3D Solid Elements Research Articles

Modeling of the Achilles Subtendons and Their Interactions in a Framework of the Absolute Nodal Coordinate Formulation.

Experimental results have revealed the sophisticated Achilles tendon (AT) structure, including its material properties and complex geometry. The latter incorporates a twisted design and composite construction consisting of three subtendons. Each of them has a nonstandard cross-section. All these factors make the AT deformation analysis computationally demanding. Generally, 3D finite solid elements are used to develop models for AT because they can discretize almost any shape, providing reliable results. However, they also require dense discretization in all three dimensions, leading to a high computational cost. One way to reduce degrees of freedom is the utilization of finite beam elements, requiring only line discretization over the length of subtendons. However, using the material models known from continuum mechanics is challenging because these elements do not usually have 3D elasticity in their descriptions. Furthermore, the contact is defined at the beam axis instead of using a more general surface-to-surface formulation. This work studies the continuum beam elements based on the absolute nodal coordinate formulation (ANCF) for AT modeling. ANCF beam elements require discretization only in one direction, making the model less computationally expensive. Recent work demonstrates that these elements can describe various cross-sections and materials models, thus allowing the approximation of AT complexity. In this study, the tendon model is reproduced by the ANCF continuum beam elements using the isotropic incompressible model to present material features.

Performance of timber board models for prediction of local bending stiffness and strength - with application on Douglas fir sawn timber

Efficient utilization of structural timber requires accurate methods for machine strength grading. One of the most accurate methods presented this far is based on data of local fiber orientation on board surfaces, obtained from laser scanning. In this paper, two potential improvements of this method are examined. The first one consists of replacing a model based on simple integration over cross sections of boards for calculation of local bending stiffness by a 3D solid finite element (FE) model from which local bending stiffness is derived. The second improvement concerns replacement of a simple model for the fiber orientation in the interior of board by a more advanced one taking location of pith and growth direction of knots into account. Application of the alternative models on a sample of more than 200 Douglas fir boards, size 40 mm X 100 mm X 3000 mm, cut from large logs, show that each of the evaluated model improvements contributes to improved grading accuracy. When local bending stiffness is calculated utilizing the herein suggested FE model in combination with the improved model of fiber orientation in the interior of boards, a coefficient of determination to bending strength as high as 0.76 is obtained. For comparison, a coefficient of determination of 0.71 is obtain using the simpler original models.

Architected frames for elastic wave attenuation: Experimental validation and local tuning via affine transformation

We experimentally demonstrate the capability of architected plates, with a frame-like cellular structure, to inhibit the propagation of elastic flexural waves. By leveraging the octet topology as a unit cell to design the tested prototypes, a broad and easy-to-tune bandgap is experimentally generated. The experimental outcomes are supported by extensive numerical analyses based on 3D solid elements. Drawing from the underlying dynamic properties of the octet cell, we numerically propose a tailorable design with enhanced filtering capabilities. We transform the geometry of the original unit cell by applying a uniaxial scaling factor that, by breaking the in-plane symmetry of the structure, yields independently tuned struts and consequently multiple tunable bandgaps within the same cell. Our findings expand the spectrum of available numerical analyses on the octet lattice, taking it a significant step closer to its physical implementation. The ability of the octet lattice to control the propagation of flexural vibrations is significant within various applications in the mechanical and civil engineering domains, and we note such frame-like designs could lead to advancements in energy harvesting and vibration protection devices (e.g., lightweight and resonance-tunable absorbers).

A 3D finite-strain beam model for thermo-mechanical deformations of 2D shape memory alloys in 3D space

In this paper, a robust constitutive model adapted to a 3D beam theory in the finite strain regime is proposed to simulate thermo-mechanical behaviors of shape memory alloys (SMAs) under triaxial normal-shear loadings. For the first time, four internal parameters are considered to capture martensitic transformation, orientation/reorientation of martensite variants, normal-shear deformation coupling, and asymmetric/anisotropic strain generation in polycrystalline SMAs. Solution algorithms of the model are presented for stress- and strain-control cases based on the elastic-predictor inelastic-corrector return mapping process. To develop the Cauchy-Green deformation tensor, a 3D exact displacement field is proposed based on the centroid movements and rotations of the cross-section. A finite element formulation along with the Newton-Raphson and Riks techniques is also established to trace the non-linear equilibrium path of 3D SMA beam structures in the large defamation regime. Higher-order shape functions are also considered to avoid shear and membrane locking issues. To explore and demonstrate the capabilities of the proposed model, the results of the triaxial and 3D SMA constitutive models are compared with existing experimental results on uniaxial tension, and combined tension-torsion tests. Afterwards, the results of 3D solid element and proposed 3D beam element are compared with experimental results of deep stretch SMA helical springs under three loading/unloading cycles. An excellent qualitative and quantitative correlation is observed between numerical and experimental results verifying the model accuracy and the solution procedure. The combination of the proposed triaxial SMA constitutive model with 3D beam theory leads to a significant reduction in computational time and storage requirements without any accuracy loss. Extra simulations are then conducted for a simplified model of a 3D biomedical vascular SMA stent under various loading/unloading conditions. The simulations reveal that the new 3D finite-strain SMA-beam element is well appropriate for modeling of 3D spatial lattice-based stents. Due to simplicity and accuracy, the 3D SMA beam model could serve in future efforts for a computationally efficient modeling of large defamations of complicated 3D SMA structures with 2D members (e.g., SMA lattices). • A robust constitutive model is developed to simulate behaviors of SMAs under triaxial normal-shears loadings. • The solution algorithms combined is extended to trace the non-linear equilibrium path of 3D SMA beam structures. • The results of present 3D Beam model has been compared with existing experimental results as well as 3D solid elements. • A good qualitative and quantitative correlation is observed between numerical and experimental results. • The proposed triaxial SMA beam model leads to a significant reduction in computational time without loss inaccuracy.

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.

Influence of PVB Interlayer Mechanical Properties on Laminated Glass Elements Design in Dependence of Real Time-Temperature Changes.

Most used laminated glass is composed of float glass plies bonded together with a viscoelastic Polyvinyl Butyral (PVB) interlayer. The shear stiffness of the polymeric interlayer is the key factor in the behavior of laminated glass. Structural engineers in the past were designing laminated glass regardless of the shear coupling of the plies. This approach with a high level of reliability led to expensive laminated glass structures due to insufficient knowledge of foil properties. Most of the current standards suggest methods that consider the shear coupling of the plies. This paper presents the experimental data from a static loading test performed on a laminated glass panel exposed to changing temperatures. The deformations were observed for 48 h. The measured results were compared with the known analytical design approaches and in addition with the finite element modeling (FEM) analysis in the available software for laminated glass design. A simplified design approach that simulates foil behavior in dependence on load duration and temperature change was adopted in this study. Design approaches that use effective thickness calculations are used with the Young and shear relaxation modulus provided by the foil producer. The imprecision of the Eurocode standards for glass design, and the propensity to change the approach to the calculation by introducing more precise parameters were expounded. The results when combining the time-temperature superposition (TTS) and the Wölfel–Bennison approach were found to be in very good agreement with the FEM analysis of 3D solid elements in Abaqus and measured data.

Modelling and Simulation Strategies for Fluid-Structure-Interactions of Highly Viscous Thermoplastic Melt and Single Fibres-A Numerical Study.

A virtual test setup for investigating single fibres in a transverse shear flow based on a parallel-plate rheometer is presented. The investigations are carried out to verify a numerical representation of the fluid–structure interaction (FSI), where Arbitrary Lagrangian–Eulerian (ALE) and computational fluid dynamics (CFD) methods are used and evaluated. Both are suitable to simulate flexible solid structures in a transverse shear flow. Comparative investigations with different model setups and increasing complexity are presented. It is shown, that the CFD method with an interface-based coupling approach is not capable of handling small fibre diameters in comparison to large fluid domains due to mesh dependencies at the interface definitions. The ALE method is more suited for this task since fibres are embedded without any mesh restrictions. Element types beam, solid, and discrete are considered for fibre modelling. It is shown that the beam formulation for ALE and 3D solid elements for the CFD method are the preferred options.

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.

Stability Behavior and Optimization of Tension Plates in Transmission Lines in Heavy Ice Zones

Finite element model of a typical ultra-high voltage direct current transmission line section, in which buckling collapse of the tension plate took place during operation, is established. In the finite element model, the tension plate and the connected hardware fittings are discretized with 3D solid elements and the sub-conductors, spacers, clamps and insulator strings with spatial beam elements. Dynamic responses of the line after ice shedding are numerically simulated and the maximum loads on the tension plate in the cases with different ice thicknesses and ice-shedding are obtained. Buckling behaviors of the tension plate are analyzed and the conditions leading to buckling collapse are discussed. Finally, the topology optimization of the tension plate is performed and two optimized schemes of the tension plate are proposed based on the optimization result and manufacture cost. Efficiency analysis demonstrates that the buckling loads of the optimized tension plates increase more than 20% nearly without increasing weight.

Research on the optimized environment of large bridges based on multi-constraint coupling

To reduce the pollution emissions of bridges to the environment, researchers need to conduct more in-depth research and design the structure. Today's architectural, structural, and mechanical engineers pay more attention to funders' requirements and pursue the maximization of economic benefits. The research begins with establishing a theoretical model of the bridge's robustness under dead and dynamic loads: applying a Three-Dimensional (3D) solid finite element model, swarm intelligence optimization algorithm, and mathematical model of quadratic interpolation approximation solves the problems of multiple loads, discrete data, and convergence. Based on the establishment and analysis data of the research model, the research and analysis of the optimal topology bridge model are completed, and the optimal structure size is obtained. The carbon emissions from the bridge optimization decreased by 2242.92 t, accounting for 25% of the total emissions. This data is shocking, and it also gives investors and governments a painful reminder that they must pay more attention to the sustainable construction and development of the construction industry and achieve the goal of zero carbon emissions in the construction industry as soon as possible.

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.

Micropolar beam-like structures under large deformation

Results from experimental torsion and bending tests show the existence of a size effect, which conventional continuum models are unable to describe. Therefore, the incorporation of the micropolar media into numerical approaches for the analysis of materials with a complex microstructure looks necessary. So far, most studies utilize Cosserat continuum theory with 3D finite solid elements, even though, it covers only few beam elements developed within a linear strain–displacement relationship, and therefore only works in a small deformation regime. In this study, the authors aim to develop a size-dependent 3D continuum beam element based on the absolute nodal coordinate formulation (ANCF) with microstructure inclusions. Comparing analytical solutions within the Cosserat continuum model and models based on the proposed and already existing 3D micropolar solid elements, one can see a good correlation between them, with a faster convergence rate for the developed ANCF beam element. That allows exploiting the developed beam element within the non-linear deformation range, which is usually bypassed because of high computational costs, thus, accounting fully for differences between two media descriptions.

Dynamic Properties Comparison of 1D, 2D, and 3D Model for Concrete Box-Girder Bridge of 40-meter Span

Concrete box-girder structure is considered the thin-walled structure, undergoing deformation and forces, as well as having structural rigidity in three dimensional directions. However, it’s commonly modeled as 1D structure for the sake of design practicality, which influences the numerical result of its dynamic properties when compared to both real time SHMS and field test result. To see how far the difference of the dynamic properties between 1D, 2D, and 3D model of concrete box-girder structure, the concrete box-girder structure is modeled as 1D (frame), 2D (shell), and 3D (solid) element with MIDAS Civil 2019. Considering the allowable deflection and stress limited by design code, concrete box-girder structure is modeled and analyzed as linearly elastic material. The dynamic properties obtained from these 3 models were compared with those obtained from real time SHMS and field test. These results indicate that both natural frequency and period of 2D and 3D models are close to those of real time SHMS and field test. However, the natural frequency of 1D model is slightly larger than the real SHMS and field test, indicating that 1D model gives the slightly overestimate natural frequency and structural rigidity compared to the reality. Unlike 2D and 3D model, the structure is accounted to have the uniform sectional rigidity along transversal direction in 1D model. This is why 1D model seems to have higher structural rigidity compared to 2D and 3D model, which subsequently yields the higher natural frequency than 2D and 3D model. This research proves that the designers’ discretion is advised if 1D model is used for the sake of design practicality.

Active auto-adaptive metamaterial plates for flexural wave control

In this paper, a novel design concept for active auto-adaptive metamaterial (AAAMM) plates is proposed based on an active auto-adaptive (AAA) control strategy guided by the particle swarm optimization (PSO) technique. The AAAMM plates consist of an elastic base plate and two periodic arrays of piezoelectric patches. The periodic piezoelectric patches placed on the bottom plate surface act as sensors, while the other ones attached on the top plate surface act as actuators. A two-dimensional (2D) simplified metamaterial (MM) plate model is established by the Hamilton principle. The finite element method (FEM) with quadratic shape functions is adopted for numerically solving the 2D simplified MM plate model, which is validated by two more accurate but also much more complicated FEM models using three-dimensional (3D) piezoelectric and 3D elastic solid elements, and by its 2D counterpart model solved by the plane wave expansion (PWE) method. The conventional displacement, acceleration and velocity feedback control methods are introduced and analyzed. Then, a novel AAA control strategy based on combining the displacement and acceleration feedback control methods and guided by the PSO technique is developed. The main objective of the present paper aims at the vibration or flexural wave suppression and isolation of elastic plate structures based on an auto-adaptive control strategy, which has wide-range engineering applications. Numerical results will be presented and discussed to show that the proposed AAAMM plates can automatically and intelligently evolve different feedback control schemes to adapt to different stimulations on demand. Compared to the conventional MM plates, the proposed AAAMM plates exhibit improved and enhanced band-gap characteristics and suppression performance for flexural waves at frequencies inside and outside the band-gaps.

Efficient Modeling and Simulation of PMUT Arrays in Various Ambients.

This paper presents a numerical reduced-order modeling (ROM) approach for complex multi-layered arrays of piezoelectric micromachined ultrasonic transducers (PMUTs). The numerical modeling technique adopted to generate an array of PMUTs consisting of a considerable number of transducers allows for a large reduction in computational cost without reducing accuracy. The modeling idea is based on coupling shell elements applied to the PMUT structural layers with 3D-solid elements applied to the piezoelectric layer. A set of eigenfrequency and frequency domain analyses are presented considering a single ROM of a PMUT performing in different ambients and the performing central frequencies are obtained for every considered scenario. A unique arrangement of 228 PMUTs is presented and tested for its ability to transmit and receive acoustic waves. The operating frequency band of the array and the level of interference and cross-talk among different PMUTs in the near field are estimated. Finally, the results from a preliminary experimental test performed to analyze the acoustic abilities of an 8 × 8 array of PMUTs are presented. A corresponding numerical model is created and the obtained results matched the experimental data, leading to a validation of the modeling technique proposed in this work.

Shear enhancement in RC beams with stirrups simultaneously loaded within 2d and at 3d from supports

Shear enhancement occurs in reinforced concrete (RC) beams when loads are applied within around 2d of supports where d is the beam effective depth. This paper examines shear enhancement in RC beams, with stirrups, which are loaded both within 2d of supports and at 3d from supports where shear enhancement is minimal. Simultaneously loading beams both inside and outside 2d of supports commonly occurs in practice but has not previously been systematically studied. A total of eight beams were tested in two groups of four having different reinforcement arrangements. The tests suggest that the shear resistance depends on the angle of the failure plane which is related to the loading arrangement. A strut and tie model (STM) is developed for analysing beams simultaneously loaded within and outside 2d of supports. The accuracy of the STM predictions is shown to be improved by relating strut strength to the strain in the flexural reinforcement. The proposed STM and nonlinear finite element analysis (NLFEA) with 3D solid elements are used to investigate parametrically the influence of loading arrangement on shear resistance. The strength predictions of the STM are shown to compare well with those of NLFEA. Comparisons are also made with shear strengths calculated using fib Model Code 2010 (MC2010) and the draft new generation of Eurocode 2 (prEN1992-1:21). The differing philosophies of these two methods are discussed.

Efficient design of Kevlar/basalt hybrid composite laminates under ballistic impact

Advanced composite materials such as Kevlar and basalt are most commonly used for the efficient design of body armor to predict the safety and reliability of the armor systems. The aim of this study is to develop the lightweight and efficient design of armor plate using the 3D Kevlar/basalt hybridization and different stacking sequences of composite laminates impacting with two impactors under high-velocity impact. Damage initiation and damage propagation based on the Yen criteria are developed to investigate the different failure modes of composites. The hybrid composite panels are modeled using 3D solid element considering the four different types of panels such as H3B3, H3K3, B3K3 and K3-16 impacting with fragment simulating projectile (FSP) and 9 mm full metal jacket(FMJ) projectiles. The efficient design of hybrid panel B3K3 showed excellent ballistic performance parameters in comparison to the other hybrid panels designed under the FSP and FMJ projectiles.

Computationally efficient model to predict the deformations of a cellular foot orthotic

BackgroundFoot orthotics (FOs) are frequently prescribed to provide comfortable walking for patients. Finite element (FE) simulation and 3D printing pave the way to analyse, optimize and fabricate functionally graded lattice FOs where the local stiffness can vary to meet the therapeutic needs of each individual patient. Explicit FE modelling of lattice FOs with converged 3D solid elements is computationally prohibitive. This paper presents a more computationally efficient FE model of cellular FOs. MethodThe presented FE model features shell elements whose mechanical properties were computed from the numerical homogenization technique. To verify the results, the predictions of the homogenized models were compared to the explicit model's predictions when the FO was under a static pressure distribution of a foot. To validate the results, the predictions were also compared with experimental measurements when the FO was under a vertical displacement at the medial longitudinal arch. ResultsThe verification procedure showed that the homogenized model was 46 times faster than the explicit model, while their relative difference was less than 8% to predict the local minimum of out-of-plane displacement. The validation procedure showed that both models predicted the same contact force with a relative difference of less than 1%. The predicted force-displacement curves were also within a 90% confidence interval of the experimental measurements having a relative difference smaller than 10%. In this case, using the homogenized model reduced the computational time from 22 h to 22 min. ConclusionThe presented homogenized model can be therefore employed to speed up the FE simulation to predict the deformations of the cellular FOs.

Warping torsion of FGM beams with spatially varying material properties

This contribution extends the author’s previous research results concerning effect of spatially varying material properties on warping torsion of beams with open cross-section made of Functionally Graded Material (FGM). The author’s FGM WT beam finite element is used in the calculations of the primary quantities. The secondary deformations due to the angle of twist is considered. The warping part of the first derivative of the twist angle, caused by the bimoment, is accounted as an additional degree of freedom at the beam nodes. The author’s Reference Beam Method, (RBM), is used for homogenization of the spatially varying material properties in the real beam onto effective constant or longitudinally varying stiffnesses for the homogenized beam. Enhanced equations for calculation of the normal and shear stresses with the influence of the deformation effect caused by the primary and secondary torsion moment are established. These equations also contain effect of the warping ordinate function and its gradients that depend on spatially varying material properties. The focus of the numerical investigation is on non-uniform torsional analysis of straight FGM cantilever beams with I- cross-section. An effect of the warping ordinate function and its gradients on the normal and shear stresses is evaluated and discussed. A significant effect of the spatial variability of material properties on the deformation as well as on the stress state in the FGM beams with I-cross-section, has been found. The real beams with spatially varying material properties are modelled with only a single FGM WT beam finite element. Obtained results for the primary and secondary variables are compared with the ones calculated by a very fine mesh of standard 3D-solid finite elements. A very good agreement of all the results has been achieved.

Vibration performance of timber-concrete composite floor section –verification and validation of analytical and numerical results based on experimental data

ABSTRACT Vibration performance of a one-way simply supported timber-concrete composite (TCC) floor section has been studied using analytical as well as numerical methods. Focal points have been verification and validation of results from analytical and numerical calculations of vibration response based on experimental data. For the analytical calculations, floor bending stiffness and vibrational response are determined from methods proposed in the current and revised versions of Eurocode 5. The numerical calculations based on the finite element (FE) method are done using 3D solid elements with orthotropic material parameters. When comparing the results of the FE analysis, better agreement with the experimental data is reached for the fundamental frequency when 3D solid elements are used rather than 3D beam elements. Furthermore, better agreement with the experimental data is reached for RMS acceleration by FE analysis rather than the method based on Eurocode 5. For detailed analysis, the authors suggest performing dynamic FE analysis and calculating vibration response from the TCC floor’s modal responses as eigenmodes and natural eigenfrequencies below 40 Hz. For future studies, it is recommended that the verification of vibration response may be accomplished by applying standard EN 16929.