the composites having interpenetrating microstructure. The effects of voids on the thermal expansion behavior are analyzed further.

Finite element model updating using simulated annealing hybridized with unscented Kalman filter

This paper proposes a method for finite element (FE) model updating of civil structures. The method is a hybrid global optimization algorithm combining simulated annealing (SA) with the unscented Kalman filter (UKF). The objective function in the optimization problem can be defined in the modal, time, or frequency domains. The algorithm improves the accuracy, convergence rate, and computational cost of the SA algorithm by local improvements of the accepted candidates though the UKF. The proposed methodology is validated using a mathematical function and numerically simulated response data from linear and nonlinear FE models of realistic three-dimensional structures.

Multiobjective Optimization of a Magnetically Levitated Planar Motor With Multilayer Windings

In this paper, a novel magnetically levitated coreless planar motor with three-layer orthogonal overlapping windings is shown to have higher power density and higher space utilization compared with other coreless planar motors. In order to achieve maximum forces with minimum cost and minimum space, a multiobjective optimization of the novel planar motor is carried out. In order to reduce the computational resources required for finite-element (FE) analyses, a fast but accurate analytical tool is developed, based on expressions of the flux density of the permanent-magnet array, which are derived from the scalar magnetic potential method. The validity and accuracy is verified by 3-D FE results. Based on the force formulas and the multiobjective function derived from the analytical models, a particle swarm optimization (PSO) algorithm is applied to optimize the dimensions of the planar motor. The design and optimization of the planar motor is validated with experimental results, measured on a built prototype, thus proving the validity of the analytical tools.

Identification of new material model for machining simulation of Inconel 718 alloy and the effect of tool edge geometry on microstructure changes

Johnson–Cook (J-C) material model is often used for Finite Element (FE) modeling of cutting processes and it affects significantly the results of simulation. Since experimentally determination of J-C equation parameters is an expensive and time-consuming task, in this paper, a new and efficient methodology was implemented based on the evolutionary optimization algorithm to identify new J-C material constants for Inconel 718 superalloy. Then, orthogonal cutting process of Inconel 718 was simulated using the new material models. The results of simulation were compared extensively with experimental results of cutting forces, chip geometry, and maximum temperature to select and then validate the most suitable material model. After that, a user subroutine was implemented in FE code to model microstructure changes using the dynamic recrystallization mechanism in cutting process of Inconel 718. The Zener–Hollomon and Hall–Petch equations were used to respectively predict the grain size and hardness. The results of simulation were verified successfully with corresponding experiments in terms of near-surface profile. At the end, the effect of tool edge geometry including honed and chamfered tool edge was investigated on microstructure changes.

Numerical modeling of stress corrosion cracking of polymers

A unified chemo-mechanical model is developed to simulate stress corrosion cracking (SCC) of high density polyethylene (HDPE) in a chlorinated environment. The model consists of three components, each of which captures a critical aspect of SCC. A chemical kinetics–diffusion model is used to simulate the reactions and migration of chemical substances. The fracture behavior of HDPE is captured by a cohesive crack model, in which the cohesive properties are considered to be dependent on the extent of the chemical degradations. The time-dependent creep behavior of the bulk HDPE material is described by an elastic–viscoplastic constitutive model. This chemo-mechanical model is numerically implemented for finite element (FE) analysis of SCC of HDPE structures. The simulations show two different failure mechanisms depending on the applied stress level: at high stresses, the failure is primarily due to the excessive plastic deformation whereas at low stresses the chemical reactions and diffusion are the dominant factors leading to failure. In addition, examination of detailed crack growth kinetics reveals that at low stress levels the disinfectant concentration has a significant effect on the crack growth behavior through the relative dominance between the chemical reaction and diffusion processes.