Solid Finite Element Research Articles

Vibrations of launch vehicle fairings with conical shape

Vibrations of launch vehicle conical fairings are investigated. Fairings are simulated using thin conic shells. The modal analysis of a thin elastic shell is based on the use of the developed finite element model of an inhomogeneous shell. In general, the technique makes it possible to investigate the geometrically nonlinear deformation, stability, and post-buckling behavior of a wide class of thin elastic shells. The modal analysis of the structure is implemented at each step of the static thermomechanical load. The subspace iteration method is used to determine the spectrum of the lowest vibration frequencies of shells of an inhomogeneous structure. The shell behavior analysis method is based on the relations of the three-dimensional theory of thermoelasticity and uses the finite element moment scheme. A thin elastic shell is simulated by a universal solid isoparametric finite element. The parameters of natural vibrations of conical shells of revolution with different thicknesses are investigated. Comparison of the calculation results obtained by the finite element moment scheme with the data of other authors shows a fairly good agreement between the solutions.

Calculation Method of Rotational Constraint Stiffness for a New Tower-Pier Connected System

The universal hinge support (UHS) is a new connection system for the tower and pier of a single-tower cable-stayed bridge (STCSB), which could conform the multi-direction rotation of the tower and release the bending moment at the bottom of the tower in all directions. However, UHS is not an ideal hinge in practical projects, and the rotational constraint stiffness (RCS) of UHS is constantly changed with construction. In order to determine the RCS of UHS in situ, parametric analysis was performed by establishing a theoretical mechanical model of plane rotation and a refined solid finite element (FE) model of UHS. The slope of the linear rising segment of the load–displacement curve obtained from the numerical simulation was considered as the RCS of the UHS. The relationships between RCS and the vertical force, geometric parameters, and material parameters were established, and then the calculation formula of RCS was further proposed. To verify the accuracy of the proposed formula, a case study for a real bridge was conducted in this paper. The results show that the error of the tower rotation displacement can be reduced by about 90% using the proposed method compared with the conventional method, which regards the hinge as an ideal one, and the precision is greatly improved. This study has enormous potential to quickly determinate the RCS of UHS in practical applications, and plays a great promotion role in enriching the structural system of cable-stayed bridges.

Theory and implementation of sub-model method in finite element analysis

Through finite element analysis (FEA) software to study mechanical performance of a bridge structure is currently a commonly used method. The keys to obtain accurate results are to select the appropriate element type and establish a refine mesh model. With the construction of a large number of kilometer-level long-span bridges in practical projects, the time cost of establishing and analyzing a fine mesh solid finite element model (FEM) of a long-span bridge with complex structure can not be ignored. In order to find the balance between accuracy and efficiency, sub-modeling technique can be used to analyze the bridge structure. It is often thought that the sub-modeling technique is only applicable to shell and solid elements, but in fact it is also applicable to plane frame models. Based on two-dimensional (2-D) beam element model, the theory of sub-model was theoretically deduced. Meanwhile the sub-modeling technique was applied and verified by an example of plane frame model. Furthermore, based on the three-dimensional (3-D) solid FEM of a skew bridge, the influence of mesh size on the calculation accuracy was illustrated. Based on sub-modeling technique of nodal displacements, the results of the global model and the sub-model for the skew bridge were compared and studied in terms of stress field and plastic damage of concrete. It is found that the sub-model technique based on nodal displacements is suitable for solid FEM.

Crush simulations of composite energy absorbing structural systems

A recently developed material model for orthotropic composites is demonstrated by modeling an energy absorbing crush event used in the development of automotive components. The material model (MAT213) provides a wide variety of capabilities such as tension/compression asymmetric behavior, visco-elastic/plastic behavior, damage modeling, rate and temperature effects with the ability to support these features in shell and solid finite elements. Data from limited laboratory testing of composite coupons is used to construct the material model input. Data from laboratory conducted crush testing is used to validate the material model. The predictions from the explicit finite element (FE) simulations are compared against the laboratory data as well as a popular constitutive model used in the automotive industry (MAT058). Results show that even with incomplete material data to build the constitutive model, MAT213 yields superior results that match experimental validation data reasonably well.

Dynamic amplification in masonry arch railway bridges

Dynamic amplification of loads in masonry arch railway bridges is not well understood. There is a scarcity of experimental data and previous numerical studies have only addressed a few specific bridge geometries. Despite this, guidance documents provide empirical and unvalidated formulae to calculate dynamic amplification for masonry arch railway bridges. To improve our fundamental understanding of the problem, determine appropriate modelling strategies and evaluate the reliability of guidance documents, simple 2D and 3D models are explored in this paper. The 2D approach idealises key bridge components (pier, arch, fill and backing elements) with straight Timoshenko beams, springs and lumped masses. It uses an analytical dynamic stiffness formulation, which is computationally efficient and well-suited to explore a range of bridge models. The higher fidelity 3D modelling approach uses shell and solid finite elements and is used to evaluate the limitations of 2D models. In both approaches, linear-elastic material behaviour is assumed and train loads are idealised as moving vertical loads distributed over an effective area. The modelling results indicate a complex relationship between train speed and dynamic amplification that depends critically on bridge geometry and axle spacing. In general, the multi-span bridge configurations experienced higher dynamic amplification over operational train speeds. The results also higlight deficiencies in existing code provisions and demonstrates how efficient numerical models may replace these provisions.

The usability and limitations of the various absolute nodal coordinate beam elements subjected to torsional and bi-moment loading

This paper explores the usability of several beam elements based on the Absolute Nodal Coordinate Formulation (ANCF) subjected to torsional and bi-moment loading scenarios. ANCF beam element solutions are compared against an analytical solution and beam and solid finite element solutions. When subjected to bi-moment loading, most of studied higher-order ANCF beam elements suffer from strong “non-smooth” displacement continuity between elements, and therefore they should be used with caution. The distribution of warping displacement was shown to be unacceptable for four-node higher-order ANCF beam elements. Numerical results revealed that the higher-order elements failed to characterize local loading scenarios such as a bi-moment. This problem can be alleviated using very fine beam discretization, which would be more computationally intensive.

Numerical evaluation of the perfobond (PBL) shear connector with transverse rebar using coupled rigid Body spring model (RBSM) and solid finite element method (FEM)

Numerical analyses focused on the detailed fracture process of concrete in a reinforced PBL shear connector with the transverse rebar subjected to a simple push-out test employing coupled RBSM and solid FEM model were performed to reveal the internal failure mechanism, quantitatively. The numerical model effectively captured the shear capacity and failure modes of test results. It was investigated as the shear resistance of the concrete dowel was enhanced against the increased diameter of the transverse rebar, the shear capacity was improved consequently, and the deformed behaviors transformed from shear to splitting failure. The internal failure process of a specimen with transverse rebar was highlighted; the normal stress distribution along the transverse rebar exhibited the presence of the compressive zones in the concrete dowel region due to the formation of compression struts and compressive stresses transferred from anchored parts of the transverse rebar towards the concrete dowel region and got localized around the concrete dowel and in side concrete blocks and reproduced the enhanced shear capacity compared with specimen without transverse rebar. It was evaluated that the change in shear capacity was similar to the change in axial force of the transverse rebar. The shear capacity of the PBL shear connector increased as the axial force increased, while the inverse response against rebar bending moment was observed and determined that the main contribution towards the increase in the shear capacity of the PBL shear connector was from the axial force of the transverse rebar.

Numerical simulation of fluid-driven fracturing in orthotropic poroelastic media based on a peridynamics-finite element coupling approach

In the present manuscript a peridynamics-finite element coupling approach proposed by Sun and Fish (2021) is generalized to simulate fluid-driven fracturing in orthotropic poroelastic media. For this purpose, an orthotropic non-ordinary state-based peridynamics (NOSBPD) model with a bond micromodulus and a critical energy density continuously varying with the bond orientation is proposed. The governing equations of the coupled system involving an orthotropic NOSBPD model aimed at capturing the solid fracture and finite element model (FEM) aimed at modeling fluid flow with an anisotropic permeability tensor is derived. Both the m -convergence and δ -convergence studies are performed to determine appropriate discretization parameters for the proposed orthotropic NOSBPD model. The fracture propagation in the compact tension test with different material orientations is simulated for model verification. The effects of the elasticity and permeability anisotropy, injection rates as well as the existences of multiple fractures and natural fractures have been found to have a significant effect on the fluid-driven fracture propagation in orthotropic poroelastic media. The fracture seems to deviate from the initial notch direction under different material angles, and this trend becomes more prominent with reduction of the elastic modulus and the fracture release rate perpendicular to the bending plane. The permeability anisotropy affects the fluid pattern and the fracture propagation length. The rapid injection rate gives rise to a wider damage zone and a more diffuse pore pressure field .

Calculation and analysis of ampacity and stress of overhead transmission line

To ensure the safe operation of a transmission line, it is necessary to study the radial temperature rise and the stress and strain distribution of the transmission line under on-load state. A three-dimensional solid finite element model of reinforced aluminum conductor steel was established, and the temperature and stress distribution of the conductor were calculated. The effects of operating tension, wind speed, and radial temperature difference on the temperature and stress distribution were analyzed. The radial temperature difference increases about 1.40–3.16 °C with the rise of the mean temperature of the conductor. When the ambient temperature decreases from 20 to −40 °C, the mean temperature of the conductor decreases from 50.34 to −9.31 °C, and the external layer stress increases from 44.59 to 60.19 MPa. At the same time, the external layer stress of the conductor increases with the increase in wind speed and operating tension. The stress of the outermost aluminum conductor of the conductor under the radial temperature difference load increases with the rise in the temperature difference, and the stress of the inner aluminum conductor and the inner steel core decreases with the rise in the temperature difference.

Investigation and elimination of nonlinear Poisson stiffening in 3d and solid shell finite elements

AbstractWe show that most geometrically nonlinear three‐dimensional shell elements and solid shell elements suffer from a previously unknown artificial stiffening effect that only appears in geometrically nonlinear problems, in particular in the presence of large bending deformations. It can be interpreted as a nonlinear variant of the well‐known Poisson thickness locking effect. We explain why and under which circumstances this phenomenon appears and propose concepts to avoid it.

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.

Parallel PD-FEM simulation of dynamic fluid-driven fracture branching in saturated porous media

The dynamic hydraulic fracture in porous media is often characterized by crack diverting and/or branching that affects the connectivity of the fracture network. There is a need to understand the crack branching mechanism for enhancing the unconventional resource production. In the present manuscript, the dynamic fluid-driven fracture branching in saturated porous media is studied by a parallel PD-FEM coupling approach. Under the assumption of negligible relative acceleration of the fluid with respect to the mixture, the two-field u-p model is derived based on the Biot’s theory. The dynamic coupled system is discretized into two layers with the non-ordinary state-based peridynamics layer characterizing the deformation and fracture of the solid skeleton and finite element layer representing the fluid flow. A fully implicit scheme for the time integration of the dynamic coupled system within a nonlinear framework based on the Newmark method is employed and an alternate grid/particle updating OpenMP parallel programming scheme is proposed. The efficiency and accuracy of the coupled method is first verified by several benchmark examples with either experimental data or analytical solutions, followed by a study of crucial factors affecting dynamic hydraulic fracturing branching. The parametric study shows that in general the following factors favor the crack branching: lower critical energy release rate, higher injection rate, lower Young’s modulus, higher Poisson’s ratio, lower viscosity of the fluid and higher compressibility of the fluid.

Resistance of Closely Spaced Back‐to‐back Connected Equal Leg Angle Sections

AbstractIn the framework of the European RFCS project ANGELHY, the resistance of built‐up members fabricated from angle sections is studied, amongst others. This paper focusses on the resistance of back‐to‐back connected angle sections. The studied built‐up members are connected through bolted packing plates. Due to the flexibility of this connection, the back‐to‐back connected members do not fully act as a single homogeneous member but the connection stiffness has to be accounted for. However, Eurocode 3 does not provide a clear and generally accepted method for the determination of the buckling resistance of back‐to‐back connected members that do not respect a limit distance of 15imin between the packing plates. This limit is very low and therefore there exists a need of a design method overcoming the limitations. Throughout this paper, a design method will be derived based on a comprehensive numerical study. The numerical model is based on solid finite elements and has been validated with physical tests. Owing to the use of solid elements, it is possible to model explicitly the bolts, the packing plates and all contact regions.

Seismic failure behavior of masonry domes under strong ground motions

General stability and failure behaviors of masonry domes under static loads have been investigated extensively in literature. However, a few studies have been done on the seismic failure behavior of masonry domes under strong ground shaking. This study aims to investigate the seismic failure behaviors and failure angles of masonry domes with support system including drum and buttresses using advanced 3D nonlinear numerical simulations. Four types of masonry domes with thickness-to-span ratios t/R = 0.092, such as a dome with circular drum (Dome A), a dome with circular drum and buttress (Dome B), a dome with dodecagon drum (Dome C), a dome with dodecagon drum and buttress (Dome D), built on historical structures are selected. Three-dimensional solid finite element models of the selected masonry domes are created using isotropic continuum macro modelling technique with homogenized properties. The finite element models are utilized to simulate the seismic behaviors of the masonry domes under three different strong ground motion acceleration records matched according to the target response spectrum with a return period of 475 years in the Turkish Building Earthquake Code. The seismic failure behaviors of four masonry dome models are evaluated by comparing mode shapes, displacements, maximum principal stresses, damage propagation patterns and failure angles. It is determined that the average angle intervals of hoop tension failure regions of Dome A, Dome B, Dome C and Dome D models under strong ground motions vary between 39, 25, 35 and 26 degrees, respectively.

Phase field modeling of brittle fracture in large-deformation solid shells with the efficient quasi-Newton solution and global–local approach

To efficiently predict the crack propagation in thin-walled structures, a global–local approach for phase field modeling using large-deformation solid shell finite elements considering the enhanced assumed strain (EAS) and the assumed natural strain (ANS) methods for the alleviation of locking effects is developed in this work. Aiming at tackling the poor convergence performance of standard Newton schemes, a quasi-Newton (QN) scheme is proposed for the solution of coupled governing equations stemming from the enhanced assumed strain shell formulation in a monolithic manner. The excellent convergence performance of this QN monolithic scheme for the multi-field shell formulation is demonstrated through several paradigmatic boundary value problems, including single edge notched tension and shear, fracture of cylindrical structure under mixed loading and fatigue induced crack growth. Compared with the popular alternating minimization (AM) or staggered solution scheme, it is also found that the QN monolithic solution scheme for the phase field modeling using enhanced strain shell formulation is very efficient without the loss of robustness, and significant computational gains are observed in all the numerical examples. In addition, to further reduce the computational cost in fracture modeling of large-scale thin-walled structures, a specific global–local phase field approach for solid shell elements in the 3D setting is proposed, in which the full displacement-phase field problem is considered at the local level, while addressing only the elastic problem at the global level. Its capability is demonstrated by the modeling of a cylindrical structure subjected to both static and fatigue cyclic loading conditions, which can be appealing to industrial applications.

Self-expandable stent for thrombus removal modeling: Solid or beam finite elements?

The performance of self-expandable stents is being increasingly studied by means of finite-element analysis. As for peripheral stents, transcatheter valves and stent-grafts, there are numerous computational studies for setting up a proper model, this information is missing for stent-retrievers used in the procedure of thrombus removal in cerebral arteries. It is well known that the selection of the appropriate finite-element dimensions (topology) and formulations (typology) is a fundamental step to set up accurate and reliable computational simulations. In this context, a thorough verification analysis is here proposed, aimed at investigating how the different element typologies and topologies - available to model a stent-retriever - affect simulation results. Hexahedral and beam element formulations were analyzed first individually by virtually replicating a crimping test on the device, and then by replicating the thrombectomy procedure aiming at removing a thrombus from a cerebral vessel. In particular, three discretization refinements for each element type and different element formulations including both full and reduced integration were investigated and compared in terms of the resultant radial force of the stent and the stress field generated in the thrombus. The sensitivity analysis on the element formulation performed with the crimping simulations allowed the identification of the optimal setting for each element family. Both setting lead to similar results in terms of stent performance in the virtual thrombectomy and should be used in future studies simulating the mechanical thrombectomy with stent-retrievers. The carried out virtual thrombectomy procedures confirmed that the beam element formulation results were sufficiently accurate to model the radial force and the performance of the stent-retriever during the procedure. For different self-expandable stents, hexahedral formulation could be essential in stress analysis.

A reliable FEA-based calculation approach of convective heat transfer coefficient for Steady-State Thermal analysis of X-ray water-cooled mirrors

As an indispensable part for the construction of synchrotron radiation or X-ray free-electron laser facilities, the accuracy of simulation analysis is of great significance to engineering construction. Steady-State Thermal analysis is commonly used to analyze the thermal stress and strain of the crucial optical components at the beamlines, such as the reflection mirror. Especially, according to the Reynolds numbers of cooling mediums, the Dittus–Boelter equation or Gnielinski equation is usually used to calculate the convective heat transfer coefficient between the fluid and the solid wall. However, there is a non-negligible error calculated by this method. In this paper, in order to obtain the more accurate simulation results, the fluid–solid coupling finite element analysis was adopted, and a reliable fitted equation for calculating the convection heat transfer coefficient is proposed and compared with the classical theoretical calculation results. The compared results show that the proposed approach can effectively reduce the simulation errors and improve the analytical efficiency.

Computationally Efficient Modeling of Lightweight Expeditionary Airfield Surfacing Systems at Large Length Scales

Expeditionary airfield matting systems are lightweight, portable surfaces that enable the rapid deployment of infrastructure to support aircraft operations. Individual matting components are assembled via interlocking joints to construct arrays that serve as temporary aircraft operating surfaces. The paper outlines the homogenization of the AM2 portable airfield matting system and its interlocking mechanisms to permit computationally efficient analyses toward understanding mechanisms that influence the global behavior of these arrays and underlying subgrade during aircraft maneuvers. An equivalent orthotropic two-dimensional continuum was developed from finite element analysis of a detailed three-dimensional model and its flexural behavior was validated against experimental data and solid finite element models. Interlocking joints were characterized using node-to-node connector elements based on subscale finite element studies. Both components were implemented into a full-scale model representative of a typical test section, and responses to static high tire pressure aircraft loads were analyzed over a soil foundation representing a California bearing ratio of 6%, yielding promising agreement with experimental data. Results of this study reveal an inherent coupling between load transfer, mat deflection, and near-surface subgrade stress with dependence on tire location, mat core shear flexibility, and joint stiffness.

A global thermo-mechanical model to mitigate welding residual stress and deformation in production of an aluminum bio-inspired AUV with a curved outside corner joint

Welding mechanics of large-scale complex-shaped structures is generally either disregarded or implicitly presumed due to high complexity and time consumption — even in the case of numerical analysis, typically it is limited to local thermo-mechanical models of straight butt or tee welded joints. Nevertheless, not only is this study aimed at presenting a time-saving global thermo-mechanical model of a curved outside corner joint but also at exploiting combined effects of welding parameters to mitigate deformation and residual stress. The global thermo-mechanical model is thereby constructed by combination of shell and solid finite elements providing Thermal-Elastic-Plastic (TEP) analysis for an aluminum Autonomous Underwater Vehicle (AUV) of which novel hull shape inspired by catfish morphology results in a longitudinal curved outside corner welded joint. A suitable polynomial mathematical function enabled the welding heat source to move steadily along the curved path of the joint. Saving up computational time 3.5 times greater than conventional full 3D method, the global shell/3D TEP FEM is validated well against experimental temperature, distortion and residual stress distributions when locating the boundary between shell and solid elements with the size of solid zone up to the 3 times thickness of base metal based on accuracy of molten metal penetration, deformation and residual stress prediction. A stark difference of about 120% in maximum amount of longitudinal residual stress is observed between global and local models. Finally, optimal outcomes are employed in production of the AUV so that 33% reduction in welding speed mitigated residual stress by 22% whereas welding length and sequence were more effective on distortion.

Impact of pulse dynamic loading direction and surface curvature on the stress-strain state of a three-layered spherical shell

On two size types of the semispherical three-layered structures, impact of the surface curvature and impact of the pulse dynamic loading on the stress-strain state (SSS) of these structures has been investigated. The layered hemispheres have been analyzed with the clamped footing and diameters (D1=0.30 m, D2=0.60 m), which had similar bearing layers’ thickness (h1=h3=0.010 m), polymeric filler with h2=0.020 m thickness, reinforced with the 5 discrete stiffening rings rigidly bound to the bearing layers.
 Values of normal stresses and vertical displacements of the structures’ bearing layers and distribution of these indicators along the spatial coordinate have been determined. Distribution of displacements’ and stresses’ magnitudes along the spatial coordinate α was determined by the software complex Nastran through the direct transient dynamic process algorithm within the time interval 0 ≤ t ≤ 10T. The time interval step duration was 0.25*10-6 s and the total number of steps was 200. The detailed and accurate calculation results have determined the choice of the solid finite element type.
 Value of the Gaussian curvature of the layered shell structures impacts their stress-strain state. Increase of the surface curvature of spherical structures under the impact of the dynamic pulse load increases the displacement and stress of their bearing layers.
 In addition to the vertical displacements and normal stresses of the bearing layers of the analyzed semispherical three-layered structures, their first natural frequency (f1) was also calculated.