Nonlinear Incremental Analysis Research Articles

Influence of wall-to-floor connections and pounding on pre- and post-diction simulations of a masonry building aggregate tested on a shaking table

AbstractThis paper presents numerical simulations within the frame of the project SERA—AIMS (Seismic Testing of Adjacent Interacting Masonry Structures). The study includes blind pre-diction and post-diction stages. The former was developed before performing the shaking table tests at the laboratory facilities of LNEC (Lisbon), while the latter was carried out once the test results were known. For both, three-dimensional finite element models were prepared following a macro-modelling approach. The structure consisted of a half-scaled masonry aggregate composed by two units with different floor levels. Material properties used for the pre-diction model were based on preliminary tests previously provided to the participants. The masonry constitutive model used for the pre-diction study reproduced classical stress–strain envelope, whereas a more refined model was adopted for the post-diction. After eigenvalue analysis, incremental nonlinear time history analysis was performed under a unique sequence based on the given load protocol to account for damage accumulation. In the post-diction, the numerical model was calibrated on the data recorded during the shaking table tests and nonlinear dynamic analysis repeated under the recorded accelerogram sequence. The interaction between the two units was simulated through interface elements. Moreover, the timber floors were accounted following different strategies: not modelling or considering nonlinear wall-to-floor connections. Advantages and disadvantages are then analysed, comparing the pre-diction and post-diction results with the experimental data. Numerical results differ from the experimental outcomes regarding displacements and interface pounding, although a clear improvement is visible in the post-diction model.

Innovative Method for Masonry Columns Confinement

The paper deals with the presentation of a novel confinement approach for masonry columns, capable to overcome the drawbacks of the existing techniques either in terms of mechanical behavior or technological aspects. The research develops along with two main phases: numerical (completed) and experimental (in progress). Thus, they are here reported the numerical studies that show the improvements of the performances of masonry columns if reinforced through a non-conventional hooping system using “Dyneema ribbons”. The numerical models are realized using 3D solid f.e. with dimensions adjusted to fit the deformation gradients. The nonlinearity is concentrated at the mortar-brick joints. The bonding between ribbons and mortar is modelled using appropriate interface elements aimed at reproducing the stress transfer during installation and in working condition. It is also reported the design of a device able to guarantee a correct ribbons installation on site. Incremental non-linear static-equivalent analyses have been performed. The numerical analyses also compare similar solutions but with different strength and stiffness (Nylon ribbons).

Incremental nonlinear stability analysis of stochastic systems perturbed by Lévy noise

AbstractWe present a theoretical framework for characterizing incremental stability of nonlinear stochastic systems perturbed by either compound Poisson shot noise or finite‐measure Lévy noise. For each noise type, we compare trajectories of the perturbed system with distinct noise sample paths against trajectories of the nominal, unperturbed system. We show that for a finite number of jumps arising from the noise process, the mean‐squared error between the trajectories exponentially converge toward a bounded error ball across a finite interval of time under practical boundedness assumptions. The convergence rate for shot noise systems is the same as the exponentially stable nominal system, but with a tradeoff between the parameters of the shot noise process and the size of the error ball. The convergence rate and the error ball for the Lévy noise system are shown to be nearly direct sums of the respective quantities for the shot and white noise systems separately, a result which is analogous to the Lévy–Khintchine theorem. We demonstrate both empirical and analytical computation of the error ball using several numerical examples, and illustrate how varying the parameters of the system affect the tightness of the bound.

Quality control and safety assessment of prestressed concrete bridge decks through combined field tests and numerical simulation

This paper presents a systematic approach for the quality control and safety assessment of existing bridge decks through combined field tests and numerical simulation. The methodology is described in the context of a case study represented by the Zappulla multi-span viaduct (southern Italy), whose deck is realized with simply supported prestressed concrete girders and overlying reinforced concrete slab. Quality control is carried out through an extensive in-situ testing campaign comprising concrete coring, carbonation tests, sclerometric tests combined with ultrasonic pulse velocity for concrete strength evaluation, as well as pachometer and georadar tests for identification of steel reinforcement and prestressing tendons, respectively. Additionally, field tests including static and dynamic loading tests are performed to investigate the bridge response under serviceability conditions. Field-test results along with experimental findings on the material characterization are used to calibrate a finite element (FE) model of the bridge deck, which is subsequently adopted for structural safety assessment of the bridge deck at ultimate limit state (ULS). Two methods for evaluating the safety conditions at ULS are comparatively investigated, namely the Eurocode-compliant semi-probabilistic partial factor method and a deterministic method that computes the global safety factor of the bridge deck in its actual working conditions based on nominal values of loads and resistances. In addition to linear analysis, incremental non-linear static analysis is performed to determine the push-down response of the bridge deck via a concentrated plasticity approach. The proposed procedure, inherently encompassing both serviceability and ultimate loading conditions and synergistically combining material characterization and field-test results with a critical statistical interpretation, accompanied by numerical FE simulation with an eye to design code requirements, provides a reliable tool for the quality control and safety assessment of other similar existing bridges.

A robust cumulative damage approach for the simulation of delamination under cyclic loading conditions

Interlaminar damage evolution is one of the topics of main interest for composite materials research. An excellent level of knowledge has been achieved in the frame of the studies on delaminations propagation under static loading conditions (as a consequence of low velocity impacts). On the contrary, delaminations evolution under cyclic loading conditions is still an open challenge for the scientific community. Since expensive experimental campaigns are needed to assess the fatigue behaviour of Carbon Fibre Reinforced Polymers (CFRPs), the development and implementation of robust and efficient computational finite elements methodologies has become relevant. In this framework, a robust numerical finite element procedure able to simulate the fatigue driven delamination growth is proposed in this paper. A Paris-law based fatigue tool has been implemented in the commercial Finite Element Code ANSYS MECHANICAL via the Ansys Parametric Design Language (APDL) together with a static delamination procedure (named SMXB) previously developed by the authors. The proposed numerical procedure, based on the Virtual Crack Closure Technique (VCCT), is characterised by load step and element size insensitivity within non-linear incremental analyses. The proposed fatigue procedure, named FT-SMXB, has been preliminary validated at coupon level, by comparing the numerical results to literature experimental data on a unidirectional graphite/epoxy Double Cantilever Beam (DCB) specimen. Actually, the excellent agreement between the achieved numerical results and the literature experimental benchmark data proves the accuracy and the potential of the proposed methodology. Subsequently, a numerical application on a composite stiffened panel with skin stringer debonding under compressive-compressive fatigue loading conditions, has been performed. The Excellent agreement found between the obtained numerical results and available experimental literature data, for this application, in terms of number of cycles to failure and debonding propagation as a function of number of cycles, proves that the use of the proposed numerical tool can be extended, with profit, to geometrically complex and more realistic fatigue test cases.

Full-scale experimental and numerical investigation on the ductility, plastic redistribution, and redundancy of deteriorated concrete bridges

Due to structural degradation, the performance of concrete bridges may degrade with time and result in catastrophic consequences. A novel approach is developed for evaluating the time-variant reliability of multi-girder concrete bridges considering the effects of the load-carrying mechanism and redundancy. By considering three failure modes at both the component and system levels, a new performance indicator is proposed for quantitatively evaluating the load elastic distribution and plastic redistribution among multiple girders. The adverse effects of material deterioration on the structural capacity, ductility, redundancy, load-carrying capacity, and failure mechanism are also investigated and incorporated into the analytical procedure, in which an incremental nonlinear finite element analysis of a 3D fiber beam element is used. Furthermore, the results associated with full-scale destructive tests of two in situ deteriorated bridges, a reinforced concrete (RC) and a prestressed RC (PRC) T-girder bridge, are adopted to evaluate the accuracy of the proposed approach. The feasibility and satisfactory performance of the proposed framework are evaluated using these two real-world bridges. The results demonstrate that the load-carrying mechanism and redundancy significantly affect the structural ultimate load-carrying capacity and time-variant reliability of deteriorating structures.

Resolution of Time-Dependent Navier-Stokes Equations with a new Boundary Condition

In this work, a numerical solution of the unsteady incompressible Navier- Stokes equations with a new boundary condition is proposed. The method suggested is based on an algorithm of discretization by finite element method in space and the Euler full-implicit scheme in time. The matrix system is solved at each iteration with a preconditioned GMRES method. Also, we proposed two types of a posteriori error indicator, with one being for the time discretization and the other for the space discretization. We prove the equivalence between the sum of the two types of error indicators and the full error. In order to evaluate the performance of the method, the numerical results of two-dimensional backward-facing step flow are compared with some previously published works or with others coming from commercial code like ADINA (Automatic Dynamic Incremental Nonlinear Analysis) system.

A New Method for Drawing the Capacity Spectrum for Seismic Analysis and Structural Rehabilitation

A review of previous studies shows that there are two general views on how to determine demand in structures through incremental nonlinear static analysis. In the first view, multi-modal methods are used to determine demand in structures. In this view, the applied load pattern is applied to the structure according to the shape of each vibration mode, assuming that the structure deformation follows the shape of the vibration mode, the capacity spectrum is drawn and after determining the target displacement and the corresponding demand for each vibration mode, the final demand is determined by combination of response modes. In the second view, structural analysis is performed as a single run nonlinear static analysis and the effect of different vibration modes is shown in one load pattern. In this method, the load pattern that has somehow the effect of different modes is applied to the structure and the structure is analyzed under this load pattern. In the second view, due to the non-conformity of the structure deformation and the lateral load of a particular vibration mode of the structure, the conventional capacity spectrum method cannot be used. Therefore, the purpose of this paper is to propose a method for drawing the capacity spectrum and determining the target displacement in single run nonlinear static analysis for non-adaptive load patterns. After presenting the equations, three frames including 3-storey, 9-storey and 20-storey frames have been selected and the results of the proposed method have been evaluated along with modal pushover method and time history analysis for the frames. Comparison of the results of the proposed method and the modal pushover with the results of the nonlinear time history analysis shows that the proposed method is more efficient in determining the lateral displacement of the stories and roof than the conventional modal pushover method.

Influence factors on the ground surface rupture zone induced by buried normal fault dislocation*

The seismic disaster presents a zonal distribution along the fault strike. In this paper, rupture zone of ground surface soil caused by the uniform dislocation, inclined dislocation and warped dislocation of buried normal fault are studied by constituting a three-dimensional finite element model in Automatic Dynamic Incremental Nonlinear Analysis (ADINA). According to the critical value of surface rupture, the variational features and influencing factors of width and starting position of the “avoiding zone” in engineering construction are analyzed by using 96 model calculations. The main results are as follows: (1) Since the rupture zone of the ground surface soil from the point of mechanics is different from the “avoidance zone” from the point of engineering safety, the equivalent plastic strain and the total displacement ratio should be considered to evaluate the effect of the seismic ground movement on buildings. (2) During fault dislocation, plastic failure firstly occurred on the ground surface soil of the footwall side, and then the larger deformation gradually moved to the side of the hanging wall of the fault with the increase of fault displacement. (3) When the vertical displacement of buried fault reaches 3 m, the width of “avoiding zone” in engineering construction varies within the range of 10–90 m, which is most affected by the thickness of overlying soil and the dip angle of the fault.

Strategies to improve the structural integrity of tied-arch bridges affected by instability phenomena

A numerical study is proposed to investigate the nonlinear behavior of steel tied-arch bridges, whose arch ribs are inclined inwardly. The main aim of the paper is to assess if the arch rib inclination may be an effective strategy to enhance the structural integrity of the bridge structure against out-of-plane buckling mechanisms. The nonlinear behavior of the structure is investigated throughout an advanced 3D finite element model, which accurately reproduces nonlinear sources involved in the cable system and structural elements. An analysis that combines results obtained by traditional elastic buckling analysis and incremental nonlinear elastic analysis is employed to properly evaluate the maximum capacity of the structure. Comparisons between bridge structures with inclined and vertical ribs configurations are proposed focusing attention on both structural and economic aspects. Results show that rib inclination provides several structural benefits to the bridge while reducing overall construction costs.

Continuum mechanics based beam elements for linear and nonlinear analyses of multi-layered composite beams with interlayer slips

In this study, we present continuum mechanics based beam elements for linear and nonlinear analyses of multi-layered composite beams with interlayer slips. Nonlinear kinematics of multi-layered beams allowing interlayer slips and the finite element formulation for nonlinear incremental analysis are derived. An important feature of the proposed beam element is an advanced modeling capability that originates from individual modeling of each beam layer using cross-sectional elements and layer degrees of freedom, which are embedded in the beam formulation. Complicated layered beam geometries including arbitrary numbers of layers and interlayers, varying and composite cross-sections, and eccentricities can be easily modeled without additional interface elements or constraints. Further, the proposed beam finite element is successfully applicable for predicting geometric and material nonlinear behaviors of the multi-layered beams including nonlinear load-slip relations at interlayers. The superb performance and predictive capability of the proposed beam element are demonstrated through several representative numerical examples.

Experimental investigation and numerical simulation of mechanical properties and thermal stability of tin alloy processed by equal channel angular extrusion (ECAE)

In this study, experimental investigation and numerical simulation of the compressive stiffness, effective plastic stress-strain behaviour, the hardness and thermal stability of tin alloy parts subjected to equal channel angular extrusion (ECAE) process were investigated. The numerical simulation was carried out using Automatic Dynamic Incremental Non-linear Analysis (ADINA) and the results were compared with the experiment. The as-received and extruded Sn alloy samples were subjected to metallographic examination using scanning electron and optical microscopy. The external fracture that was observed during ECAE did not show at the interior parts on the optical image. The results of compressive and hardness tests showed that stiffness, modulus, and hardness values increased with the number of extrusions. However, the maximum compressive stress and strain also increased marginally after the second ECAE pass. The thermal properties and transformations of the sample were studied with differential scanning calorimetry (DSC). The effective strain of the samples was simulated and observed to increase with each extrusion pass. The severe plastic deformation brought about by ECAE processing increased dislocation density (work hardening) in the affected parts accounting for an increase in the modulus of the alloy. ECAE processing is, therefore, a potential tool for enhancing the mechanical properties of tin alloy.

Principle of cluster minimum complementary energy of FEM-cluster-based reduced order method: fast updating the interaction matrix and predicting effective nonlinear properties of heterogeneous material

The present paper studies the efficient prediction of effective mechanical properties of heterogeneous material by the FCA (FEM-Cluster based reduced order model Analysis) method proposed in Cheng et al. (Comput Methods Appl Mech Eng 348:157–168, 2019). The principle of minimum complementary energy and its cluster form for the RUC subjected to applied uniform eigenstrains and the PHBCs (Periodic Homogeneous Boundary Conditions) are developed. By using the known interaction matrix, an alternative form of the principle of cluster minimum complementary energy is constructed and proved very efficient for updating the interaction matrix and the effective elastic modulus when the material properties of clusters change. Moreover, the proposed principle of cluster minimum complementary energy is applied for the incremental nonlinear analysis of the cluster reduced order model, and thus greatly improves the prediction of nonlinear effective properties of the RUC in online stage computed in Cheng et al. (Comput Methods Appl Mech Eng 348:157–168, 2019). A number of numerical examples illustrate the effectiveness and efficiency of the FCA approach with the proposed principle of cluster minimum complementary energy.

Numerical insights on the structural assessment of historical masonry stellar vaults: the case of Santa Maria del Monte in Cagliari

The aim of this paper is to present an in-depth numerical investigation on the statics of historical masonry stellar vaults, a special class of masonry ribbed vaults whose three-dimensional geometry features a star-shaped projection on the horizontal plane. In particular, the mechanical behavior of the masonry stellar vault belonging to the church of Santa Maria del Monte in Cagliari (Italy) is analyzed and illustrated as an especially meaningful case study. This church, which was built during the second half of the sixteenth century, is a beautiful example of Gothic-Catalan style, and its ribbed stellar vault is one of the most representative of this type in the town of Cagliari. The geometric outline of the vault has been obtained through laser scanning techniques and a procedure of reverse engineering. Starting from a three-dimensional representation of its geometry, the ultimate load-bearing capacity of the stellar vault can be accurately estimated through a recently developed, NURBS-based upper-bound limit analysis scheme. A comparison with incremental nonlinear analyses carried out with the commercial finite element code DIANA is presented. Furthermore, the paper also includes a sensitivity study aimed at investigating the role of ribs on the ultimate load-bearing capacity of the structure.

Substitute Frame and adapted Fish-Bone model: Two simplified frames representative of RC moment resisting frames

This paper aims to develop simplified frame models applicable for Reinforced Concrete (RC) moment frames. For this purpose, the existing Modified Fish-Bone (MFB) model, which is usually used for steel moment frames, is adapted for RC moment frames using modified Ibarra-Medina-Krawinkler springs with deteriorating peak-oriented behavior. Pre-analysis demonstrates that the MFB model requires some modifications for RC moment frames to (a) eliminate the imposed redundant compressive forces to the single column which was caused by the unbalanced shear forces between two half-beams at each story, and (b) simulate the migration of contraflexure point in the beams of original RC frames. The challenges stem from (a) the different negative and positive moment capacities in RC beams, and (b) the peak-oriented hysteretic behavior of rotational springs representing beam plastic hinges. More detailed investigation indicates that eliminating the redundant compressive force is the most effective modification, but the migration of contraflexure point due to different negative and positive moment capacities and even the single curvature bending condition of original beams is not crucial. The reason is investigated using step-by-step incremental nonlinear analysis and illustrated that the contraflexure point is usually located in the mid-span at each step, except for a transient phase in the reverse loading. This minor effect is fundamentally based upon the peak-oriented hysteretic behavior of RC beams. Hence, two simplified models branch from the Modified Fish-Bone model: (i) the Adapted Fish-Bone (Adapted MFB) model in which the first crucial modification is applied, and (ii) the Substitute Frame in which both modifications are reflected and seems to be more compatible for RC moment frames. In the end, the accuracy of the proposed models is evaluated using two sets of far-fault and one set of near-fault ground motions. The comprehensive nonlinear dynamic analysis demonstrates that the two proposed models can estimate engineering demand parameters with high accuracy, while they greatly simplify the modeling process, computational effort and visualization of results.

FEM-Cluster based reduction method for efficient numerical prediction of effective properties of heterogeneous material in nonlinear range

A novel FEM-Cluster based reduced order method or FEM-Cluster based Analysis method (FCA) which enables efficient numerical prediction of effective properties of heterogeneous material in nonlinear range is proposed. The cluster concept initially presented in the work by WK Liu et al. is introduced and extended to derive a full FEM multi-scale formulation of the Representative Unit Cell (RUC) to circumvent the heavy burden due to huge computational efforts required for a direct numerical simulation (DNS) of the high-fidelity RUC. The proposed FEM-Cluster based reduced order method is formulated in a consistent framework of finite element method. The offline clustering process with construction of the cluster-interaction matrix derived under the assumption of the linear elasticity is carried out by the devised FE procedure of RUC. The online elasto-plastic process is performed by the incremental non-linear FE analysis using the constant cluster-interaction matrix, which plays a role in the present work conceptually similar to the initial elastic modular matrix used in the ”initial stiffness method” for the traditional incremental elasto-plastic analysis. Accurate and efficient numerical prediction of effective properties of heterogeneous material in nonlinear range are developed in a consistent way. The performances of the proposed reduced order model and its numerical implementation are studied and demonstrated. Several numerical examples show its efficiency and applicability.

Analysis of a multi-story reinforced concrete residential building damaged under its self-weight

Abstract Reinforced concrete framed residential buildings are remarkably common in Turkey. Observations after recent earthquakes revealed that a great portion of the present building stock has inadequate seismic resistance. Moreover, collapses of several multi-story reinforced concrete buildings under their self-weight have also been observed despite any dynamic activity. The tragic example of the collapse of the “Zumrut” residential building under its self-weight in 2004 and the death of its 93 occupants have highlighted the need to re-examine the structural safety of existing buildings throughout the country. In this study, a multi-story reinforced concrete building located in the same city where the Zumrut disaster occurred, has been investigated. The damage occurred under its self-weight and their causes have been studied in detail. Four columns located in the basement of this nine-story reinforced concrete building have suddenly started to crack and fracture. At this stage, the authors were invited to the building for investigation during which initiation of another column failure was observed. After securing the building, concrete test samples were taken from each floor. The building is then modeled in 3D using a finite element software. A series of analyses have been carried out based on some reasonable assumptions. The demand-to-capacity ratios for each structural member were determined and a vertical incremental nonlinear pushover analysis was performed so that the possible failure mechanisms could be determined. The results indicated that the limited reserve capacity of columns and variation in material properties led to the observed failure.

A New Formulation on Seismic Risk Assessment for Reinforced Concrete Structures with Both Random and Bounded Uncertainties

A new formulation on seismic risk assessment for structures with both random and uncertain-but-bounded variables is investigated in this paper. Limit thresholds are regarded as random variables. The median of random variables is described through an improved multidimensional parallelepiped (IMP) convex model, in which the uncertain domain of the dependent bounded variables can be explicitly expressed. The corresponding Engineering Demand Parameters are taken to be dependent and follow a multidimensional lognormal distribution. Through matrix transformation, a given performance function is transformed into the regularized one. An effective method based on active learning Kriging model (ALK) is introduced to approximate the performance function in the region of interest rather than in the overall uncertain space. Based on ALK model, the failure probabilities for different limit states are calculated by using Monte Carlo Simulation (MCS). Further, the failure probabilities for different limit states in 50 years can be obtained through coupling the seismic failure probability with the ground motion hazard curve. A six-story reinforced concrete building subjected to ground motions is investigated to the efficiency and accuracy of the proposed method. The interstory drift and the acceleration as two responses of the case study are, respectively, obtained by utilizing Incremental Dynamic Analysis and nonlinear history analysis.

A ‘boundary layer’ finite element for thin multi-strake conical shells

Multi-strake cylindrical and conical shells of revolution are complex but commonplace industrial structures which are composed of multiple segments of varying wall thickness. They find application as tanks, silos, circular hollow sections, aerospace structures and wind turbine support towers, amongst others. The modelling of such structures with classical finite elements interpolated using low order polynomial shape functions presents a particular challenge, because many elements must be sacrificed solely in order to accurately represent the regions of local compatibility bending, so-called ‘boundary layers’, near shell boundaries, changes of wall thickness and at other discontinuities. Partitioning schemes must be applied to localise mesh refinement within the boundary layers and avoid excessive model runtimes, a particular concern in incremental nonlinear analyses of large models where matrix systems are handled repeatedly.In a previous paper, the authors introduced a novel axisymmetric cylindrical shell finite element that was enriched with transcendental shape functions to capture the bending boundary layer exactly, permitting significant economies in the element and degrees of freedom count, mesh design and model generation effort. One element is sufficient per wall strake. This paper extends this work to conical geometries, where axisymmetric elements enriched with Bessel functions accurately capture the bending boundary layer for both ‘shallow’ and ‘steep’ conical strakes, which are characterised by interacting and independent boundary layers, respectively. The bending shape functions are integrated numerically, with several integration schemes investigated for accuracy and efficiency. The potential of the element is illustrated through a stress analysis of a real 22-strake metal wind turbine support tower under self-weight. The work is part of a wider project to design a general three-dimensional ‘boundary layer’ element.

Debonding of FRP and thin films from an elastic half-plane using a coupled FE-BIE model

A Finite Element-Boundary Integral Equation (FE-BIE) coupling method is proposed to investigate a flexible bar weakly attached to an elastic orthotropic half-plane. Firstly, the analysis focused on the case of a bar subjected to horizontal forces and thermal loads considering interfacial displacements linearly proportional to the tangential traction. Secondly, the debonding behaviour of a composite reinforcement glued to a substrate has been modelled. Using an incremental nonlinear analysis, a bilinear elastic-softening interfacial traction-slip law has been implemented simulating the delamination of pure mode II. Finally, the influence of the anchorage length on the ultimate bearing capacity of the adhesive joint has been investigated.