Solid Finite Element Research Articles

A block-based numerical strategy for modeling the dynamic out-of-plane behavior of unreinforced brick masonry walls

AbstractIn this paper, a numerical procedure is proposed to simulate the dynamic out-of-plane response of unreinforced masonry (URM) walls. A state-of-the-art damaging block-based model, originally developed for quasi-static simulations, is extended for the first time in a dynamic regime. The blocks are represented using solid 3D finite elements governed by a plastic-damage constitutive law for both tension and compression. A cohesive-frictional contact-based formulation is used to account for interactions between the blocks. A simplified mechanical characterization is formulated to improve efficiency in wall-level analyses. Dynamic simulation is performed using a generalized HHT-$$\alpha$$ α direct integration implicit solver and by implementing Rayleigh damping in the bulk. Such consideration allows the use of both mass and stiffness proportional terms of the Rayleigh damping without compromising efficiency. The strategy is applied to simulate incremental dynamic experiments performed on full-scale walls, showing good agreement between numerical and experimental results. The calibrated numerical model is then optimized to reduce computational effort while maintaining accuracy. The optimized model is used to investigate the effect of relative support motion on the one-way bending out-of-plane seismic response of URM walls, demonstrating the potential of the modeling strategy to explore the effect of boundary conditions that occur in real buildings but are often overlooked in laboratory experiments. This investigation also explores the adequacy of simplifications in capturing the effect of relative support motion, which can be adopted for simple modeling strategies commonly used in standard engineering practice.

Modeling of in-plane floor flexibility in existing reinforced concrete buildings

The paper addresses the problem of determining the mechanical characteristics of an orthotropic slab that best represents the in-plane behavior of a complex reinforced concrete (RC) floor system. To represent the structural behavior of the real RC floor, a reference model composed of solid finite elements is developed. The mechanical parameters of the equivalent orthotropic slab are determined by different homogenization techniques. In particular, two numerical algorithms and an analytical procedure to derive the elastic parameters of the equivalent slab representing the in-plane behavior of a single floor cell are proposed. Then, to determine which homogenization technique best predicts the structural behavior, representative one-story and six-story structures are modeled using both the equivalent slabs obtained using the three proposed techniques and the reference floor model. A discussion of the suitability of modeling floor in-plane flexibility taking account of only the top RC slab, for the considered case studies, is also provided.

Numerical and Theoretical Study on Flexural Performance and Reasonable Structural Parameters of New Steel Grating–UHPFRC Composite Bridge Deck in Negative Moment Zone

As the bridge’s structural component is directly subjected to vehicle loads, the stress performance of the bridge deck has a significant impact on the safety, durability, and driving comfort of the bridge. In order to improve the bending performance of the bridge deck in the negative moment zone, a new type of steel grating–UHPFRC composite bridge deck was proposed in this paper. Firstly, structural details and advantages of the new steel grating-UHPFRC composite bridge deck were introduced. Secondly, the finite element program ABAQUS was used to establish a refined solid finite element model of the new bridge deck. The mathematical program MATLAB (PYTHON) was also used to analyze the effects of the structural parameters on bending bearing capacity and put forward reasonable structural parameters of the new bridge deck, considering the technical and economic indexes. Thirdly, the simplified plasticity theory was applied to analyze the bending bearing capacity of the new bridge deck, and the corresponding formula for bending bearing capacity calculation was derived and verified by numerical model results. In addition, the cost–benefit analysis and environmental impact assessment of the new bridge deck were also conducted. The results show that the bending bearing capacity of the new bridge deck in the negative moment zone increases with the increase of the width of the bridge deck, the thickness of the wing plate, and the height of the web plate, with a trend of increasing and then decreasing when the horizontal inclination of the web plate decreases. The bridge deck width does not have a significant effect on improving the bearing capacity. The bearing capacity calculated by theoretical formulas is close to that calculated by numerical models and the maximum relative deviation is 9.1%. The new steel grating-UHPFRC composite bridge deck proposed in this paper is superior to conventional steel-UHPC composite bridge deck in terms of cost-benefit and environmental impact.

Progressive failure analysis of laminar composites under compression using smeared crack-band damage model and full layerwise theory

This paper presents an original finite element (FE) model that integrates the smeared crack band (SCB) approach and full layerwise plate theory (FLWT). The model enhances the computational efficiency of progressive failure analysis (PFA) of laminar composites in compression, by utilizing the layerwise approach which reduces a 3D model to a 2D one. The model distributes damage throughout the FE domain, with fracture mechanisms represented by material stiffness degradation controlled by damage variables (based on equivalent strains specifically defined for each failure mode). Mesh dependency issues are addressed by scaling fracture energy using a characteristic element length, and failure initiation and modes are determined using the 3D Hashin failure criterion.Accurately describing lamina response in fiber direction under compression requires linear-brittle softening with a stress plateau. The study showed that a model considering 30 % of residual stress accurately predicts maximum stress regardless of mesh refinement, demonstrating results’ minor dependence from the selected element size.The model accuracy has been confirmed by comparing the obtained results against experimental and benchmark data from the literature. The size effect study demonstrated a decrease in maximum stress of the open-hole laminates in compression with increasing specimen in-plane size. This trend is consistent with experimental and reference numerical observations, confirming the model accuracy and applicability even for relatively coarse meshes. Therefore, computational efficiency is improved, with preserved accuracy of conventional solid finite element models.

Simplified soil–structure interaction modeling techniques for the dynamic assessment of end shield bridges

In this paper, the dynamic behavior of four railway bridges with integrated retaining walls, considering the effect of soil–structure interaction (SSI), is investigated both numerically and experimentally. Among these bridges, two are single-span, and the remaining two are three-span. Each bridge is equipped with numerous accelerometers and is excited by a hydraulic actuator across various frequencies. Full 3D solid Finite Element (FE) models incorporating the railway bridges and surrounding soils are developed and calibrated using the Frequency Response Functions (FRFs) from each accelerometer. Furthermore, simplified 3D solid and 2D beam models are created for each railway bridge, incorporating springs and dashpots to account for the effect of surrounding soils. The values for these springs and dashpots are obtained from simple equations, except for the impact of the backfill soil in the simplified 2D beam models, which are derived from the impedance functions of the soil medium. The performance of these simplified models is then compared to the calibrated 3D models in terms of modal properties of the first bending mode and the maximum acceleration response during high-speed train passages. The results indicate that the simplified models closely align with the calibrated models in terms of modal properties and high-speed train passage response and can be used as simple and efficient alternatives for practical usage in bridge design.

A layered solid finite element formulation with interlaminar enhanced displacements for the modeling of laminated composite structures

A layered solid finite element formulation with interlaminar enhanced displacements for the modeling of laminated composite structures

The efficiency of ring stiffener shape on the deformation of cylindrical shell structures – numerical analysis with solid finite element

The efficiency of ring stiffener shape on the deformation of cylindrical shell structures – numerical analysis with solid finite element

A Component Method for Full-Range Behaviour of Embedded Steel Column Bases

This paper introduces a component model for analysing embedded column bases to predict rotational stiffness, moment resistance, and the full-range moment–rotation response. The key components identified include the embedded column, concrete in compression on the column side, concrete in compression beneath the base plate, concrete in punching shear above the base plate, and anchor bolts. The embedded column is modelled as a Timoshenko beam, considering both shear and flexural deformations, while other components are represented by springs. Methods are provided for determining their uniaxial constitutive behaviour. A simplified iterative solution method is proposed, where the embedded column is further simplified into three rigid segments to specifically address shear and bending deformations. A corresponding simplified finite element model is developed for accurate numerical solutions. The validity of the component model is confirmed through comparisons with the results of existing tests and refined solid finite element analysis for H-steel column bases. The simplified iterative solution method effectively predicts strength but underestimates the stiffness of deeply embedded column bases. This is due to the trilinear deformation pattern simplification, which concentrates flexural deformation at the upper bearing stress resultant force point, leading to an overestimation of steel column rotation on the foundation surface.

Modal analysis of KRK Bridge by using ansys workbench

The modal analysis of KRK bridge is presented in this paper. The solid model and finite element model of KRK bridge are established by ANSYS WORKBENCH 2023 R2. The model is a whole, not made up of multiple parts. Due to the limited finite element number of WORKBENCH, there may be some deviation between the model studied in this paper and the reality. The mass of the model used in this paper is consistent with reality. The modal analysis is carried out under the boundary condition that the bottom of the bridge column is fixed and the two ends are not fixed. The model does not shift in any direction. The aim is to find six modes that have their own natural frequencies and modal modes. The natural frequency of the model is obtained, and the resonance and collapse of the model are avoided during use.

Contact interface damping effect on internal friction and rotordynamic instability

Rotating machinery shafting is typically comprised of multiple components that are assembled to ensure reliable operation, proper alignment minimal vibration. However, conventional rotordynamics approximates the shafting as a single, continuous member, neglecting contact interfaces between the components. The presence of an interface can induce microslip, which generates internal friction that may cause instability and machinery failure. A novel approach of modeling the interface viscous damping effect on rotordynamics is proposed by combining a GW (Greenwood and Williamson) contact model with the Yoshimura damping model. All structural components are modeled using 3D solid finite elements. Modal damping ratio is utilized to identify the instability onset speed (IOS). The results show that internal friction has a destabilizing effect on whirl motion above the first critical speed, but has a stabilizing effect on the motion below the first critical speed. The destabilizing effect can be reduced by increasing the bearing damping, however excessive bearing damping can drive the effective damping towards negative values. Increasing the number of interfaces reduces stability while increasing an interface preload prevents microslip, and increases stability. Lastly, smoother surfaces at the interfaces increase the IOS.

Spectral element-finite element modeling and dynamic analysis of a fluid-delivering cracked pipe subjected to both pulsation and base excitations

Previous studies on cracked pipes have predominantly focused on single excitation, but in practical engineering, pipe systems often experience a combined effect of fluid pulsation and base excitations, which can potentially trigger more complex dynamic behaviors. Moreover, the solid finite element (FE) models are generally adopted to simulate the breathing effect and stress singularity, but the solution efficiency is unacceptable. Therefore, this study presents a spectral element-finite element (SE-FE) method to construct the dynamic models of the fluid-delivering cracked pipes (FDCPs), which combines the efficiency of spectral element (SE) with the adaptability of FE. Furthermore, a fluid pulsation model is constructed using measured data. Specifically, dynamic models of intact and cracked pipe segments are constructed using SE and FE, respectively, and interface coupling is achieved by the penalty function method. Subsequently, an experimental system for fluid pulsation excitation is established, and then a fluid pulsation model is constructed. Finally, the dynamic behaviors of a FDCP under compound excitation are analyzed. The results show that the fluid pulsation in the FDCP is higher than that in the intact pipe due to the breathing effect. Moreover, the beat vibration will be triggered when the pulsation frequency approaches the base excitation frequency. This study can provide a better understanding for the dynamic behaviors of FDCP, thereby providing a reference for crack damage detection.

Rainbow trapping of out-of-plane mechanical waves in spatially variant beam lattices

We numerically and experimentally investigate the propagation of mechanical waves in two-dimensional periodic and spatially graded elastic beam lattices. Experiments on metallic lattices admit the characterization of the linear elastic wave dispersion over a wide range of frequencies, resulting in complete, experimentally-constructed dispersion surfaces in excellent agreement with predictions obtained from finite element-based Bloch wave analysis. While Timoshenko beam theory is shown to be sufficiently accurate for predicting the lowest modes, experiments prove that solid finite elements are required to capture the dispersion relations at higher frequencies as well as when mode coupling occurs. Based on an improved numerical procedure, group velocity maps further highlight the directionality of wave dispersion and allow for the simple identification of bandgaps. In addition to classically studied periodic trusses, we extend the framework to spatially graded structures and demonstrate acoustic rainbow trapping in beam lattices undergoing out-of-plane vibrations. Our experiments confirm broadband vibration attenuation of the typical meta-wedge type previously observed only in optics and few mechanical studies. Results further show convincing agreement between Bloch theory-based predictions, finite element simulations, and experimental measurements. Such spatially-variant architected lattices show great promise for steering the motion of elastic waves in applications from wave guiding and wave shielding to energy harvesting.

Numerical design calculation of bolted lap joints at elevated temperatures

This paper presents experimental and numerical studies to investigate the mechanical behaviour of bolted lap joints at elevated temperatures. The load-deformation curves, failure modes, and resistance values of the specimens were obtained from experimental studies. A solid finite element model generated using ABAQUS software was validated and verified by the experimental results and analytical models to investigate the different failure modes and predict the fire resistance of bolted lap joints at elevated temperatures, respectively. Then, the component-based finite element model (CBFEM) was prepared to analyse the fire behaviour of bolted lap joints as an alternative to design specifications for structural fire engineers. The CBFEM was verified by the validated solid model and analytical models in terms of load-deformation curve, fire resistance, and failure modes. Parametric studies were performed to investigate the influence of several parameters on the fire response of bolted lap joints. The study shows that the CBFEM may be used to design bolted lap joints at elevated temperatures and the 5 % limit strain for plates proposed in EN 1993-1-5 can be applicable for predicting the fire resistance of steel connections.

Features of bond-slip relations: 3D finite element analysis based on tests of short RC ties

The interaction between concrete and reinforcement is highly complex and is of fundamental importance for predicting the behaviour of reinforced concrete (RC) structures. While the interaction of the two materials is often characterised by a bond – slip law, there are currently no such laws capable of accurately predicting serviceability characteristics, such as deflection, crack spacing, and width. This paper examines the effect of various parameters on the shape of bond – slip relation at loads before yielding of reinforcement. The study is based on a mesoscopic numerical analysis, utilizing the finite element method along with a friction cohesive zone model to explore the bond-slip phenomena in short RC ties. The numerical model is combined with an experimental campaign involving six short concrete ties reinforced with 20 mm bars. Steel strain profiles were monitored within the reinforcement using electrical strain gauges. These experimental steel strain profiles served as a robust tool for controlling and calibrating numerical models. The numerical models employed solid finite elements to simulate both reinforcement and concrete, with special zero-thickness plain elements applied to simulate the friction cohesive contact at the steel-concrete interface. Bond-slip relations were obtained from the numerically modelled reinforcement strain profiles. It was shown that concrete strains can be ignored when assessing slip. The effect of the embedded length of reinforcement under the fully confined conditions was demonstrated to have little effect on bond-slip relations. It was also shown that the maximum bond stress is strongly related to the thickness of the concrete cover. The effect of load intensity on the bond – slip behaviour was investigated. It was shown that under full confinement, the initial bond stiffness was not affected by load intensity. However, degradation of bond stiffness with increasing load due to internal cracking took place in the RC ties with a small cover/diameter ratio.

FSI Modeling and simulation analysis of superimposed valves in flow state of hydraulic shock absorbers*

Abstract This study, through rigorous bench testing, has identified the pivotal parameters influencing the oil flow state within the shock absorber. Based on the Reynolds number parameter model, a reduced parameter model was established, incorporating the number of holes in the throttle valve, their diameters, and the diameters of the piston and piston rod as fundamental parameters. To ensure the model’s precision, this study developed high-accuracy solid and fluid finite element models, defined specific time steps for both laminar and turbulent flows along with their respective numerical methods, and executed a detailed Fluid-Structure Interaction (FSI) finite element simulation analysis. The findings indicate that fluid-structure interaction simulation accurately captures the shock absorber oil’s flow states across laminar, transitional, and turbulent phases, identifying the maximum Reynolds number position, with the simulation’s velocity-specific results aligning closely with the parameter model, showing a maximum deviation of 22%, a minimum of 2%, and an overall average error of 9.1%.

A nonlinear analytical method for pipeline strain under soil thaw subsidence load in permafrost region

In frozen terrain, the transportation of heated oil triggers thermal soil thaw and collapse, leading to pipeline distortion and breakdown. During substantial ground settlement in such terrains, current strain prediction techniques for pipelines fall short, neglecting significant pipeline bending, non-linear material behaviors, or detailed pipeline-permafrost interplay. To address this, a model focusing on pipeline-soil dynamics is devised, incorporating material non-linearity and pronounced pipeline distortion. This model derives analytical strain solutions for pipelines by aggregating incremental distortions of pipeline components via a strain iteration technique. Concurrently, a three-dimensional solid finite element model is crafted, assessing pipeline strains across varying subsidence zone dimensions, factoring in the complicated permafrost environment. The model's efficiency is affirmed by its less than 3% discrepancy from finite element method results, showcasing its enhanced accuracy and dependability in predicting pipeline strains under extensive soil settlement scenarios.

A robust finite strain isogeometric solid-beam element

In this work, an efficient and robust isogeometric three-dimensional solid-beam finite element is developed for large deformations and finite rotations with merely displacements as degrees of freedom. The finite strain theory and hyperelastic constitutive models are considered and B-Spline and NURBS are employed for the finite element discretization. Similar to finite elements based on Lagrange polynomials, also NURBS-based formulations are affected by the non-physical phenomena of locking, which constrains the field variables and negatively impacts the solution accuracy and deteriorates convergence behavior. To avoid this problem within the context of a solid-beam formulation, the Assumed Natural Strain (ANS) method is applied to alleviate membrane and transversal shear locking and the Enhanced Assumed Strain (EAS) method against Poisson thickness locking. Furthermore, the Mixed Integration Point (MIP) method is used to make the formulation more efficient and robust. The proposed novel isogeometric solid-beam element is tested on several single-patch and multi-patch benchmark problems, and it is validated against classical solid finite elements and first-order Lagrange solid-beam element. The results show that the proposed formulation can alleviate the locking effects and significantly improve the performance of the isogeometric solid-beam element. With the developed element, efficient and accurate predictions of mechanical properties of lattice-based structured materials can be achieved. The proposed solid-beam element inherits both the merits of solid elements e.g. flexible boundary conditions and of the beam elements i.e. higher computational efficiency.

Development and validation of an innovative uplift-restraining friction pendulum bearing

This paper presented an innovative uplift-restraining friction pendulum bearing (UR-FPB) to address the limitations of traditional FPBs, which are unable to withstand vertical tensile loads. The UR-FPB is composed of a friction set acting as the horizontal sliding module and an anti-uplift set acting as the vertical uplift-restraining module. Based on this configuration, the study derived the theoretical force-displacement relationships of the UR-FPB, established three solid finite element models in Abaqus, and proposed a hybrid modeling method based on OpenSees. Then the practical effectiveness of this bearing and the credibility of the theoretical analysis models and hybrid numerical models were validated. The theoretical and numerical results demonstrate that the frictional behavior of the UR-FPB in horizontal sliding is characterized by multi-stage hysteresis relationships. The numerical results on the sliding characteristics and the corresponding hysteresis relationships are highly consistent with the theoretical results. The UR-FPB has a large horizontal sliding capacity similar to that of traditional FPBs, while the design of the anti-uplift configuration does not reduce or limit this sliding capacity. Significantly, the study investigated the uplift-restraining behavior of the UR-FPB and its effect on the horizontal responses. The analysis results suggest that the UR-FPB has a good uplift-prevention capacity and this paper recommends that the design value of tensile capacity should not exceed the yield force in tension. Therefore, this novel uplift-restraining friction bearing has an expected effectiveness, which can simultaneously resist vertical tensile loads and function as a horizontal seismic isolator. The proposed hybrid modeling method may provide a useful reference to model the behavior of the UR-FPB in software used for response-history analysis.

The influence of shear surface quality on the mechanical properties of long-span prestressed continuous rigid-frame bridge

PurposeThe long-span continuous rigid-frame bridges are commonly constructed by the section-by-section symmetrical balance suspension casting method. The deflection of these bridges is increasing over time. Wet joints are a typical construction feature of continuous rigid-frame bridges and will affect their integrity. To investigate the sensitivity of shear surface quality on the mechanical properties of long-span prestressed continuous rigid-frame bridges, a large serviced bridge is selected for analysis.Design/methodology/approachIts shear surface is examined and classified using the damage measuring method, and four levels are determined statistically based on the core sample integrity, cracking length and cracking depth. Based on the shear-friction theory of the shear surface, a 3D solid element-based finite element model of the selected bridge is established, taking into account factors such as damage location, damage number and damage of the shear surface. The simulated results on the stress distribution of the local segment, the shear surface opening and the beam deflection are extracted and analyzed.FindingsThe findings indicate that the main factors affecting the ultimate shear stress and shear strength of the shear surface are size, shear reinforcements, normal stress and friction performance of the shear surface. The connection strength of a single or a few shear surfaces decreases but with little effect on the local stress. Cracking and opening mainly occur at the 1/4 span. Compared with the rigid “Tie” connection, the mid-span deflection of the main span increases by 25.03% and the relative deflection of the section near the shear surface increases by 99.89%. However, when there are penetrating cracks and openings in the shear surface at the 1/2 span, compared with the 1/4 span position, the mid-span deflection of the main span and the relative deflection of the cross-section increase by 4.50%. The deflection of the main span increases with the failure of the shear surface.Originality/valueThese conclusions can guide the analysis of deflection development in long-span prestressed continuous rigid-frame bridges.

Fluid-Structure Interactions Response of a Composite Hydrofoil Modelled With 1D Beam Finite Elements

_ In this paper, the hydroelastic response of a NACA0015 composite hydrofoil is studied experimentally and numerically. The foil is made of composite materials with fibers not aligned with the span of the foil, which results in the occurence of a bend-twist coupling in the material. Computations are performed using a partitioned approach. The flow problem is solved using a boundary element method. The structural response of the foil is modelled with two different finite element models. In the first one, the foil is modelled with 2D shell and 3D solid finite elements and in the second model, the foil is modelled with 1D beam finite elements. The experiments are conducted in an open circulation water channel. Hydrodynamic forces and structural displacements are measured for several angles of attack, free stream velocities and submergence depth. This paper shows that the mechanical behaviour of a composite hydrofoil submitted to hydrodynamic loads can be modelled with 1D beam finite elements. This model gives results very similar to a finite element analysis realized with 2D shell and 3D solid finite elements, which are commonly used to model composite structures. The present work also shows that the experimental results can be well predicted by numerical simulations, but it requires a precise modeling of the bend-twist coupling in the materials constituting the foil. Keywords Hydrofoil; Equivalent Beam; Fluid-Structure Interactions; Composite; Bend-Twist Coupling