Nonlinear Finite Element Model Research Articles

Numerical analysis for assessing the effects of crown pillar thickness on ore dilution around the sub-level open stopes

Sub-level open stopes with delayed backfill are being used to extract massive, tabular, and steeply dipping ore bodies for increased productivity. Crown pillars in the orebody divide mining zones to increase productivity by enabling simultaneous production in two or more zones. Despite their effectiveness, these mining techniques may be accompanied by substantial amounts of overbreak, resulting in considerable ore dilution. This study investigates the effects of crown pillar thickness under various geo-mining conditions on hanging wall overbreak. Under plane strain conditions, 240 non-linear finite element models with the Mohr-Coulomb elastoplastic failure criteria were used for numerical analysis. The outcomes are analyzed in terms of Equivalent Linear Relaxation Depth (ELRD) and Equivalent Linear Overbreak Sloughage (ELOS). The results show that by increasing the crown pillar thickness from 5 m to 8 m, the ELRD and ELOS are reduced by roughly 45 % and 74 %, respectively, for a given material property.

Evaluation of Spiral Pneumatic Rubber Actuator Using Finite Element Analysis for Radial Transportation

Emerging actuators with various soft materials and a traveling wave motion are frequently discussed. Various configurations have been proposed and their resulting performances investigated, but it remains challenging to realize large strokes. This study presents an experimentally validated nonlinear finite element model to predict the deformation produced by a spiral pneumatic rubber actuator to generate a traveling wave motion. The actuator consists of a membrane mounted on a rubber substrate with three air chambers in a spiral configuration. The sequential deformations of the successive chambers interact with each other and produce radial traveling waves on the membrane surface, driving the objects placed on the actuator. Finite element analysis with ANSYS computer software was used to analyze the elastic movement by considering the influence of different initial structural types. The simulation results indicated an optimal structure with specific ratios. A reasonable correlation was obtained during experimental validation; the predicted displacement values were approximately 17% smaller than the experimental values. Finally, the transportation performance of the prototype was tested, and a velocity of 2.28 mm/s in the desired direction was achieved. We expect that our demonstration will expand the range of applications of the spiral pneumatic rubber actuator to include conveying or worm-like robots.

Curly beam with programmable bistability

Bistable beams with prebuckled sinusoidal shape are prominently constructed into mechanical metamaterial unit cells with bi- and multi-stability. While the effects of boundary conditions and thickness on their bistability were more studied, few investigations have been focused on the effect of the beam shape. We systematically created new geometries by adding a second sinusoidal term varying in amplitudes and wavelengths, onto the prebuckled bistable beam shape. Nonlinear large deformation finite element modeling showed effective tuning of the forward and backward forces, snapping energy, and the maximum strain, by the wavelength and amplitude. Decent improvements in the overall stability of their second stable state were observed. The enhancement of the relatively weak snap-through behavior of the single beams was demonstrated by pairing a large variety of curly beams into double-beam configurations. Experimental observations on the 3D printed polylactic acid unit cells strongly supported the simulation results, and demonstrated the possibility of building multistable structures. The design of bistable beams with consistent thickness and comparable overall shapes, yet differing mechanical behavior, has opened up new avenues for the development of bi- and multistable structures in programmable mechanical metamaterials, particularly with materials fabricated at the resolution limit of the respective techniques.

Numerical analysis on axial crushing damage of aluminum/CFRP hybrid thin-walled tubes

Metal/CFRP hybrid structures have been increasingly applied in the automotive industry due to their favorable weight-saving and crashworthiness. In this article, a nonlinear finite element (FE) model is established to study the axial crushing behavior of aluminum/CFRP thin-walled tube structures. A progressive damage constitutive model is employed to capture the intra-laminar response of composites; Johnson-Cook model is used to describe the crushing process of aluminum layers and a bilinear cohesive zone model is applied for modeling the inter-layer delamination during the collapse process. A user material subroutine VUMAT involving these damage models is coded and executed to attain the numerical solution based on ABAQUS/Explicit solver. The axial crushing processes of thin-walled tubes with different configurations are simulated, and the corresponding damage characteristics are analyzed thoroughly. The influence of aluminum layer arrangement and cross-sectional shape on the crashworthiness and energy absorption of thin-walled tubes is discussed, which provides a design basis for the application of energy absorption elements.

Deployment analysis of composite thin-walled lenticular tubes with effect of storage time and temperature

Composite Thin-walled Lenticular Tube (CTLT) is increasingly utilized in small satellites missions as a lightweight, foldable, and rollable structural material that facilitates the construction of large deployable systems. The CTLT is initially flattened and coiled around a central hub for storage before launch, during which elastic energy is stored as deformation energy, allowing it to be self-deployed on demand for use in orbit. This work presents a comprehensive investigation into the coiling, storage and deployment behaviors of CTLT that wraps around a central hub. A nonlinear explicit dynamic finite element model was developed with both deformable CTLT and rigid-bodies mechanisms including the central hub and guide rollers, as well as the complex interactions among them. The coiling mechanics characteristics such as stored strain energy and rotational moment were presented and validated against experimental data in the literature. Then, the dynamic deployment behaviors were analyzed in terms of two different deployment methods, namely, controlled deployment and free deployment. The effect of material property change during storage was also discussed through numerical experiments.

Calculation of the load-bearing capacity of the bent plates taking into account the diagrams of concrete deformation

Objective. The influence of the nature of the descending branch of concrete compression and stretching diagrams on the ultimate load-bearing capacity of bent cross-section reinforced concrete structures under various loading conditions close to destruction according to the nonlinear finite element model is investigated.Method. The solution is performed by the finite element method in a physically nonlinear formulation using N.I.Karpenko's deformation theory. Deformation diagrams are used with different steepness of the descending branch. Calculations are performed by a step-by-step iterative method of successive loads on a layered model.Result. The results of numerical calculation of slab reinforced concrete elements under various conditions of physical nonlinearity of concrete are presented.Conclusion. The insignificant influence of the steepness of the descending branch on the load-bearing capacity of plate bendable structures has been found and the use of simplified diagram dependencies is fully justified for numerical calculations using a nonlinear model.

Numerical Prediction of Bond-Slip Behavior in Simple Pull-Out Concrete Specimens

In this study the simple pullout concrete cylinder specimen reinforced by a single steel bar was analyzed for bond-slip behavior. Three-dimension nonlinear finite element model using ANSYS program was employed to study the behavior of bond between concrete and plain steel reinforcement. The ANSYS model includes eight-noded isoperimetric brick element (SOLID65) to model the concrete cylinder while the steel reinforcing bar was modeled as a truss member (LINK8). Interface element (CONTAC52) was used in this analysis to model the bond between concrete and steel bar. Material nonlinearity due to cracking and/or crushing of concrete, and yielding of the steel reinforcing bar were taken into consideration during the analysis. The accuracy of this model is investigated by comparing the finite element numerical behavior with that predicted from experimental results of three pulloutspecimens. Good agreement between the finite element solution and experimental results was obtained.

Experimental & numerical investigation of all-steel assembled cruciform buckling-restrained braces

In this paper, an all-steel assembled cruciform buckling-restrained brace is proposed for the first time. It is mainly composed of 26 main components, including one external restraint steel tube, eight internal restraint steel tubes, one inner core, and 16 high-strength bolts for connection. Four BRB specimens were designed in the test stage, and all specimens were subjected to displacement-controlled axial cyclic load. As a result, hysteretic performance, energy dissipation, and ductility were summarized and analyzed for each specimen. In addition, 50 nonlinear finite element models are established using the large-scale commercial finite element software ABAQUS for numerical simulation analysis. The results of the experiment and numerical simulation show that: (1) A new type of all-steel assembled cruciform buckling-restrained braces (BRB) with stable hysteretic performance has been successfully designed, and a corresponding simplified but refined three-dimensional nonlinear finite element model that can be in good agreement with the test results has been established. (2) The traditional concept of restraining ratio has been disassembled into the concept of internal and external restraining ratios in this BRB configuration. (3) The concept of restraining length ratio of this BRB configuration and related design standards are proposed.

Flexural Behavior of Cold-Formed Steel Composite Floor Infilled with Desert Sand Foamed Concrete

Desert sand foamed concrete (DSFC), which offers advantages, such as fire resistance, sound insulation, construction convenience, and environmental benefits, has not been used in cold-formed steel (CFS) composite floors. In this study, four full-scale specimens were designed and tested under four-point bending to investigate the effect of foamed concrete filling and holes. The load–deflection curves and strain distribution at mid-span were measured and analyzed. The experimental results indicated that the failure modes of the CFS composite floors were local buckling at the top flange for specimens without holes and tensile failure at the bottom flange for specimens with holes, respectively, which differed from the web crippling observed in non-composite floors. Moreover, due to the presence of foamed concrete, the flexural stiffness was significantly improved by 117.6% and 73.6% for the specimens without holes and with holes, respectively, while ultimate capacity increased by 224.9% and 121.8%, respectively. Through the nonlinear finite element models validated against experimental results, it was found that the flexural behavior was improved with the increase in CFS thickness and foamed concrete strength. The impact of the holes was not obvious for specimens infilled with holes.

Nonlinear Finite Element Model for Bending Analysis of Functionally-Graded Porous Circular/Annular Micro-Plates under Thermomechanical Loads Using Quasi-3D Reddy Third-Order Plate Theory.

A nonlinear finite element model for axisymmetric bending of micro circular/annular plates under thermal and mechanical loading was developed using quasi-3D Reddy third-order shear deformation theory. The developed finite element model accounts for a variation of material constituents utilizing a power-law distribution of a two-constituent material, three different porosity distributions through plate thickness, and geometrical nonlinearity. The modified couple stress theory was utilized to account for the strain gradient effects using a single material length scale parameter. Three different types of porosity distributions that have the same overall volume fraction but different enhanced areas were considered as a form of cosine functions. The effects of the material and porosity distribution, microstructure-dependency, the geometric nonlinearity, and various boundary conditions on the bending response of functionally-graded porous axisymmetric microplates under thermomechanical loads were studied using the developed nonlinear finite element model.

Numerical and Experimental Behavior Analysis of Slabs Strengthened Using Steel Plates and Slurry-Infiltrated Mat Concrete (SIMCON) Laminates

This study has two main aims; firstly, investigating the behavior of slabs that are strengthened with different types of reinforcements and with Slurry-Infiltrated Mat Concrete (SIMCON) laminates, having different dimensions and thicknesses and subjected to static and dynamic (impact) loads. Secondly, the development of a non-linear finite element (FE) model to simulate the behavior of the tested slabs utilizing the ABAQUS/Standard package. The modeling of the NSC slabs strengthened with either SIMCON or steel plates involves using three-dimensional solid elements that are partially integrated with the modeling of concretes using the 8-node brick element (C3D8R). The results of the experimental and numerical investigations are compared to examine whether the slab modeling is sufficient. The comparison includes the element type, material characteristics, real constants, and convergence study. The predicted ultimate load-carrying capacity versus vertical deformation response is compared with the lab results that correspond with it, as obtained via the FE analysis of all tested slabs. In addition, the results of the FE analysis of slab specimens that are strengthened with steel plates were compared to the results of the ones strengthened using SIMCON laminates. The obtained results have led to a number of significant observations. Considering the punching shear strength, it was found that using SIMCON strengthening in different dimensions increased the slab’s punching shear capacity and outperformed steel-strengthened slabs. As for the plate stiffness, SIMCON-strengthened slabs presented higher stiffness rates than steel-strengthened slabs, to the extent that even 20 mm SIMCON strengthening outperformed the steel plate-strengthened slabs of any thickness or dimensions. The axial load-displacement relationships indicate that all the numerical models show a stiffer behavior when compared with the experimental axial load-displacement relationships. The slab thickness of SIMCON significantly affects the load-carrying capacity, and it increases with the increase in thickness. Likewise, using strengthening from steel plates gives a higher load-carrying capacity. Finally, since the results of the yield line analyses for these slabs are found to match the experimental results closely, this method is considered to be suitable for practical use in determining the strength of plated slabs. Therefore, the conclusion is drawn that the proposed FE model can be sufficiently used in evaluating the dynamic responses of slabs strengthened with SIMCON or steel plates and subjected to cyclic and impact load.

Equivalent flat-web thicknesses and modified flange-based moment resistance for corrugated-web steel I-girders

This study proposed analytical formulations for equivalent flat-web thicknesses at horizontal and inclined fold sections and modified flange-based moment resistance for corrugated-web girders (CWGs), accounting for the accordion effect due to corrugations. The finite element (FE) analysis approach was used for examining the nonlinear flexural behavior of CWGs. Numerical models were first validated against flexural tests from two documented CWG studies. For additional verification, nonlinear theoretical analysis of flat-web girders was compared and verified against detailed FE-based analysis results. A detailed parametric study was performed to examine the effect of corrugated-web trapezoidal profiles and girder geometry on the moment resistance of CWGs using the validated nonlinear FE modeling. Then, the parametric study results were used in the theoretical nonlinear moment-curvature analysis on equivalent flat-web girders to derive the proposed formulations for flat-web thicknesses at horizontal and inclined fold sections of a CWG. Alternatively, a modified flange-based moment resistance formulation was proposed for CWGs by accounting for the accordion effect of their trapezoidal corrugated webs. Both the proposed formulations simplified the accordion effect analysis in CWGs and can result in potentially economical girder designs and further development of design specifications for CWGs.

Experimental Research on the Mechanical Properties of MURSP-Type Steel-Concrete Composite Beams in Negative-Moment Region

To verify the effectiveness of uplift-restricted and slip-permitted (URSP) connectors in alleviating crack formation in the negative-moment region of steel-concrete composite beams (SCCBs) and improve the engineering adaptability of URSP connectors, this paper proposes a modified uplift-restricted and slip-permitted (MURSP) connector. Static load tests and theoretical analysis were conducted on two overhanging beams with MURSP connectors and ordinary studs to analyze the influence of different stud forms on the deflection, crack, and slip of SCCBs in the negative-moment region. Finally, a nonlinear finite element modeling method for MURSP-type steel-concrete composite beams was developed, and a finite element model was established. The results showed that the use of MURSP connectors could effectively alleviate the concrete cracking problem in the negative-moment zone of SCCBs. Compared with the common stud SCCB, the crack load of the MURSP-type SCCB was higher, the maximum crack width was lower, and the crack distribution was more uniform; however, the overall flexural stiffness of the overhanging beam with MURSP connectors was reduced by 3.08%. The interface slip of the overhanging beam with the MURSP connectors increased suddenly in the initial stage of loading, whereas the increase was more gradual in the later stage. The SCCB model established in this study was in good agreement with the results of experimental beams. The finite element analysis results showed that the ordinary stud and MURSP connector exhibited different stress and deformation states in the negative-moment region of SCCBs, and the deformation states changed from bending type to shear type.

Static Stiffness Properties of High Load Capacity Non-Pneumatic Tires with Different Tread Structures

A high load capacity non-pneumatic tire (HC tire) was designed and manufactured to solve the problems of air leakage, puncture, blowout, shoulder void, and delamination, which occur in traditional high load capacity tires, as well as significantly increase the unit load of tires. Experiments and numerical simulations were conducted to investigate the static stiffness properties of the HC tire. Additionally, the manufacturing process of the tire was highlighted. The tire mainly comprised polyurethane and silicon manganese steel, and a ‘π’-shaped support substructure was adopted. The tread structure was made up of a built-in spiral steel ring and a non-steel ring. The uniaxial tensile mechanical properties of the used metal and elastomer materials were tested, and the linear elastic constitutive model and Marlow constitutive model, respectively, were used to describe their mechanical characteristics. The stiffness properties of the HC tire, including torsional, longitudinal, vertical, and lateral stiffnesses, were evaluated using a tire comprehensive stiffness tester. Nonlinear finite element models of the HC tire were established, and their accuracies were verified through vertical stiffness tests. The stiffness properties of the HC tire in other directions were simulated as well. An in-depth comparative analysis of the simulation and experimental data was performed. The results demonstrated that the unit load of the unreinforced HC tire was 2.972 times and 1.615 times higher than that of the solid tire and pneumatic tire, respectively. The spiral steel ring embedded in the tread increased the vertical and longitudinal stiffness but reduced the torsional stiffness of the HC tire, thus reversing the variation trend of the lateral stiffness at the 0° and 5° test points. The findings can serve as a reference for theoretical research on, and the structural optimization of, non-pneumatic tires with a high load capacity.

Behaviour of back-to-back built-up cold-formed steel equal angles with complex edge stiffeners under axial compression

The application of built-up cold-formed steel (CFS) structures becoming popular in civil engineering fields such as trusses, bridges, transmission towers and railway coaches. This work presents the numerical analysis of axially compressed back-to-back built-up CFS equal angle sections. A nonlinear finite element (FE) model was developed that considered geometric imperfections, material nonlinearity, and intermediate fastener. The published experimental test data were used to compare the FE model, and the results shown good agreement. The effect of the slenderness ratio and edge stiffening direction on the axial strength of back-to-back built-up CFS equal angle sections is investigated by using parametric study.

Direct strength prediction of cold-formed steel fixed-ended singly-symmetric columns buckling in flexural–torsional modes

The work reported in this paper is a sequel of previous numerical investigations carried out by the authors on the post-buckling behaviour, strength and Direct Strength Method (DSM) design of cold-formed steel (CFS) fixed-ended plain and lipped channel columns (both singly-symmetric with respect to the major-axis) buckling in flexural–torsional modes and experiencing global-global interaction – a coupling phenomenon involving major-axis flexural–torsional (FMT) and minor-axis flexural (Fm) buckling that was first unveiled in those studies. In the specific context of plain and lipped channel columns, a DSM-based design approach for columns buckling in FMT modes and failing in either pure FMT or FMT-Fm interactive modes was developed and shown to provide accurate, mostly safe and reliable predictions of the experimental (only a few) and numerical failure loads available. The success of this research effort encouraged the authors to extend the scope of the investigation to fixed-ended columns with other singly-symmetric cross-section shapes, namely return-lip, web-stiffened and web/flange-stiffened lipped channels, hat-sections and rack-sections (deemed representative of any arbitrary singly-symmetric cross-section). The results attained during this investigation are presented and discussed in detail – they concern the post-buckling behaviour, strength and DSM-based design of the columns analysed, including fairly extensive failure load sets (Ansys non-linear shell finite element models are used to obtain them). The main output of this work is a DSM-based design approach for arbitrary CFS fixed-ended singly-symmetric columns exhibiting pure FMT or FMT-Fm interactive failures.

Behavior of hollow self-compacted concrete beams reinforced with aluminum sections

This paper presents a study on improving the flexural performance of self-compacting hollow concrete beams with embedded aluminum sections, both experimentally and numerically. The experimental program involved testing three specimens to illustrate the impact of the bare and aluminum-reinforced voids on the mechanical properties of the hollow beams relative to the solid reference beam. A three-dimensional (3D) non-linear finite element model (FEM) was initially developed using ABAQUS software and validated against experimental results. The validated model examined the effects of void area (16–49% of the beam cross-section), void configuration (square or circular), longitudinal tensile reinforcement ratio (0.41–1.19%), and shear reinforcement ratio (0–0.56%) on the failure patterns and load–displacement relationships of hollow reinforced concrete (RC) beams with or without reinforced internal aluminum sections. Results showed that the embedded aluminum reinforcement promoted a more uniform distribution of flexural cracks along the effective length of the hollow RC beams and delayed the formation of shear cracks compared to the bare specimens. Furthermore, the embedded aluminum reinforcement effectively restored the ultimate capacity of the hollow beams with a void area ranging from 16 to 36% of the beam cross-section. Despite having the same area, the ultimate load-carrying capacity of both bare and reinforced beams featuring circular voids was higher than those with square voids.

Experimental and numerical study of the flexural response of Ultra High Performance Concrete (UHPC) beams reinforced with GFRP

This paper investigates the flexural behavior of Ultra High Performance Concrete (UHPC) beams reinforced with glass fiber-reinforced polymer (GFRP) bars. A series of four-point loadings tests were conducted on full-scale beams reinforced with Glass FRP (GFRP) bars. The GFRP-UHPC beams were designed as either under-reinforced or over-reinforced to examine the differences in their failure modes. Steel reinforced beams, serving as reference specimens, were also cast and tested. All the beams measured 185 mm in width, 250 mm in depth, and 2200 mm in length. The influence of reinforcement ratio, number of bars, and surface texture of GFRP bars on the flexural behavior was studied. The test results showed that changing the mode of failure from GFRP rupture to concrete crushing improved the ductility flexural capacity of the UHPC beams. It was also shown that the bending stiffnesses, flexural capacities, and strain responses of the UHPC beams were enhanced upon increasing the reinforcement ratio. The experimental data was compared with the ACI 440 and CAN/CSA S806 code provisions. It was found that the recent ACI440 ultimate moment equation provided acceptable results for the under-reinforced beams but was slightly unconservative for the over-reinforced beams. A nonlinear finite element (FE) model was also developed considering both material and geometric nonlinearities using ABAQUS. The developed FE model verified well with the experimental results and can be utilized to simulate different loading scenarios and sections of GFRP UHPC beams.

Test and direct strength method on slotted perforated cold-formed steel channels subjected to eccentric compression

This paper aims to investigate the buckling behaviors of cold-formed steel (CFS) channels with slotted web holes determined by the Steel Stud Manufacturers Association (SSMA) under eccentric compression, and propose the simplified direct strength method (DSM) formulas for engineering practicing. An experimental study on 20 specimens was conducted, including 18 slotted perforated specimens with nine eccentricities increasing from −20 mm to 20 mm and 2 unperforated specimens subjected to axial compression. Two kinds of nominal lip lengths for cross sections were selected as 15 mm and 20 mm. The experimental results indicated that the failure modes of slotted perforated specimens subjected to eccentric compression depended on the position of the eccentricity. Compared with the slotted perforated specimens subjected to pure axial compression, the ultimate loads of specimens subjected to positive eccentric compression decreased by 21.70 % on average, while they decreased by 16.38 % on average for those subjected to negative eccentric compression. Moreover, a nonlinear elasto-plastic finite element model (FEM) was developed and validated against the experimental results. Furthermore, combined with the experimental results, extensive FE parametric analyses were conducted to predict the eccentricity impact coefficient formulas. Finally, based on DSM of unperforated CFS members subjected to pure axial compression in AISI S100-16 and the eccentricity impact coefficient formulas, the suitable DSM design formulas for slotted perforated CFS channels determined by the SSMA under eccentric compression were proposed, without the need to calculate the elastic buckling critical stress for slotted perforated CFS channels.

Axial compressive strength of slender UHPFRC-filled steel tubes

Ultra-high performance fiber-reinforced concrete (UHPFRC)-filled steel tube (UHPFRC-FST) slender columns have not been studied to date, although ample research exists on this system as short columns. Furthermore, current code provisions (e.g. CAN/CSA S16) were developed for normal strength concrete and are thus potentially inadequate for UHPFRC-FSTs. In this study, a robust three-dimensional nonlinear finite element model was developed and validated using LS-DYNA software to simulate behaviour of slender UHPFRC-FSTs of circular cross-section under concentric axial compressive loads. An extensive parametric study was then performed, varying slenderness ratio (kL/r) based on column length (L) where r is the radius of gyration, diameter-to-thickness ratio (D/t) of the steel tube, effective length factor (k), and tube’s yield strength (Fy). The study showed that axial load-carrying capacity reduced by 78% when slenderness ratio increased from 12 to 157. The column transitions from material failure by diagonal shear plane in concrete, to global buckling at a slenderness ratio of about 80. Axial load-carrying capacity also reduces rapidly with D/t until a ratio of about 45 and then reduces at a much lower rate thereafter. CAN/CSA S16 code provisions grossly underestimate the load-carrying capacity of slender UHPFRC-FSTs by 13 to 46% as slenderness ratio increased from 12 to 157. The underestimation also increased dramatically with diameter-to-thickness ratio, from 8% atD/t = 10 to 40% atD/t = 80, and with effective length factor k, by 15% at k=0.5 to 48% at k=2. 0. A modification to CAN/CSA S16:19 equation is proposed based on multiple regression analysis of the results of the parametric study.