Displacement-based Approach Research Articles

Review of the strain-based formulation for analysis of plane structures Part I: Formulation of basics and the existing elements

Since the introduction of the finite element approach, as a numerical solution scheme for structural and solid mechanics applications, various for mulation methodologies have been proposed. These ways offer different advantages and shortcomings. Among these techniques, the standard displacement-based approach has attracted more interest due to its straightforward scheme and generality. Investigators have proved that the other strategies, such as the force-based, hybrid, assumed stress, and as sumed strain provides special advantages in comparison with the classicfinite elements. For instance, the mentioned techniques are able to solve difficulties, like shear locking, shear parasitic error, mesh sensitivity, poor convergence, and rotational dependency. The main goal of this two-part study is to present a brief yet clear portrait of the basics and advantages of the direct strain-based method for development of high-performance plane finite elements. In this article, which is the first part of this study, assump tions and the basics of this method are introduced. Then, a detailed review of all the existing strain-based membrane elements is presented. Although the strain formulation is applicable for different types of structures, most of the existing elements pertain to the plane structures. The second part of this study deals with the application and performance of the reviewed elements in the analysis of plane stress/strain problems.

Modelling of seismic actions in earth retaining walls and comparison with shaker table experiment

This paper is concerned with the response behaviour of a retaining wall in seismic conditions from a two-dimensional perspective. The backfill was levelled behind the wall for some distance. Both the wall and the backfill were found on a stiff elastic medium. The manner in which the backfill affected the response behaviour of the wall when subject to base excitations was of interest. The wall was idealised into a linear elastic element which responded mainly in flexural actions. The novelty of the paper is in the use of shaker table testing of a scaled down model of the retaining wall and backfill to validate the accuracies of results from numerical simulations. The comparison is mainly based on displacement time - histories at the top of the wall. The alignment with displacement-based approach for the seismic assessment of structures is distinguished from many other investigations which typically put the focus on the behaviour of the backfill pressure. Laboratory testings of backfill materials including triaxial tests have been conducted to determine the value of parameters for characterising the hysteresis properties of the backfill. Calibration of backfill material model has also been shown to simulate the pre yield, post yield and damping behaviour of backfill. The ultimate objective of the paper is to present a viable means of achieving realistic and accurate modelling of the seismic response behaviour of a retaining wall and to provide data for benchmarking simplified (macro) numerical models to be developed in the future for supporting seismic design and assessment.

Displacement Spectra Damping Factors for Preliminary Design of Structures with Hysteretic Energy-Dissipation Devices

ABSTRACT A methodology based on probabilistic seismic risk analysis to estimate damping factors (Fmd) which modify the spectrum of elastic displacement with uniform annual exceedance rates (UAER), is proposed. Such factors take into account both a) energy dissipation of the hysteretic dissipaters and b) seismic hazard of the site. It is shown the importance of taking into account the type of soil for a proper selection of the dissipater characteristics. Mathematical expressions for Fmd factors are proposed. An example in which Fmd factors are applied using a displacement-based design approach is presented. The results are verified with time-history analyses.

Quantifying the Likelihood of Exceeding a Limit State via the Displacement-based Assessment Approach

ABSTRACT The displacement-based assessment procedure of Priestley and co-authors was formulated to provide either a pass-fail type of assessment or an indication of the likelihood of exceeding a selected limit state. To account for the effect of uncertainty in demand and capacity as part of the displacement-based assessment, it has also been shown that the SAC-FEMA approach can be adopted. In this work, the displacement-based assessment approach is improved by developing new relationships between intensity and inelastic displacement demand that permits the impact of multiple intensity levels on the likelihood of exceeding a limit state to be assessed contemporarily. The benefit of the new approach is illustrated by comparing the annual probability of exceeding key limit states as obtained through multi-stripe analyses with results obtained from the simplified approach. Results indicate that the simplified method performs reliably for the cases considered. Limitations with the new approach and future research needs are identified.

Full-range bondstress-slip model for externally bonded FRP plates including a frictional component

Bondstress-slip models of externally bonded FRP plates have long been quantified using push/pull shear tests in which the bonded joint is slightly greater than the effective length of the plate. This inhibits the formation of a frictional component that may arise in long bonded joints. Moreover, previous researchers have used several factors to represent the bondstress-slip model parameters which gave a rise to a number of models. With that in mind, the first aim of this study was to assess the factors that affect the bondstress-slip parameters (τmax, δ1 and δmax), and to propose a simplified bilinear bondstress-slip model that correlates well with experimental data. The second objective was to predict the frictional component in the bondstress-slip model that develops in FRP plated flexural members using a partial-interaction displacement-based approach, assess the factors that affect the frictional component and investigate the debonding mechanism of FRP plated members with a frictional component. As such, a database consisting of 98 pull/push shear tests available in the open literature was assembled and used to assess the factors that influence the bilinear bondstress-slip model parameters. Subsequently, a simplified bilinear bondstress-slip model was proposed and validated against 288 pull/push shear test results. Next, 8 FRP plated beams were investigated using a displacement-based analysis where it was seen that the frictional component depended largely on the length of the plated members. Also, it was seen that poor correlation with experimental results was observed when a bilinear model without a frictional component was used in the analysis, where the predicted ultimate strength was 66 – 78% of the experimental value. The findings of this study illustrate the importance of considering the frictional component in the bondstress-slip model, and how this may affect the strength, deformation and ductility of the plated member.

Effect of the plate bondstress-slip property on the flexural strength of FRP Plated RC beams using a displacement-based approach

This study presents the theoretical results of a displacement-based approach for CFRP plated RC beams while varying the bondstress-slip relationship of the plate to see the influence of this material property on the global behavior. The experimental programme included three ordinary and three plated RC beams that had similar dimensions and similar material properties. From the displacement-based analysis, it was shown that the theoretical and experimental results for the ordinary RC beams were almost identical. However, for the CFRP plated RC beams, it was shown that using a linear-descending bondstress-slip model for the FRP plate in the analysis underestimated the flexural capacity of the plated beam as the theoretical results were about 75% of the experimental values. Moreover, through a parametric study, it was shown that adding an ascending branch to the FRP plate’s bondstress-slip property (e.g., using a bilinear bondstress-slip model) results in better correlation with the experimental values at service loads in comparison to using only a linear-descending branch without an ascending component. In addition, it was also shown that adding a frictional component to the bondstress-slip model of the FRP plate to allow the force in the plate to build up as debonding ensues gives closer results to the experimental values observed in the laboratory. The accurate simulation of the FRP plate’s bondstress-slip material property was seen to greatly affect the plated member’s capacity and ductility behavior.

A Comparison of Simplified Modelling Approaches for Performance Assessment of Piles Subjected to Lateral Spreading of Liquefied Ground

The lateral spreading of the ground due to liquefaction during earthquakes may considerably damage the embedded piles, which is an important issue in the seismic design of pile foundations. In this paper, nonlinear pseudostatic analyses were performed for the responses of piles subjected to actions of laterally spreading ground, which were modelled as flow displacement and flow pressure, respectively. The former is a displacement-based approach, in which the free-field ground displacement profile is assigned to the pile-soil interaction system; while the latter is a force-based approach, which regards the actions of laterally spreading ground as flow pressure and directly applies it to the pile. The concept of the Winkler foundation was utilized to account for the interaction between pile and soil. The soil springs with elastic-plastic p-y curves were used to describe the relationship of soil reaction versus lateral displacement around the pile. The distributed plastic hinges were deployed to simulate the possible flexural failure of the pile. One of the pile failure cases caused by liquefaction-induced lateral spreading in the 1995 Kobe Earthquake was adopted for case study. The analyzed pile response to flow displacement and flow pressure was compared with the field observations, and the validity and capability of both approaches were accordingly discussed. The influence of axial load on laterally loaded piles, namely, the P-delta effect was also examined. These results help to reasonably assess the performance of piles subjected to lateral spreading of liquefied ground.

A new displacement-based approach for pulsating tension load tests of post-installed anchors for the use in structural applications under seismic actions

The usage of post-installed anchors in structural applications and seismic retrofit solutions has become more and more popular over the past decades. The current approaches for seismic assessment of post-installed anchors follow primarily a force-based approach and were developed focusing on non-structural applications. On the structural level, performance based approach is becoming increasingly popular and important for the seismic design of structures as well as for seismic retrofitting of structures. This approach targets on the performance objectives that are closely related to the displacement behavior rather than on specific load levels to allow a better balance between construction costs and safety of structures. This performance based approach is also reflected in recent guidelines for seismic testing of reinforced concrete (RC) structural components. Yet in anchor design and qualification, the main focus is on force-based test and assessment methods. Such force-controlled assessment procedures may not provide sufficient information required to assess the performance of anchorages in structural applications where anchorages are subjected to strong demands and might be pushed beyond their linear behavior range. In this paper, a new displacement-based approach for testing of post-installed anchors under seismic actions is introduced. With this new approach, it is possible to obtain the complete hysteretic behavior over the entire range of the load-displacement response. The test setup, cyclic test protocol and typical results of the tests performed on five different post-installed anchor types are described and discussed in the paper. The anchors are tested under pulsating tension loads following (i) the force-controlled protocol specified by the existing qualification guidelines, and (ii) the new displacement-controlled protocol recommended in this work, and the results of the tests are compared. The results of the tests following the displacement-controlled protocol are found to be more suitable for the assessment of anchors used in structural strengthening applications under seismic actions due to their ability to provide the full information required for characterization of the anchors under seismic loads. The proposed approach holds promise to replace/augment the current testing procedures for seismic assessment of post-installed anchors. Based on the evaluation of the experimental results new assessment conditions are being developed for the assessment of post-installed anchors under seismic actions that will be presented by the authors in a future paper.

Seismic vulnerability and loss assessment of an isolated simply-supported highway bridge retrofitted with optimized superelastic shape memory alloy cable restrainers

Restrainers, being of relatively low cost and easy to install, are often used to prevent unseating of bridge spans. The potential of using superelastic shape memory alloy (SMA) restrainers in preventing such failure has been discussed in the literature; however, the impact of such smart restrainers with optimized configurations in reducing the failure probability of bridge components and system as well as the long-term economic losses given different earthquake scenarios has not been investigated yet. This study presents a probabilistic seismic fragility and long-term performance assessment on isolated multi-span simply-supported bridges retrofitted with optimized SMA restrainers. First, SMA restrainers are designed following the displacement-based approach and their configuration is optimized. Then, seismic fragility assessment is conducted for the bridge retrofitted with optimized SMA restrainers and compared with those of the original bridge and the bridges with elastic restrainers (steel and CFRP). Finally, long-term seismic loss (both direct and indirect) are evaluated to assess the performance of the retrofitted bridges in a life-cycle context. Results showed that among three considered restrainers, SMA restrainers make the bridge less fragile and help the system lower long-term seismic loss. The design event (DE, 2475-year return period) specified in Canadian Highway Bridge Design Code (CHBDC, CSA S6-14 2014) may underestimate the long-term seismic losses of the highway bridges. Under DE, the damage probability of the bridge retrofitted with optimized SMA restrainers experiencing collapse damage is only 0.7%. Under the same situation, its expected long-term loss is approximate 17.6% of that with respect to the unretrofitted bridge.

Estimating lumbar passive stiffness behaviour from subject-specific finite element models and in vivo 6DOF kinematics

Passive rotational stiffness of the osseo-ligamentous spine is an important input parameter for estimating in-vivo spinal loading using musculoskeletal models. These data are typically acquired from cadaveric testing. Increasingly, they are also estimated from subject-specific imaging-based finite element (FE) models, which are typically built from CT/MR data obtained in supine position and employ pure rotation kinematics. We explored the sensitivity of FE-based lumbar passive rotational stiffness to two aspects of functional in-vivo kinematics: (a) passive strain changes from supine to upright standing position, and (b) in-vivo coupled translation-rotation kinematics. We developed subject-specific FE models of four subjects’ L4L5 segments from supine CT images. Sagittally symmetric flexion was simulated in two ways: (i) pure flexion up to 12° under a 500 N follower load directly from the supine pose. (ii) First, a displacement-based approach was implemented to attain the upright pose, as measured using Dynamic Stereo X-ray (DSX) imaging. We then simulated in-vivo flexion using DSX imaging-derived kinematics. Datasets from weight-bearing motion with three different external weights [(4.5 kg), (9.1 kg), (13.6 kg)] were used. Accounting for supine-upright motion generated compressive pre-loads ≈ 468 N (±188 N) and a “pre-torque” ≈2.5 Nm (±2.2 Nm), corresponding to 25% of the reaction moment at 10° flexion (case (i)). Rotational stiffness estimates from DSX-based coupled translation-rotation kinematics were substantially higher compared to pure flexion. Reaction Moments were almost 90% and 60% higher at 5° and 10° of L4L5 flexion, respectively. Within-subject differences in rotational stiffness based on external weight were small, although between-subject variations were large.

Retrofit of Reinforced Concrete Moment Frames in NZ Using Dual Supplemental Damping

The repair and seismic strengthening of a mid-1990s building structure in Christchurch, New Zealand, using fluid viscous dampers and buckling-restrained braces provides a case-study for mixed-system retrofit to improve the seismic performance of ductile reinforced concrete moment frames. The building was designed and detailed to essentially current standards but was very flexible and utilised a precast hollow-core floor system with thin topping slab which is vulnerable to deformations associated with moment frames, as demonstrated in recent New Zealand earthquakes. This paper highlights a simple displacement-based approach to setting retrofit design targets and performance verification. The retrofit using viscous dampers provided an efficient means to reduce ground motion-induced deformations and accelerations. The structural benefits to the rest of the project included no need for foundation strengthening and floor diaphragm strengthening being limited to only the perimeter hollow-core units. Development of the final design and viscous damper specification involved close coordination with the manufacturer to optimise the damper design, fabrication tolerances and site installation methods.

Flexural strength of FRP plated RC beams using a partial-interaction displacement-based approach

Designing FRP plated RC beams using full-interaction moment-curvature analysis would often suggest that the RC structure is brittle with debonding often occurring prior to yielding of the reinforcement steel. For that reason, researchers have looked into a displacement-based approach that takes into account the member debonding mechanism. The force in the plate within the debonded region was assumed to remain at the intermediate crack debonding force, PIC, and the ultimate strength was determined by considering compatibility of displacements along the member length. However, from laboratory testing, it is seen that the force in the externally bonded FRP plate keeps building up until failure occurs. Therefore, in this study, an extension to the displacement-based approach developed by previous researchers for FRP plated beams is presented where the residual bondstress of the plate within the debonded region is incorporated in the analysis. This is achieved by adopting a bond-slip model with a residual shear component that allows for the force in the plate to increase beyond PIC. The ultimate strength of the FRP plated beams is determined when the plate displacement matches that of the concrete near the plate end. A comparison with the experimental results of seven adhesively plated beams shows that incorporating the residual bondstress of the externally bonded plate yields significant improvement in accuracy and give better correlation with experimental findings.

Performance-based Seismic Analysis of Rocking Masonry Façades Using Non-linear Kinematics with Frictional Resistances: A Case Study

ABSTRACT In this paper the seismic assessment of rocking masonry walls is evaluated through the displacement-based approach. In particular, a case study is selected to analyse the rocking failure mechanism of the façade of an ancient masonry church, damaged during the 2016–17 Central Italy seismic sequence. For this purpose, a non-linear kinematic analysis is developed to define the load factor at the activation of the failure mechanism and its evolution until collapse, at large displacements. An advanced macro-block model is adopted to take into account the stabilising contribution of frictional resistances exerted by the interlocked walls. The seismic input is described through acceleration-displacement response spectra (ADRS), provided both by seismic codes and selected real accelerograms, and the seismic analysis is addressed according to the capacity spectrum method (CSM), in the form incorporated into the latest Commentary to the Italian Technical Standard for Construction (CNTC19). The capacity is compared with the seismic demand through safety indexes, in terms of both forces and displacements, and the relevant influence of the frictional resistances on increasing the capacity is discussed. Incremental static analysis (ISA) curves are presented as another approach useful to highlight the relation between the peak ground acceleration (PGA) and the displacement demand.

Seismic Vulnerability of a Rockfill Dam through Different Displacement-based Approaches

ABSTRACT The paper focuses on the assessment of the seismic performance of Menta Dam, a bituminous faced-rockfill dam located in Southern Italy. The dam was designed in the ‘70s and a comprehensive assessment of hydraulic and seismic vulnerability has been recently performed according to most recent Italian dam regulations. The present work aims at predicting the displacement capacity of the embankment as an indicator to assess the overall seismic vulnerability of the system. To this aim, different displacement-based methods, which can be classified in the framework of simplified dynamic analyses, have been applied. The results of empirical approaches and of Newmark’s type dynamic analyses are compared to the ones obtained by a novel application of Direct Displacement-Based Assessment (DDBA) method for embankment structures. The latter approach seems to be promising, since it is capable to furnish the maximum displacement experienced by the dam crest for progressively increasing seismic actions, and its probability of exceedance; hence, the likelihood of reaching a threshold damaged condition can be deduced and usefully plotted in terms of fragility curves.

Hybrid simulation of a structure to tsunami loading

A new hybrid simulation technique has been developed to assess the behavior of a structure under hydrodynamic loading. It integrates the computational fluid dynamics and structural hybrid simulation and couples the fluid loading and structural response at each simulation step. The conventional displacement-based and recently developed force-based hybrid simulation approaches are adopted in the structural analysis. The concept, procedure, and required components of the proposed hybrid simulation are introduced in this article. The proposed hybrid simulation has been numerically and physically tested in case of a coastal building impacted by a tsunami wave. It is demonstrated that the force error in the displacement-based approach is significantly larger than that in the force-based approach. The force-based approach allows for a more realistic and reliable structural assessment under tsunami loading.

Deep tunnel fronts in cohesive soils under undrained conditions: a displacement-based approach for the design of fibreglass reinforcements

The fronts of tunnels excavated under particularly difficult ground conditions by employing conventional tunnelling methods are commonly supported: the stabilization is usually achieved either by improving the mechanical properties of the soil (injections, jet grouting, soil freezing, etc.) or by introducing linear inclusions. This last technique, consisting in the introduction of pipes (usually made of fibreglass reinforced polymers) in the front, is particularly popular since it is very simple to adapt the reinforcement geometry, length and number to the different conditions encountered during the excavation. The design of this reinforcement technique is nowadays based on very simplified approaches: on either empirical formula or the limit equilibrium method. In a previous paper, the authors numerically studied the mechanical response of unreinforced fronts in cohesive soils and defined a non-dimensional front characteristic curve. In this paper, the authors intend to take into consideration the role of reinforcements by following the same approach. A procedure allowing the definition of the reinforced non-dimensional front characteristic curve, once the reinforcement pattern is assigned, is introduced. The practical use of this curve is described.

Mixed beam formulation with cross-section warping for dynamic analysis of thin-walled structures

This paper presents the formulation of a three-dimensional beam finite element (FE) that accounts for cross-section warping and dynamic inertia effects. The model is the extension of an existing mixed formulation, originally developed for the static analysis of thin-walled beams, to the case of dynamic loading conditions.Four independent fields are considered to derive the element governing equations, i.e. material rigid displacements, strains and stresses and an additional displacement field, describing the out-of-plane warping displacement of the beam cross-sections. The latter is independently interpolated in the element volume by including additional degrees of freedom (DOF) to the nodal translations and rotations classically considered in beam formulations.To obtain a consistent form of the element mass matrix, the cross-section displacement shape functions are computed, relating the generalized cross-section displacement fields to the element nodal variables. In mixed FE formulations, these are not assigned a priori, as in displacement-based approaches, but are derived on the basis of material stiffness and element geometry, together with compatibility conditions. Thus, the Unit Load method is applied to deduce the expressions of the shape functions consistent with the force-based approach, assuming the simply-supported beam as reference element configuration.As opposed to the original FE model, the additional warping DOFs are not condensed-out with the definition of the element quantities but are treated as additional global unknowns. This permits a correct description of the inertia effects and ensures continuity of the warping displacement fields between adjacent FEs.Correlation studies are presented to validate the proposed model and investigate the effects of cross-section warping on the dynamic behavior of thin-walled structures. For selected specimens, the studies compare solutions obtained adopting the proposed beam element with those resulting from shell or brick FE models. Modal decompositions and time-history analyses are conducted, assuming both linear elastic and nonlinear constitutive behavior for the latter.

Analysis of multiple-core sandwich cylindrical shells using a sublaminate formulation

An advanced modelling approach is presented for the linear analysis of multilayered cylindrical shells. It relies on the combined use of a sublaminate shell formulation along with the Ritz method. The approach is particularly suitable for the analysis of sandwich shells, and can be naturally applied for studying non-conventional configurations characterized by the presence of multiple cores. The formulation relies upon a displacement-based approach and makes it possible the analysis of thin and thick configurations, without restrictions regarding the shallowness of the shell. The quality of the predictions is assessed by comparison against 3D solutions, and the advantages offered by current modeling approach are highlighted in terms of required theory-related degrees of freedom. The flexibility of the formulation is exploited to illustrate the analysis of a triple-core sandwich panel, giving evidence of the advantages offered by the proposed approach for modeling shells characterized by an arbitrary degree of complexity. Novel results are presented for future benchmarking purposes.

Finite Strain Homogenization Using a Reduced Basis and Efficient Sampling

The computational homogenization of hyperelastic solids in the geometrically nonlinear context has yet to be treated with sufficient efficiency in order to allow for real-world applications in true multiscale settings. This problem is addressed by a problem-specific surrogate model founded on a reduced basis approximation of the deformation gradient on the microscale. The setup phase is based upon a snapshot POD on deformation gradient fluctuations, in contrast to the widespread displacement-based approach. In order to reduce the computational offline costs, the space of relevant macroscopic stretch tensors is sampled efficiently by employing the Hencky strain. Numerical results show speed-up factors in the order of 5–100 and significantly improved robustness while retaining good accuracy. An open-source demonstrator tool with 50 lines of code emphasizes the simplicity and efficiency of the method.

Seismic demand and capacity assessment of suspended ceiling systems

In recent years, scientific interest for the study of Non-Structural Elements (NSE) has significantly increased and the importance of the seismic safety of these elements has become a widely discussed topic. Several technologies able to guarantee the seismic safety of NSE were created. In particular the sector of suspended ceiling has seen the development of different systems for achieving this purpose. Specific internal joints between profiles, perimeter brackets and bracing systems have been created to realize “anti-seismic” suspended ceilings. Several shake table tests, also defined qualifying tests, have been performed to analyze the behaviour of these systems.This work presents new original studies on seismic behaviour of suspended ceilings with an experimental fragility approach. Recently cyclic quasi-static tests have been realized at the University of Padova by means of a specifically developed experimental setup. First, experimental results were processed to define the hysteretic capacity curves of a typical metal T-Grid suspended ceiling. Then, these curves were exploited by means of numerical analyses to determine the elastic and inelastic response of the suspended ceiling installed at various levels of five multi-storey frames characterized by different vibration periods. Linear dynamic analyses of the frames subjected to 7 spectra-compatible artificial seismic signals were performed to obtain floor acceleration signals and spectra. Then three alternative numerical approaches were employed to define the seismic demand on the suspended ceiling. Using a displacement-based approach, capacity curves and elastic floor spectra were compared in the ADRS (Acceleration Displacement Response Spectrum) domain to evaluate the elastic displacements and accelerations of the suspended ceiling (Spectral Analysis). Also, Linear and Non-Linear Time-History analyses of the NSE were performed according to a cascade approach. The comparison of the seismic demands resulting from elastic, inelastic and spectral analyses is reported in the paper for each of the frames.