Nonlinear Finite Element Procedures Research Articles

Structural response of hybrid timber ‐ cold formed steel floors

AbstractThe paper examines the composite performance of hybrid steel‐timber lightweight floor assemblies incorporating cold‐formed steel (CFS) profiles and plywood (PW) flooring panels with varying degrees of shear connection achieved by means of self‐drilling screws. Material, push‐out, and three‐point short‐span floor tests with or without web openings were carried out. The results and observations from the tests provide a detailed insight into the inelastic properties and ultimate response of such floor systems. Push‐out tests indicate that denser connector arrangements increase connection stiffness, while push‐out and short beam tests suggest an optimum connector spacing equal to the beam depth for a balance between structural performance and constructability. The experimental observations indicate that the ultimate condition of the short composite beams was characterized by CFS web crippling under the load application point, followed by a pull‐through of the self‐drilling screws. Web openings reduced the strength of the floor elements compared to the members with full webs. Complementary numerical studies are undertaken using nonlinear finite element procedures which were validated against the beam tests, offering a detailed insight into the stress levels in the timber, steel, and connectors. Codified procedures for determining the capacity of composite CFS sections are compared with the test results, and guidance for the practical design and construction of such systems is given.

Inelastic cyclic response of RBS connections with jumbo sections

This paper examines the cyclic performance of reduced beam section (RBS) moment connections incorporating larger member sizes than those allowed in the current seismic provisions for prequalified steel connections, through experimentally validated three-dimensional nonlinear numerical assessments. Validations of the adopted nonlinear finite element procedures are carried out against experimental results from two test series, including four full-scale RBS connections comprising large structural members, outside the prequalification limits. After gaining confidence in the ability of the numerical models to predict closely the full inelastic response and failure modes, parametric investigations are undertaken. Particular attention is given to assessing the influence of the RBS-to-column capacity ratio as well as the RBS geometry and location on the overall response. The numerical results and test observations provide a detailed insight into the structural behavior, including strength, ductility, and failure modes of large RBS connections. It is shown that connections which consider sections beyond the code limits, by up to two times the weight or beam depth limits, developed a stable inelastic response characterized by beam flexural yielding and inelastic local buckling. However, connections with very large beam sections, up to three-times the typically prescribed limits, exhibited significant hardening resulting in severe demands at the welds, hence increasing susceptibility to weld fracture and propagation through the column. The findings from this study point to the need, in jumbo sections with thick flanges, for a deeper RBS cut than currently specified in design, to about 66% of the total beam width. This modification would be required to promote a response governed by extensive yielding at the RBS while reducing the excessive strain demands at the beam-to-column welds. Moreover, for connections incorporating relatively deep columns, it is shown that more stringent design requirements need to be followed, combined with appropriate bracing outside the RBS, to avoid out-of-plane rotation.

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This investigation examines the performance of hybrid reinforced concrete flat slabs, incorporating fully-integrated shear-heads at connections to steel columns, through a series of numerical evaluations and parametric studies. Validations of the adopted nonlinear finite element procedures, which employ concrete damage plasticity constitutive models, are carried out against experimental results on hybrid members. Complementary verifications on conventional reinforced concrete flat slabs are also undertaken to ensure the reliability of the selected ranges for key modelling parameters. Comparison of the numerical simulations against the test results shows close correlations in terms of ultimate strength, deformations and stress levels in the constituent elements of hybrid members. This is followed by a series of parametric assessments on key structural parameters for hybrid flat slabs with steel shear heads. The results of these investigations enable the identification of three modes of failure as a function of the interaction between the shear-head and surrounding concrete. The findings permit the development of improved analytical models for predicting the response as well as the ultimate strength of such members. In addition, recommendations are given for the determination of shear-head dependent parameters, which are required for practical design purposes, with a particular focus on the embedment length and section size of the shear-head elements. The suggested expressions for assessing the shear-head characteristics offer a more reliable design approach in comparison with existing methods and are suitable for effective practical application and implementation in codified procedures.

Nonlinear numerical simulation of punching shear behavior of reinforced concrete flat slabs with shear-heads

This paper examines the structural response of reinforced concrete flat slabs, provided with fully-embedded shear-heads, through detailed three-dimensional nonlinear numerical simulations and parametric assessments using concrete damage plasticity models. Validations of the adopted nonlinear finite element procedures are carried out against experimental results from three test series. After gaining confidence in the ability of the numerical models to predict closely the full inelastic response and failure modes, numerical investigations are carried out in order to examine the influence of key material and geometric parameters. The results of these numerical assessments enable the identification of three modes of failure as a function of the interaction between the shear-head and surrounding concrete. Based on the findings, coupled with results from previous studies, analytical models are proposed for predicting the rotational response as well as the ultimate strength of such slab systems. Practical recommendations are also provided for the design of shear-heads in RC slabs, including the embedment length and section size. The analytical expressions proposed in this paper, based on a wide-ranging parametric assessment, are shown to offer a more reliable design approach in comparison with existing methods for all types of shear-heads, and are suitable for direct practical application.

Ultimate strength of stiffened panels subjected to non-uniform thrust

The current study is focused on the evaluation of the ultimate strength of stiffened panels found in ship hull structures that are subjected to combined uniaxial thrust, in-plane and out-of-plane bending moments. This loading condition, which is in general ignored when performing buckling checks, applies to representative control geometries (stiffener with attached plating) as a consequence of the linearly varying normal stresses along the ship's depth induced by the hull-girder vertical bending moment. The problem is generalized by introducing a non-uniform thrust described by a displacement ratio and rotation angle and by introducing the slenderness ratios, within the practical range of interest. The formed design space is explored through methods sourcing from Design of Experiments and by applying non-linear finite element procedures. Surrogate empirical models have been constructed through regression analysis and Response Surface Methods. An additional empirical model is provided to the literature for predicting the ultimate strength under uniaxial thrust. The numerical experimentation has shown that is a significant influence on the ultimate strength of stiffened panels as the thrust non-uniformity increases.

Numerical assessment of reinforced concrete members incorporating recycled rubber materials

This paper is concerned with the inelastic behaviour of reinforced concrete beam-column members incorporating rubber from recycled tyres. Detailed three-dimensional nonlinear numerical simulations and parametric assessments are carried out using finite element analysis in conjunction with concrete damage plasticity models. Validations of the adopted nonlinear finite element procedures are carried out against experimental results from a series of tests involving conventional and rubberised concrete flexural members and varying levels of axial load. The influence of key parameters, such as the concrete strength, rubber content, reinforcement ratio and level of axial load, on the performance of such members, is then examined in detail. Based on the results, analytical models are proposed for predicting the strength interaction as well as the ductility characteristics of rubberised reinforced concrete members. The findings permit the development of design expressions for determining the ultimate rotation capacity of members, using a rotation ductility parameter, or through a suggested plastic hinge assessment procedure. The proposed expressions are shown to offer reliable estimates of strength and ductility of reinforced rubberised concrete members, which are suitable for practical application and implementation in codified guidance.

Large displacement analysis of ellipsoidal pressure vessel heads using the fundamental of differential geometry

This paper presents an investigation of the large displacement analysis of ellipsoidal pressure vessel heads, based on the membrane shell theory. The strain components of deformed shell configurations could be obtained by using the fundamental knowledge of differential geometry. Energy functional of the ellipsoidal shell was derived from the principle of virtual work, which is expressed in the appropriate forms. Based on the nonlinear finite element procedures, the nodal displacements of the shell configuration were numerically obtained. Analytical method for the small displacement was derived in order to validate the numerical results obtained from the FEM. Interesting features from parametric study of normal and tangential displacements for arbitrary shapes of ellipsoidal shells are presented and discussed. It is revealed that the point of zero normal displacement for arbitrary shapes of ellipsoidal shells is always the same point which is independent of the applied internal pressure and thickness of shell. Furthermore, there exists the maximum point of tangential displacement and it is always at the same points of the radial distance when the internal pressure and thickness of shells are varied.

Monotonic and cyclic performance of threaded reinforcement splices

This paper examines the fundamental uniaxial monotonic and cyclic response of reinforcement bars connected with threaded mechanical couplers. Based on a survey of available splicing forms, two types of threaded couplers with different geometric configurations, namely ‘parallel threaded couplers’ and ‘parallel threaded sleeve couplers’ are selected for detailed assessment. An experimental study consisting of twenty-four bare (in-air) and embedded (in-concrete) specimens incorporating threaded couplers and non-spliced counterparts, is described. The results enable direct assessment of strength as well as complete deformation characteristics, including the post-cracking and post-yield response, for both monotonic and cyclic conditions. After describing the material properties and specimen details, the main observations are reported based on detailed measurements of crack kinematics including crack width and spacing through a digital image correlation system. Complementary numerical studies, undertaken using nonlinear finite element procedures which are validated against the tests, enabled supplementary parametric investigations accounting for wider ranges of coupler geometries. The findings show that existing guidelines may be used for assessing the crack width and spacing, by accounting for the characteristic bond behaviour at the rebar and coupler regions. The complete deformational response may be obtained by using a suggested stiffness reduction factor that depends on the coupler geometry. Several ‘in-air’ performance parameters may also be used as a basis for the selection and implementation of couplers in applications requiring ductile member behaviour.

Behaviour of rubberised concrete members in asymmetric shear tests

This paper deals with the experimental behaviour of rubberised concrete members subjected to asymmetric four-point shear loading. A detailed account of tests on 15 prismatic members using conventional concrete as well as rubberised concrete, with relatively high replacement ratios of both fine and coarse mineral aggregates with rubber particles, is given. The results enable direct assessment of strength and complete deformation characteristics including the post-peak response for ultimate behaviour governed both by shear and mixed-mode tensile-shear. After describing the material properties, mix designs and member details, the main observations from detailed measurements of the crack kinematics through a digital image correlation monitoring system, with focus on members developing shear-governed response, are reported. Complementary numerical studies are undertaken using nonlinear finite element procedures which are validated against tests developing shear-governed failures. In order to provide further insight into the key response characteristics, particularly those related to ultimate strength, a number of numerical sensitivity studies employing various constitutive parameters are also carried out. Moreover, comparative assessments in terms of shear resistance, toughness and force transfer across the cracked interfaces are performed and discussed. The detailed test measurements, coupled with the results obtained from the numerical simulations, permit the definition of expressions for representing the shear resistance as a function of the rubber content and concrete compressive strength.

08.23: Performance and design of shear‐keys in hybid RC beam and steel column systems

ABSTRACTThis study describes experimental and numerical investigations into the inelastic performance of hybrid structural configurations consisting of reinforced concrete (RC) beams connected to steel columns by means of fully‐embedded structural steel profiles (shear‐keys). Experimental observations from a series of fourteen full‐scale hybrid steel/RC specimens are presented. To provide further insights into the key response characteristics, detailed numerical analyses for the tested configurations are also carried out. The numerical studies are undertaken using nonlinear finite element procedures which are validated against the experimental results from the hybrid tests presented in this paper. The ability of the numerical models to provide faithful predictions, using a consistent set of material parameters, provides a high level of confidence in the reliability of the simulation techniques. Data from the numerical models are then sutilised to evaluate the shear‐force distribution along the length of the shear‐key. The contribution from the shear‐key to the overall vertical force transferred to the column is comparatively assessed amongst the various configurations presented. For more simplified design considerations, an idealised distribution of the effective shear forces along the shear‐key is also proposed in the current study. Bases on the findings, recommendations for the practical design of shear‐keys in hybrid specimens are suggested and discussed.

08.58: Ultimate behaviour and design of hybrid flat slabs with steel shear heads

ABSTRACTThis investigation examines the performance of hybrid reinforced concrete flat slabs, incorporating fully‐integrated shear‐heads at connections to steel columns, through a series of numerical simulations and parametric studies. Validations of the adopted nonlinear finite element procedures, which employ concrete damage plasticity constitutive models, are carried out against experimental results on hybrid members. Comparison of the numerical simulations against the test results shows close correlations in terms of ultimate strength, deformations and stress levels in the constituent elements of hybrid members. This is followed by a series of parametric assessments on key structural parameters for hybrid flat slabs with steel shear heads. The results of these investigations enable the identification of three modes of failure as a function of the interaction between the shear‐head and surrounding concrete. The findings permit the development of improved analytical models for predicting the rotational response as well as ultimate strength of such members. In addition, recommendations are given for the determination of shear‐head dependent parameters, which are required for practical design purposes, with particular focus on the embedment length and section size of the shear‐head elements. The suggested expressions for assessing the shear‐head characteristics offer a more reliable design approach in comparison with existing methods and are suitable for effective practical application and implementation in codified procedures.

Numerical modelling and parametric assessment of hybrid flat slabs with steel shear heads

This investigation examines the performance of hybrid reinforced concrete flat slabs, incorporating fully-integrated shear-heads at connections to steel columns, through a series of numerical evaluations and parametric studies. Validations of the adopted nonlinear finite element procedures, which employ concrete damage plasticity constitutive models, are carried out against experimental results on hybrid members. Complementary verifications on conventional reinforced concrete flat slabs are also undertaken to ensure the reliability of the selected ranges for key modelling parameters. Comparison of the numerical simulations against the test results shows close correlations in terms of ultimate strength, deformations and stress levels in the constituent elements of hybrid members. This is followed by a series of parametric assessments on key structural parameters for hybrid flat slabs with steel shear heads. The results of these investigations enable the identification of three modes of failure as a function of the interaction between the shear-head and surrounding concrete. The findings permit the development of improved analytical models for predicting the response as well as the ultimate strength of such members. In addition, recommendations are given for the determination of shear-head dependent parameters, which are required for practical design purposes, with a particular focus on the embedment length and section size of the shear-head elements. The suggested expressions for assessing the shear-head characteristics offer a more reliable design approach in comparison with existing methods and are suitable for effective practical application and implementation in codified procedures.

Experimental and numerical assessment of mixed RC beam and steel column systems

This study describes experimental and numerical investigations into the inelastic behaviour of structural assemblages consisting of reinforced concrete (RC) beams connected to steel columns by means of fully embedded shear-keys. A detailed account of the experimental results and observations from a series of fourteen full-scale hybrid steel/RC specimens is presented. In order to provide further insights into the key response characteristics, particularly those related to ultimate failure conditions, a number of numerical sensitivity assessments are also carried out. The numerical studies are undertaken using nonlinear finite element procedures which are validated against previous tests on RC members as well as the experimental results from the hybrid tests presented in this paper. The ability of the numerical models to provide faithful prediction of both RC and hybrid test results, in terms of stiffness, strength and failure mode, using a consistent set of material modelling parameters, provides confidence in the reliability of the simulation techniques. Possible failure conditions for mixed RC/steel members are assessed using a suggested hybrid Mode Index (MI). Based on the experimental and numerical evaluations, simplified analytical representations of the failure surfaces, corresponding to the ultimate modes of behaviour for the hybrid configurations examined in this study, are proposed and discussed.

A three-dimensional nonlinear meshfree algorithm for simulating mechanical responses of soft tissue

This paper presents an effective three-dimensional (3D) nonlinear explicit dynamic meshfree algorithm for the simulation of soft tissue mechanical responses. In the algorithm soft tissues are considered to be hyperelastic and nearly incompressible materials. The algorithm is based on the element-free Galerkin (EFG) method using total Lagrangian formulation and moving least square (MLS) approximation. This approximation uses a relatively large number of nodes for shape functions creation, which can significantly delay mesh distortion in large deformation computations. Essential boundary conditions are imposed exactly by coupling MLS shape functions with a finite element (FE) interpolation in the close region of essential boundary. Although volumetric integration is not exact, the large support domains of the MLS shape functions alleviate some of the key weaknesses of FE methods such as hour-glassing and volumetric locking. Explicit integration is performed in time domain, using a recently proposed method to calculate the critical time step. Verification against the results obtained using the established nonlinear finite element procedures available in the ABAQUS code confirms the accuracy of the presented meshfree algorithm. Application of the algorithm in modeling of the brain indentation indicates its ability to facilitate robust and accurate prediction of the organ responses subjected to large localized deformations consistent with the loading due to surgery.

Flexure analysis of spoolable reinforced thermoplastic pipes for offshore oil and gas applications

This article is concerned with the numerical modelling and analysis of the mechanical behaviour of composite pipes used for offshore oil and gas applications. Specifically, the bending of the reinforced thermoplastic pipes during the reeling process of reel-lay installation is modelled using non-linear finite-element procedures. In particular, the possible buckling of the reeled composite pipes has been investigated. Composite pipes reinforced with one angle-ply and two angle-ply layers are considered and the effects of different diameter-to-thickness ratios and different angle-ply combinations on the mechanical behaviour of these pipes have been studied.

Patient-specific non-linear finite element modelling for predicting soft organ deformation in real-time; Application to non-rigid neuroimage registration

Long computation times of non-linear (i.e. accounting for geometric and material non-linearity) biomechanical models have been regarded as one of the key factors preventing application of such models in predicting organ deformation for image-guided surgery. This contribution presents real-time patient-specific computation of the deformation field within the brain for six cases of brain shift induced by craniotomy (i.e. surgical opening of the skull) using specialised non-linear finite element procedures implemented on a graphics processing unit (GPU). In contrast to commercial finite element codes that rely on an updated Lagrangian formulation and implicit integration in time domain for steady state solutions, our procedures utilise the total Lagrangian formulation with explicit time stepping and dynamic relaxation. We used patient-specific finite element meshes consisting of hexahedral and non-locking tetrahedral elements, together with realistic material properties for the brain tissue and appropriate contact conditions at the boundaries. The loading was defined by prescribing deformations on the brain surface under the craniotomy. Application of the computed deformation fields to register (i.e. align) the preoperative and intraoperative images indicated that the models very accurately predict the intraoperative deformations within the brain. For each case, computing the brain deformation field took less than 4 s using an NVIDIA Tesla C870 GPU, which is two orders of magnitude reduction in computation time in comparison to our previous study in which the brain deformation was predicted using a commercial finite element solver executed on a personal computer.

Dynamic Analysis of Cable Roofs Under Transient Wind: A Comparison Between Time Domain and Frequency Domain Approaches

At present, high-speed computing capabilities and advanced nonlinear dynamic finite element procedures enable detailed dynamic analysis of cable structures. Although deterministic approaches require considerable analysis time and effort in relation to modeling, running, and data processing, they seem to be the only alternative to obtain high accuracy. Detailed dynamic analysis of cable roof networks is sophisticated and requires advanced modeling expertise. This paper presents a comparison between detailed nonlinear dynamic analysis and a simplified frequency domain approach to estimate the maximum probable response of weakly nonlinear cable roofs. The approach can be considered as alternative to detailed time-domain analysis in the preliminary design phase, or can be used to validate results obtained from more elaborated numerical models. The proposed method is illustrated with two examples of cable net roofs that were also analysed in the time domain.

Subject-specific non-linear biomechanical model of needle insertion into brain

The previous models for predicting the forces acting on a needle during insertion into very soft organs (such as, e.g. brain) relied on oversimplifying assumptions of linear elasticity and specific experimentally derived functions for determining needle–tissue interactions. In this contribution, we propose a more general approach in which the needle forces are determined directly from the equations of continuum mechanics using fully non-linear finite element procedures that account for large deformations (geometric non-linearity) and non-linear stress–strain relationship (material non-linearity) of soft tissues. We applied these procedures to model needle insertion into a swine brain using the constitutive properties determined from the experiments on tissue samples obtained from the same brain (i.e. the subject-specific constitutive properties were used). We focused on the insertion phase preceding puncture of the brain meninges and obtained a very accurate prediction of the needle force. This demonstrates the utility of non-linear finite element procedures in patient-specific modelling of needle insertion into soft organs such as, e.g. brain.

Nonlinear finite element simulation for magnetic flux leakage tester

The paper reports about the building up a computer controlled measurement system based on National Instruments Data Acquisition card and National Instruments LabVIEW software package. The aim of this research is to detect manufactured surface cracks on steels by applying a magnetic flux leakage testing method. First of all, a finite element method based on the procedure to analyze the behavior has been implemented of the measurement system under construction. One important question is the position of the sensors or of the detecting coils. The finite element procedure contains a two dimensional arrangement. First, eddy currents have been neglected, but the nonlinear characteristic of the specimen has been taken into account by a single valued function. In this paper, the developed measurement system, which is partially ready to work, and the nonlinear finite element procedures are presented as well.

Multibody System Modeling of Leaf Springs

Leaf springs are essential elements in the suspension systems of vehicles including sport utility vehicles, trucks, and railroad vehicles. Accurate modeling of the leaf springs is necessary in evaluating ride comfort, braking performance, vibration characteristics, and stability. In order to accurately model the deformations and vibrations of the leaf springs, nonlinear finite-element procedures, which account for the dynamic coupling between different modes of displacement, are employed. Two finite-element methods that take into account the effect of the distributed inertia and elasticity are discussed in this investigation to model the dynamics of leaf springs. The first is based on a floating frame of reference formulation, while the second is an absolute nodal coordinate formulation. The floating frame of reference formulation allows for using a reduced-order model by employing component mode synthesis techniques, while the absolute nodal coordinate formulation enables more detailed finite-element models for the large deformation of very flexible leaf springs. Methods for modeling the contact and friction between the leaves of the spring are discussed. A comparison is also presented between the results obtained using the proposed method and simplified approaches presented in the literature. While there are many issues that can be important in leaf spring modeling, the analysis presented in this paper is focused on a few key issues that include the computer implementation, the effect of the dynamic load on the spring stiffness, the selection of the vibration modes in the reduced-order model, and the effect of the structural damping on the response of the leaf spring.