Solid Element Model Research Articles

Multiscale modelling of sandwich structured composites using direct FE2

In finite element analyses, composite laminates are often homogenised and modelled using beam and plate elements for computational efficiency. Aside from difficulties in deriving homogenised properties for nonlinear materials and the loss in fine-scale deformation details, such structural elements are notoriously inaccurate for laminates comprising plies of distinctly different in-plane stiffnesses, notably, sandwich structured composites. A multiscale layerwise beam model is proposed to address these shortcomings. The model is based on the Timoshenko-Ehrenfest beam theory with layerwise kinematics incorporated to capture the key deformation modes of bending and transverse shear, and implemented using Direct FE2 – a versatile computational homogenisation scheme. Beyond homogenisation for the structural elements, Direct FE2 also captures deformation mechanisms at the mesoscale. More importantly, it is readily implemented using available functions in commercial FE codes, allowing for ease of adoption. A foam core sandwich structure is modelled to demonstrate that the proposed approach leads to macroscale responses and resolution to the mesoscale deformations that are almost identical to that of finely meshed solid element models, while taking only 23% of the computation time.

Yarn modeling and winding process simulation based on 3D beam elements

In order to study the tension variation of cotton yarn in the winding process, a finite element model of yarn based on three-dimensional beam elements is proposed. As the size of yarn in the length direction is much larger than the cross-sectional size, this paper assumes that the yarn cross-section is circular and ignores the change of the cross-sectional area in the winding process. The winding process of yarn is simulated using Abaqus dynamic explicit, and the influence of the yarn fineness on the yarn tension during winding is analyzed. The results show that the average relative error between the simulation results and the experimental data is 14.09%, and the maximum relative error is 17.06%; therefore the model is reasonable. Compared with the solid element model of yarn, the yarn simulated by this model can save a lot of computing resources while taking into account the yarn stacking effect. The winding length that can be simulated in the same time is tens of times that of the solid element model, thus the winding simulation of nine-layer yarn on the bobbin is realized. The conclusion is that the inner yarn loop presents weak tension while the outer yarn loop has large tension.

An improved preloaded Curvic coupling model for rotordynamic analyses

Curvic couplings are commonly utilized in aircraft engines and large gas turbines for high load capacity, precision centering of stacked components in rotating assemblies. The couplings have non-axisymmetric, complex curved mating contact surfaces, which transmit torque, moment and force. Coupling contact surface roughness, and tooth and ring deformations introduce local lateral flexibilities, compared with a continuous beam model, and consequently affect rotordynamic vibration predictions. A novel approach of modeling the Curvic coupling is proposed which combines a GW contact model with a 3D solid element model of flexible teeth and coupling rings. This improves on similar approaches that assume rigid teeth and rings or omits a surface roughness – asperity model. Comparisons of the various models with experimental measurements of free-free natural frequencies of an axially preloaded shaft, demonstrate a marked improvement in accuracy with the proposed approach. A parametric study is performed which varies tooth contact pattern, tooth number, pressure angle, half pitch number, and tooth rigidity to evaluate their effects on vibration and stress. The proposed approach is also applied to an industrial rotor to illustrate the effect of the new Curvic coupling model on critical speeds. The higher fidelity flexible tooth model presented shows a significant change in critical speed relative to the rigid tooth model from the literature.

A coupled hygro-thermo-mechanical fiber beam model for reinforced concrete structures

The mechanical behavior of reinforced concrete is affected by the environmental fluctuations of temperature and humidity. In traditional structural analysis of the using beam element, the influence of coupled hygro-thermo-mechanical effect was considered by correction coefficient terms based on data fitting of specimens, which was not very suitable for the analysis of large or complex structures. In order to catch complex behavior of reinforced concrete using beam element, a coupled hygro-thermo-mechanical fiber beam model is developed for the analysis. The model uses a sequential coupled analysis approach based on the framework of original microprestress solidification (MPS) theory and fiber beam element method, which contains important features of reinforced concrete beam such as non-uniform ageing, creep, shrinkage, thermal dilation. Several concrete beam and reinforcement concrete beam experiment data, contrasting examples between the fiber beam element model and conventional 3D solid element model and a typical example of reinforced concrete box beam on structural scale were used to verify the presented model. Overall, good results were obtained in all the tests. The results show that the MPS intrinsic creep property could predict the behavior of concrete beams well. Area weighted average temperature and average relative humidity is an efficient simplified method to catch the MPS intrinsic creep property. Fiber beam element model coupled with MPS intrinsic creep property and a finer subdivision scheme can predict the behavior of beam well under complicated conditions as well as 3D solid element model. The model developed in this study can be used for large structures efficiently.

Behavior of Precast Segmental Beams Made of High-strength Concrete and Ultra-high Performance Fiber Concrete Connected by Shear Keys Technique

The segments of the precast concrete beams can be assembled by joints have interlaced shear keys. This paper presents an experimental and numerical study of ten samples, six of them were tested under the influence of direct shear; these samples represent reinforced and non-reinforced shear keyed joints made of high-strength concrete (HSC) and ultra-high performance fiber concrete (UHPFC) under the influence of different levels of confining stress. In addition, four beams were tested under the influence of bending, two of them are unconnected control beams made of HSC and UHPFC, and the other two beams are precast segmented and were assembled using reinforced shear keyed joints of the same joints tested under direct shear. All the details of the shear keyed joints are fixed in all samples and they are dry non-epoxy joints, the external prestressing technique was used. Also, Abaqus program was used for numerical modeling of all samples that were tested in the experimental program using the 3D solid element model. The success of the modeling process was verified by comparing the experimental and numerical results as the results of the relationship between load and displacement and also the failure pattern. From the experimental and numerical study, it was found that by reinforcing the shear keys and/or by increasing the confining stress of the joints made of HSC and UHPFC, the shear capacity of the joints is increased. If the value of the used confining stress is constant at a value of 3 N/mm2 and by reinforcing the shear keys with reinforcement, the maximum load increases by 18% and 48%, respectively, than its non-reinforced counterparts joints. It was also found that by increasing the confining stress of the reinforced shear keyed joints from 3 N/mm2 to 6 N/mm2, the maximum load value is increased by 18% and 16%, for HSC and UHPFC shear keyed joints, respectively.

Heterogeneous solid element for multiscale modeling of aperiodic composite structures

Heterogeneous Solid Element (HSE) is developed based on Mechanics of Structure Genome (MSG) to model a heterogeneous body as an equivalent solid element by an effective element stiffness matrix. HSE modeling includes homogenization, macroscopic global analysis, and dehomogenization to recover local strain/stress fields. HSE avoids the local periodicity assumption for traditional multiscale modeling techniques for composite structures which compute effective material properties instead. Abaqus composite solid element and MSG-based traditional multiscale modeling are used to validate the accuracy of HSE. All example results show that HSE is more accurate in predicting global structural behavior and local strains/stresses. HSE provides a novel concept for multiscale modeling by homogenizing heterogeneous microstructures into equivalent solid elements rather than material points.

Electromagnetic and mechanical properties of CORC cable due to screening current

With the development of type II high temperature superconducting (HTS) ReBCO tape, it has been widely used in high field magnets. Conductor on round core (CORC) cable is highly flexible and fully isotropic, making it one of the most important types of HTS cables. In the condition of high field and current, the electromagnetic and mechanical behaviors of CORC cable under screening current effect are not clear. In this paper, the behaviors of CORC cable under high field and current are studied for the first time by combining electromagnetic and mechanical simulation. A three-dimensional shell model and a three-dimensional solid element model of single-layer CORC cable are established by finite element software to study the electromagnetic and mechanical properties of CORC cable, respectively. Compared with the case without taking screening current into account, two current loops are induced within a pitch of the CORC cable due to the screening current, and the magnetic field homogeneity is significantly reduced. Meanwhile, two pairs of shear force are generated at the current loops meeting zones, it results in a certain degree of stress concentration. Fortunately, because the copper core provides stable mechanical support for the HTS tape, there is no significant difference of the maximum stress between two cases with and without screening current in the CORC cable.

Numerical and experimental analysis on anisotropic thermal conductivity of carding quartz fiber web based on the reconstruction model

In order to analyze the thermal and mechanical properties of the carding quartz fiber web and the needle-punched quartz fiber preform containing the carding quartz fiber web, we propose a ‘three-step’ method to establish a three-dimensional quartz carding fiber web model containing large slenderness ratio fibers. First, the thickness and areal density of the carding quartz fiber web were measured and statistical analysis of fiber length and orientation distribution was carried out, which provided data support for establishing the three-dimensional carding fiber web model. Based on the wide application of Python language in finite element software, then spatial layered fibers of the beam element were generated by running Python scripts in finite element software; second, the three-dimensional carding fiber web model of beam element was established through a deposition and compression process by the explicit method of the finite element software; finally, the three-dimensional carding fiber web model of the beam element was converted into the solid element model for heat transferring analysis by Python. The converted process is the reconstruction process. Furthermore, anisotropic heat transmission of the three-dimensional carding fiber web model that includes temperature distribution and heat flux distribution were analyzed. Meanwhile, anisotropic thermal conductivity of the three-dimensional carding fiber web model was predicted in finite element software. A hot-disk thermal analyzer was used to measure the anisotropic thermal conductivity of the three-dimensional carding quartz fiber web. Experimental anisotropic thermal conductivity showed an excellent agreement with anisotropic thermal conductivity predicted by the finite element method. Moreover, the method in this paper is not only suitable for any other fibrous materials with randomly distributed fibers and large slenderness ratio fibers, but also is more efficient and low cost to obtain detailed heat conductions and anisotropic thermal conductivity.

Numerical analysis on fatigue behavior of ultrahigh-performance concrete-Orthotropic steel composite bridge deck

Ultrahigh-performance concrete-orthotropic steel composite bridge deck is composed of the orthotropic steel deck and a thin ultrahigh-performance concrete (UHPC) overlayer. In the previous fatigue tests, two typical fatigue failure modes were found and identified. As a supplementary test after fatigue tests, air penetration method is capable of providing a reference to the quantitative and non-destructive damage detection of fatigue damage of UHPC. To further the previous study, a detailed numerical investigation is accomplished through complimentary finite element (FE) analysis. Compared with the solid element model, the refined shell-solid element model can better reflect the mechanical behavior. It is illustrated that the vertical stress can be adopted in assessing the fatigue strength of rib-to-diaphragm welded connection in the field test by means of nominal stress method. The combination of various factors would lead to fatigue shear failure of the short headed-studs. The fatigue strength of rib-to-diaphragm welded connection predicted by the hot spot stress method and the consistent nominal stress (CNS) method can basically meet the requirements of FAT90. The consistent nominal stress method can be used as the optimization method of nominal stress of fatigue detail. It is demonstrated that the fatigue life of UHPC can be estimated by S-N curves of ordinary concrete conservatively. The allowable equivalent maximum stress level can be taken as 0.55 for two million cycles of fatigue loading, and 0.52 for five million cycles of fatigue loading.

Seismic design method and plastic hinge of square steel tube confined reinforced concrete (STRC) columns

Steel tube confined reinforced concrete columns have the advantages of high bearing capacity, good ductility and convenient construction, which meet the requirements of "building industrialization", so they are widely used in high-rise buildings. Based on the plastic-damage constitutive model of concrete and elastic-plastic mixed strengthen constitutive model of steel, finite element software ABAQUS was used to build an elaborate 3D finite element solid model and perform pseudo-static analysis of square steel tube confined RC(STRC) columns. The model considered the confinement effect of the steel tube exerting on the core concrete, as well as reasonable boundary conditions and loading modes. Good agreement was achieved between the finite element analysis results and the existing quasi static experimental results regarding to the failure modes, load-displacement hysteretic curves and load-displacement skeleton curves. Based on the validated model, 136 full scale model examples were established and extensive parametric analysis was conducted. The results show that the confinement of external steel tube can reduce the peak compressive strain and increase the peak compressive stress of concrete, thus delaying the failure of RC column and improving its bearing capacity and ductility effectively. Besides, the failure displacement angle and ultimate bearing capacity increase when the thickness of steel tube increases. Finally, the seismic design method including reasonable thickness and hoop index of the steel tube were proposed for 5 material strength matching and different axial compression ratios. A method to judge the plastic hinge based on concrete strain and steel tube strain was proposed, as well as a practical calculation formula of plastic hinge length. This study can provide basis and support for the seismic design of frame columns.

On flexural properties of additive manufactured composites: Experimental, and numerical study

Components prepared by additive technologies are increasingly utilized because of shape freedom and new possibilities of fibre reinforcing. Therefore, it is important to investigate the mechanical properties and possibilities of numerical simulations of theirs. This study is focused on the experimental and numerical examination of the flexural properties of FDM long carbon fibre reinforced composites with polymeric matrix of Onyx by 3-point bending test. Two fibre volumetric contents and two reinforced layer distributions were investigated. The experiments served also as case studies for the verification of numerical models. Four types of finite element models were proposed and examined. Analytical and RVE homogenisation methods were utilized. Except the flexural properties obtained, the results suggested that the reinforced layer distribution is crucial over the fibre content. Both homogenisation methods showed comparable longitudinal material constants but very dissimilar shear and transversal constants. Nonetheless, the results suggested that the influence of transversal constants can be negligible under certain stress states. Layered shell element model and solid element model reinforced by trusses showed excellent accuracy with respect to the experiments. Optical microscopy confirmed the correct distribution of the reinforced fibres and revealed the real structure of the printed composites.

Finite element analysis of wind turbine blades subjected to torsional loads: Shell vs solid elements

In this work the modelling of wind turbine blades subjected to torsional loads is explored. Usually, wind turbine blades are modelled using Outer Mold Layer (OML) shell models, whose mid-surface does not coincide with the nodal plane, and have been shown not to capture their behaviour correctly in torsional loadings, highly underestimating the torsional stiffness of the blade. To better understand the differences between using OML shell models and solid element models, a cylinder tube first is analysed and the conclusions from this study are applied for the wind turbine models. It was observed that artificial deformation modes were responsible for the erroneous results when using offset shell elements. These results can be drastically improved by controlling the stiffness associated with the drilling Degree Of Freedom (DOF). Furthermore, a high fidelity definition of the geometry of the blade is crucial to accurately capture its behaviour in torsion. By carefully controlling these parameters, the stiffness difference between the offset shell and solid models was reduced from 35% to 5%.

Numerical Investigation of Composite Behavior and Strength of Rectangular Concrete-Filled Cold-Formed Steel Tubular Stub Columns.

The objective of this study was to investigate the composite behavior of rectangular concrete-filled cold-formed steel (CFS) tubular stub columns under axial compression. A fine finite 3D solid element model of rectangular concrete-filled cold-formed steel tubular stub column was established by ABAQUS, which utilized a constitutive model of cold-formed steel considering the cold-forming effect and a triaxial plastic-damage constitutive model of the infilled concrete. Good agreement was achieved and the average discrepancy between the experimental and FE results was less than 5%. Based on the verified models, a further parametric analysis was carried out to reveal the influence of various factors on the strength and behavior of the concrete-filled rectangular cold-formed steel tubular stub columns. The factors included constitutive models adopted for cold-formed steel, length over width ratio of the rectangular section, wall-thickness and width, and concrete strength and yield strength of the cold-formed steel. A total of 144 FE models were analyzed. The stress nephogram was reasonably simplified in accordance with the limit state and a theoretical formula considering confinement coefficient was proposed to estimate the ultimate bearing capacity of concrete-filled rectangular cold-formed steel tubular stub columns using the superposition method. The calculated results showed satisfactory agreement with both the experimental and FE results, which proved the validity and accuracy of the formula proposed in this paper. In the proposed formula, the confinement coefficient of square concrete-filled cold-formed steel tubular stub columns is larger than that of hot-rolled steel counterparts but smaller than that of the stainless steel counterparts.

Response and damage evaluation of base-isolated concrete liquid storage tank under seismic excitations

The present study analyzes flexible rectangular concrete base-isolated liquid storage tanks (LSTs) for bi-directional earthquakes. The base-isolated LST is modeled in ABAQUS finite element software. The liquid is modeled by the Equation of State (EoS) with arbitrary Lagrangian-Eulerian (ALE) remeshing algorithm, whereas the hexahedral solid finite elements model LST. Nonlinear time history analysis is performed by considering the LSTs’ material nonlinearity and the nonlinearity produced in LST due to the water-structure interaction. As illustrative examples, different LSTs are considered in the present study with five lead rubber bearing (LRB) isolators each, four at the corners and one at the center. The parameters varied for analysis are the isolators’ effective frequency, peak ground acceleration (PGA), height of water, and aspect ratio of LSTs. The response quantities of interest include Tresca stress, sloshing height, hydrodynamic pressure, overturning moment, and base shear. The numerical study results show that the liquid’s sloshing increases by about 20%–30% at optimum frequency. Still, the forces induced in the tank are considerably reduced. The height of water, and aspect ratio of LSTs significantly influences the response behavior of the isolated tank.

A New Macromodel of Beam-Column Joints for Progressive Collapse Analysis of Reinforced Concrete Structures Under Blast Loading

The macromodel, by which the beam and column are simulated by fiber beam elements, has been extensively used in the progressive collapse analysis of reinforced concrete (RC) frames due to its high computing efficiency as compared to the solid element model. However, there exist some problems that need to be solved to improve the accuracy of the macromodel. One typical issue is to develop an accurate beam-column joint model. In current practice, the beam-column joint is as part of the rectangular frame with rigid elements, neglecting the shear damage and bending moment distribution in the core region of the joint, although they are crucial to progressive collapse analysis. In this paper, a new macromodel that considers the shear damage and bending moment distribution in the core region of the beam-column joint is developed for the progressive collapse analysis of RC frame structures under blast loads. Nonlinear springs are used in the joint connection interfaces to consider the force transfers from the beams or columns to the joint. Also, nonlinear shear springs are used in the core region of the joint, whose characteristics are derived based on the actual force-deformation relationship of the sub-assemblage due to joint shear distortion, to model the shear damage of the joint under blast loading. The proposed beam-column joint macromodel is validated with the available test data in the literature. The results indicated that the proposed macromodel for beam-column joints is more accurate than the traditional beam-column joint macromodel, while the computing efficiency remains almost unchanged in progressive collapse analysis of RC structures, especially when the RC frame structures are seriously damaged or collapse under blast loadings.

Solid and 3D beam finite element models for the nonlinear elastic analysis of helical strands within a computational homogenization framework

This paper proposes a computational approach for studying the overall behaviour and local stress state of strand-type structures. This method is based on the homogenization theory of periodic beamlike structures, with the local problem posed on the strand axial period being solved using the finite element method. This approach fully utilises the strand’s helical symmetry, thus minimising the size of the computational domain. Consequently, accounting for geometric complexity and contact interactions, which are of paramount importance for bending loads, is more straightforward. The numerical model mesh size can also be reduced thanks to the use of beam elements, and one objective of this paper is to assess the accuracy of such a model in comparison with solid element models and analytical results. These comparisons are performed on both single-layer and multi-layer strands. Results demonstrate the capability of the proposed computational approach to accurately capture the nonlinear bending behaviour stemming from the stick-slip transition as well as local stress distributions. As for the beam model, it apparently offers a very good compromise between accuracy and numerical efficiency.

Spatial refinement grillage model of box-girder bridges

The objective of this study was to overcome the shortcomings of the current analysis and calculation methods of the spatial bar system model, plane beam grillage model and solid element model in the design of the box-girder bridge. For example, the spatial bar system model lacks refined analysis of spatial effects, such as the shear lag effect, effective distribution width problem, and eccentric load coefficient problem. The similarity of the plane beam grillage model on the principle of equivalence cannot accurately reflect the shear stress distribution of the box-shaped composite beam and the local force on the top and bottom plates. The solid element and shell element models cannot directly calculate the internal force of the cross section. The calculation efficiency is low, and it is difficult to combine with the overall calculation. This paper proposes a spatial grid element analysis model suitable for fine analysis of box-girder bridges, which has the completeness and reliability of the analysis results and makes up for the shortcomings of the current box-girder bridge analysis methods. Firstly, the stiffness matrix of the spatial grid element is deduced, and the analysis program of the combined box girder based on the spatial grid element is written using MATLAB software. Then an actual calculation example is analyzed, and the difference between the calculation result of the spatial grid element and the result of the literature is compared and analyzed. The correctness and applicability of the spatial grid element model is verified.

A traction force approach for fatigue assessment of complex welded structures

AbstractA new traction force approach (TFA) for weld root fatigue analysis of complex cruciform connections is introduced. The approach defines the local nominal weld stress by using a solid element model and connecting the welded parts only from the toe and root lines. This enables the peak weld forces to be distinctly defined. The TFA approach was validated with a fully connected solid element model. As a comparison, the same analyses were performed for a shell element model. The study shows that the approach that is introduced here gives a good estimate for the local weld force with a maximum error of 10% while the commonly used shell element model greatly overestimates the peak weld force, particularly for complex connections. The analysis of fatigue‐tested connections showed that by using TFA, instead of an approach based on overall nominal weld stress, the scatter range index is reduced from 3.71 to 1.98. The TFA approach is much more efficient compared to conventional approaches because of the low pre‐ and post‐processing effort.

On the Modeling of Anisotropic Fiber-Reinforced Polymer Flange Joints

Abstract Fiber-reinforced plastic composite flanges have recently experienced a spectacular development in the area of pressure vessels and piping. The current procedures used for the design of these flanges are a major concern because of their inappropriateness to address the anisotropic behavior of composite materials. The current ASME code section X related to the design procedure of composite flanges uses the same analytical method as that of section VIII division 2, which treats the flanges as isotropic materials such as metallic flanges. This study deals with Fiber-reinforced plastic (FRP) bolted flange joints integrity and bolt tightness. A new developed analytical FRP model that treats anisotropic flanges with and without a hub is presented. The model is based on the anisotropy and a flexibility analysis of all joint elements including the gasket, bolts, and flanges. It is supported experimentally with tests conducted on a real NPS 3 class 150 WN FRP bolted flange. Furthermore, three different numerical models based on three-dimensional anisotropic layered shell and solid element models were conducted to further compare and verify the results obtained from the new developed analytical approach. The results show that the new model has potential to be used as an alternative tool to FEM to analyze the stresses and deformation of problematic FRP bolted joints.

A Short Review on Numerical Modelling Approaches for Seismic Evaluation Performance of Nuclear Power Plant Structures

Nuclear power plant (NPP) structures play a crucial role in protecting the safety of the whole plant. Overall, NPP structures have complex shapes and large dimensions. Therefore, the decision of an appropriate finite element model for seismic response analysis is important. This study presents a brief review of various numerical modelling approaches for seismic evaluation performance of NPP structures. Different conventional models, i.e. lumped-mass stick model (LMSM), full three-dimensional finite element model (3D FEM), elastic solid element model (ESM), and multi-layer shell model (MLSM), which have been applied in modelling nuclear structures, are introduced. Also, the advantages and drawbacks of those models are analysed. Furthermore, a new model namely, beam-truss model (BTM), which is recently proposed, is highlighted. It reveals that LMSM is the most simplified approach for structural modelling of NPP structures. However, it is normally used for linear analyses and not able to simulate the local behaviours and vertical responses of the complex NPP structures. Even though 3D FEM is the most sufficient method for nonlinear seismic response analyses, this approach is very time-consuming and costly computation. MLSM and BTM are recommended as practical and efficient models for nonlinear analyses of NPP structures.