Nonlinear FE Model Research Articles

Similarity measures for identifying material parameters from hysteresis loops using inverse analysis

Sum-of-square based error formulations may be difficult to implement on an inverse analysis consisting of multiple tension-compression hysteresis loops. Five alternative measures of similarity between curves are investigated as useful tools to help identify parameters from hysteresis loops with inverse analyses. A new algorithm is presented to calculate the area between curves. Four additional methods are presented from literature, which include the Partial Curve Mapping value, discrete Frechet distance, Dynamic Time Warping, and Curve Length approach. These similarity measures are compared by solving a non-linear regression problem resembling a single load-unload cycle. The measures are then used to solve more complicated inverse analysis, where material parameters are identified for a kinematic hardening transversely anisotropic material model. The inverse analysis finds material parameters such that a non-linear FE model reproduces the behavior from five experimental hysteresis loops. Each method was shown to find useful parameters for these problems, and should be considered a viable alternative when sum-of-square based methods may be difficult to implement. It is important to consider multiple similarity measures in cases when it is impossible to obtain a perfect match.

Effect of 3D random pitting defects on the collapse pressure of pipe — Part II: Numerical analysis

In the second part of this investigation, a 3D nonlinear (Finite Element) FE models was established to systematically study the collapse pressure of random corroded pipe. The models are developed within the framework of the nonlinear finite element ABAQUS in combination with a user defined Python program. Two constraints technique including surface-based tie constrain (SBTC) and shell-to-solid coupling (SSC) were implemented to take the complex geometry into account without the sacrifice of model accuracy while minimizing the computational cost. It was found that SBTC is more robust to simulate the locally random corroded pipe (external corrosion) than SSC. After validation models, a parametric investigation is performed to study the influence of wave number and amplitude of out-of-roundness, random pitting factors (pitting shape, pitting density and the length of pitting affect zone (LC)). It was revealed that the amplitude (wmax) and wave number (n) of out-of-roundness, pitting density and mass loss are the main factors that govern the collapse pressure (PCO) of 3D random corroded pipe whereas pitting shape has minor impact on PCO. Finally, a simplified pitting model was proposed, it was found that the circumferential and axial bending rigidity are key parameters that govern the PCO of pipe, which is mainly determined by the minimum remaining area in circumferential and axial direction.

Behaviour of stainless steel beam-to-column joints-part 2: Numerical modelling and parametric study

This paper reports a detailed numerical (FE) study on planar stainless steel beam-to-column joints. A nonlinear FE model is developed and validated against the first set on full-scale tests on stainless steel beam-to-column joints reported in the companion paper. The FE model is shown to accurately replicate the experimentally determined, initial stiffness, ultimate resistance, overall moment-rotation response and observed failure modes. Parametric studies are conducted to obtain the moment-rotation characteristics of a wide range of beam-to-column joints classified as semi-rigid and/or partial strength. Due to the low ductility of the bolts compared to the high ductility exhibited by all other stainless steel joint components, in all cases the strength and ductility of the simulated joints is limited by the failure of the connecting bolts. The design rules for stainless steel connections, which are based on the specifications of EN 1993-1-8 for carbon steel joints, are reviewed and are found to be overly conservative in terms of strength and inaccurate in terms of stiffness thus necessitating the development of novel design guidance in line with the observed structural response. These conclusions are in agreement with the ones reported in the companion paper.

Nonlinear compressive failure analysis of biaxially loaded fiber reinforced materials

Abstract The compressive failure behavior of defected periodic fiber-reinforced composites subjected to macroscopic biaxial loadings is here analyzed from both the theoretical and numerical point of view. The coupled effects of local fiber buckling and matrix or fiber/matrix interface microcracks under unilateral self-contact are included in the analysis by adopting an original full finite deformation approach. The obtained uniqueness and stability conditions associated with a continuum rate formulation of the microscopic equilibrium problem, contain unusual nonlinear contributions arising from crack interface self-contact mechanisms whose significance for an accurate evaluation of macroscopic critical loads at the onset of instability and bifurcation is then investigated in an innovative way. To this end by using a nonlinear FE model and analytical developments, the composite failure domains are determined for radial macroscopic loading paths, ranging from biaxial compression to combined axial compression and lateral expansion, and for different microgeometrical parameters. Comparisons with stability and uniqueness domains obtained when simplified crack contact interface approaches are adopted, show the notable role of the above mentioned crack interface contributions for a realistic prediction of the real failure behavior of the composite solid.

Evaluation of Bending Capacity of a New Type of Cold-Formed Steel Frame Wall Sheathed by Fiber-Cement Pressure Panels

This paper presents experimental research and finite element analysis (FEA) on a new type of frame wall that has fiber cement pressure (FCP) panel as sheathing. Some new structural details for the connection and energy conservation are proposed. In order to evaluate the bending capacity of the FCP frame wall, eight specimens with the parameters of stud spacing, connection styles, window opening, and loading sides were tested under uniformly distributed loads. The measurements of each material property were taken before the bending tests. Failure modes, load-deformation curves, and the strain of some key points were all obtained. The results indicate that the designed parameters affected the ultimate bearing capacity and failure mode of the specimens. Moreover, a non-linear FE model was made and verified against the tests. Results of FEA agree well with the experiment in failure modes and load-deformation curves. Therefore, FEA was confirmed as reliable for the prediction of the loading process. Finally, extended parametric analysis of FCP frame wall was conducted.

Local-flexural interactive buckling of standard and optimised cold-formed steel columns

This paper aims to study the interaction of local and overall flexural buckling in cold-formed steel (CFS) channels under axial compression. Detailed nonlinear FE models were developed and validated against a total of 36 axial compression tests on CFS plain and lipped channel columns with pin-ended boundary conditions. The numerical models incorporated the non-linear stress-strain behaviour of CFS material and enhanced properties of cold-worked corner regions obtained from coupon tests. The effects of initial geometric imperfections of the specimens measured by a specially designed set-up with laser displacement transducers were also taken into account. The developed FE models produced excellent predictions of the ultimate strength of the specimens obtained from experimental tests. The validated FE models and experimental results were then used to assess the adequacy of the effective width method in Eurocode 3 (EC3) and Direct Strength Method (DSM) in estimating the design capacity of a wide range of conventional and optimised design CFS channel column sections. The results indicate that Eurocode 3 provides conservative predictions (on average 21% deviation) for the compressive capacity of plain and lipped channel sections, while in general DSM predictions are more accurate for lipped channels. A comparison between FE predictions and tested results show that geometric imperfections can change the FE predictions by up to 20% and 40%, respectively, for lipped and plain channel columns, while the strain hardening effect at the rounded corner regions of the cross-sections is negligible. The results also confirmed that the proposed numerical model is able to provide a consistent and reliable prediction on the efficiency of a previously proposed optimisation methodology.

Finite element modelling of a cold curved steel plate girder

Cold bending is a cost-effective solution that is sometimes used for curving structural steel girders. Current usage for bridge structures is limited to projects that fall outside the jurisdiction of American Association of State Highway and Transportation Officials (AASHTO) because of the lack of technical knowledge surrounding this technique. This paper presents results from a three-dimensional finite element model to assess the structural behaviour exhibited by steel girders during bending for a proprietary cold curving system. A non-linear FE model is validated against measured data obtained from a previously tested girder. The FE model is extended to explore the performance of all structural components of the girder during bending such as deformations in flanges and web, residual stresses and plastic strains. Findings from this paper provide a framework for accurately predicting the cold bent geometry and how to incorporate residual stresses and plastic strains in the design of curved girders.

Effects of manufacturing plastic prestrains found on calendered and UOE pipes and pressure vessels on structural integrity assessments regarding fatigue crack growth and LBB

High responsibility components operating under cyclic loading can have their resistance against initiation and growth of fatigue cracks highly influenced by previous thermomechanical processing. Within the interest of the present work, different manufacturing processes (such as the fabrication of pipes using UOE) or installation procedures (such as pipe reeling) can lead to nonuniform plastic prestrain fields thus affecting lifetime and safety. Previous studies conducted by the authors revealed that prestraining up to 14% considerably reduced fatigue crack growth rates (da/dN-ΔK) for a hot-rolled (1/2”) ASTM-A36 steel as a result of strain hardening and its effects on plastic zone sizes. In addition, results also revealed two interesting trends: i) the larger is the imposed prestrain, the greater is the growth rate reduction in a nonlinear asymptotic relationship; ii) the larger is imposed ΔK, the more pronounced is the effect of prestraining. Within this scenario, this work explores the effects of those results on more realistic lifetime predictions applicable to pipelines and pressure vessels. First, a nonlinear model based on the experimental results was developed to predict crack growth rates (da/dN) as a function of ΔK and varying plastic prestrain levels. Second, refined nonlinear FE models were developed to quantify plastic prestrain fields caused by manufacturing sequence of the studied pressure vessels and pipes. Such fields proved to be remarkably nonuniform, in accordance to the literature. Finally, considering an idealized cyclic internal pressure and the obtained fields, a MatLab algorithm was implemented to predict fatigue crack growth rates until LBB (Leak Before Break) condition takes place. Best practices for implementing such evaluations are presented and results revealed that effects of plastic prestrains are not negligible and should be taken into account on recommended practices and structural integrity assessments to avoid excessive conservatism or lack of safety in applications.

Response prediction of laced steel-concrete composite beams using machine learning algorithms

This paper demonstrates the potential application of machine learning algorithms for approximate prediction of the load and deflection capacities of the novel type of Laced Steel Concrete-Composite1 (LSCC) beams proposed by Anandavalli et al. (Engineering Structures 2012). Initially, global and local responses measured on LSCC beam specimen in an experiment are used to validate nonlinear FE model of the LSCC beams. The data for the machine learning algorithms is then generated using validated FE model for a range of values of the identified sensitive parameters. The performance of four well-known machine learning algorithms, viz., Support Vector Regression (SVR), Minimax Probability Machine Regression (MPMR), Relevance Vector Machine (RVM) and Multigene Genetic Programing (MGGP) for the approximate estimation of the load and deflection capacities are compared in terms of well-defined error indices. Through relative comparison of the estimated values, it is demonstrated that the algorithms explored in the present study provide a good alternative to expensive experimental testing and sophisticated numerical simulation of the response of LSCC beams. The load carrying and displacement capacity of the LSCC was predicted well by MGGP and MPMR, respectively.

Parametric Study on Mixed Torsional Behavior of U‐Shaped Thin‐Walled RC Girders

Nowadays, U‐shaped thin‐walled concrete girders have been widely applied in the urban construction of rail viaducts in China as well as worldwide. However, the mixed torsional behaviors of these structures are not well understood. In this paper, the mixed torsional behaviors of the U‐shaped thin‐walled RC girders are theoretically analyzed, and a method predicting failure modes and ultimate torques is proposed. Nonlinear FE models based on ABAQUS to simulate the mixed torsional behaviors are built and calibrated with the test results. Parametric studies considering three crucial parameters (boundary condition, span length‐section height ratio, and ratio of longitudinal bars to stirrups) are conducted based on both the above suggested calculating method and the FE modeling. The calculated and the simulated results agree well with each other and with the test results. It is found that the failure modes of the U‐shaped thin‐walled RC girders under torsion are influenced by all the three parameters. Three kinds of failure modes are observed: flexural failures dominated by warping moment, shear failures caused by warping torque and circulatory torque, and flexural‐shear failures in the cases where flexural failure and shear failure appear almost at the same time.

Integration of system identification and finite element modelling of nonlinear vibrating structures

Abstract The Finite Element Method (FEM), Experimental modal analysis (EMA) and other linear analysis techniques have been established as reliable tools for the dynamic analysis of engineering structures. They are often used to provide solutions to small and large structures and other variety of cases in structural dynamics, even those exhibiting a certain degree of nonlinearity. Unfortunately, when the nonlinear effects are substantial or the accuracy of the predicted response is of vital importance, a linear finite element model will generally prove to be unsatisfactory. As a result, the validated linear FE model requires further enhancement so that it can represent and predict the nonlinear behaviour exhibited by the structure. In this paper, a pragmatic approach to integrating test-based system identification and FE modelling of a nonlinear structure is presented. This integration is based on three different phases: the first phase involves the derivation of an Underlying Linear Model (ULM) of the structure, the second phase includes experiment-based nonlinear identification using measured time series and the third phase covers augmenting the linear FE model and experimental validation of the nonlinear FE model. The proposed case study is demonstrated on a twin cantilever beam assembly coupled with a flexible arch shaped beam. In this case, polynomial-type nonlinearities are identified and validated with force-controlled stepped-sine test data at several excitation levels.

Geometrically nonlinear FE analysis of piezoelectric laminated composite structures under strong driving electric field

To give a precise prediction of piezolaminated smart structures under strong electric field resulting in large displacements and rotations, the paper develops various geometrically nonlinear models with taking into account the electroelastic material nonlinear effect. The present nonlinear FE formulations are derived based on the first-order shear deformation theory (FSDT) with taking into account various geometric nonlinearities, which include von Kármán type nonlinearity, moderate rotation nonlinearity, and large rotation nonlinearity. The constitutive equations with consideration of piezoelectric material nonlinearity are integrated into the present FE formulations. The proposed nonlinear FE models are first validated by experimental and numerical examples in the literature, and later on implemented into numerical analysis for piezolaminated smart plates and shells with applied strong electric field.

An experimental and theoretical fatigue study on macro fiber composite (MFC) under thermo-mechanical loadings

Macro fiber composite (MFC) is widely used for various applications especially in the area of sensors, actuator, structural health monitoring and vibration control due to its improved electro-mechanical coupling and flexibility. While being used for these applications, the MFCs might be subjected to cyclic mechanical load at various operating temperatures leading to the deterioration in the sensing performance. Hence, to study the life of the MFCs (d31 & d33 type) as a sensor, an experimental setup is devised and tests are performed for various thermo-mechanical loading conditions. Experiments involve huge investment in terms of cost and time. Therefore, in the present work, a theoretical model consisting of non-linear finite analysis integrated with the cumulative damage theory is derived to predict the fatigue behaviour of the MFC. The degradation in the piezoelectric coupling coefficient obtained using the present model is able to capture the non-linear trend observed from the experimental observations and the values are in good comparison. The non-linear FE model is also extended to predict the degradation of stiffnesses and strengths of the MFCs due to various thermo-mechanical loading conditions.

Fatigue study on the sensor performance of macro fiber composite (MFC): Theoretical and experimental approach

Due to its high flexibility and enhanced electro-mechanical coupling, macro fiber composite (MFC) is widely used in the area of sensing, vibration control and structural control. While in application, MFCs are subjected to continuous cyclic mechanical load which may lead to the deterioration of piezoelectric coupling coefficient, thereby affecting its sensing performance. In order to predict the life cycle of MFC (d31&d31 type) subjected to mechanical loading, an experimental setup has been devised and the tests are carried out for various loading conditions. For lowering the effort and cost involved in the experiments, a non-linear finite element model along with cumulative damage theory is introduced. The degradation in the piezoelectric coupling coefficient obtained using the current theoretical model are in good comparison with the experimental observations. The current non-linear FE model is also extended to predict the stiffnesses and strengths of the MFC as a function of fatigue cycles.

Multiobjective crashworthiness optimization of thin-walled structures with functionally graded strength under oblique impact loading

In this paper, the crashworthiness of a new introduced thin-walled structure made of hot stamping high strength steel with functionally graded strength (FGS), i.e. wall strength varying along the axial direction with a specific gradient, is investigated. The FGS columns are comprehensively studied under both axial crushing and oblique impact loading in the nonlinear FE mode LS_DYNA. The numerical simulation result shows that parameters of gradient exponent m and top strength S of FGS columns have a remarkable effect on the crashing behavior indicators such as critical load angle, energy absorption (EA) and peak crash force (PCF). To optimize the crashworthiness of the FGS columns, multi-objective optimization based on surrogate model of Radial Basis Function (RBF) and algorithm of Non-dominated Sorting Genetic Algorithm II (NSGA-II) are performed. To effectively consider the load angle uncertainty effect and obtain a more robust design, four schemes are employed to evaluate the comprehensive crashworthiness with different weight coefficient distributions. The result shows that all the Pareto fronts of FGS columns indicate considerably better crashworthiness compared to that of the counterpart uniform strength (US) columns. The consistent optimization result under different evaluation schemes not only provide guidance for the FGS column design, but also declare a good robustness for Pareto designs obtained by multi-objective optimization design (MOD) optimization. Finally, the obtained Pareto fronts of FGS columns are obviously found to consist of two parts. The first part contains the columns that possess gradient exponent ranging from 0 to 3 with top strength keeping a constant value near 480MPa. The second part consists of the columns that possess gradient exponent keeping constants close to 0 with the top strength ranging from 700 to 950MPa. This optimum results is different from that only obtained from pure axial crushing analyze in the previous researches and shows a better reference for engineering practice.

Nonlinear FE modelling and parametric study on flexural performance of ECC beams

Engineered Cementitious Composite (ECC) is a special class of the new generation of high performance fiber reinforced cementitious composites (HPFRCC) featuring high ductility with relatively low fiber content. In this research, the mechanical performance of ECC beams will be investigated with respect to the effect of slag and aggregate size and amount, by employing nonlinear finite element method. The validity of the models was verified with the experimental results of the ECC beams under monotonic loading. Based on the numerical analysis method, nonlinear parametric study was then conducted to evaluate the influence of the ECC aggregate content (AC), ECC compressive strength (fECC), maximum aggregate size (Dmax) and slag amount (ϕ) parameters on the flexural stress, deflection, load and strain of ECC beams. The simulation results indicated that when increase the slag and aggregate size and content no definite trend in flexural strength is observed and the ductility of ECC is negatively influenced by the increase of slag and aggregate size and content. Also, the ECC beams revealed enhancement in terms of flexural stress, strain, and midspan deflection when compared with the reference beam (microsilica MSC), where, the average improvement percentage of the specimens were 61.55%, 725%, and 879%, respectively. These results are quite similar to that of the experimental results, which provides that the finite element model is in accordance with the desirable flexural behaviour of the ECC beams. Furthermore, the proposed models can be used to predict the flexural behaviour of ECC beams with great accuracy.

A Nonlinear Model Inversion Method for Joint System Parameter, Noise, and Input Identification of Civil Structures

This paper presents a framework for nonlinear system identification of civil structures using sparsely measured dynamic output response of the structure. Using a sequential maximum likelihood estimation (MLE) approach, the unknown FE model parameters, the measurement noise variances, and the input ground acceleration time histories are estimated jointly. This approach requires the computation of FE response sensitivities with respect to the unknown FE model parameters (i.e., FE parameter sensitivities) as well as the FE response sensitivities with respect to the values of the input ground acceleration at every time step (i.e., FE input sensitivities). The FE parameter and input sensitivities are computed using the direct differentiation method (DDM). The presented output-only nonlinear FE model updating method is validated using the numerically simulated seismic response of a realistic three-dimensional five-story reinforced concrete building structure. The simulated building responses to a horizontal bi-directional seismic excitation is contaminated with artificial measurement noise and used to estimate the unknown FE model parameters characterizing the nonlinear material constitutive laws of the reinforced concrete, as well as the root mean square of the measurement noise at each measurement channel, and the full time history of the seismic base acceleration. The method presented in this paper provides a powerful framework for structural system and damage identification of civil structures, when the input excitations are not measured, are partially measured, or the measured input excitations are erroneous.

Nonlinear FE Modeling of Reinforced Concrete

Nonlinear FE Modeling of Reinforced Concrete

Experimental and FE analysis of stiffened steel I-column with slender sections

Abstract This paper presents an experimental and a FE analysis of the compressive behavior of slender section columns with and without stiffeners. A series of tests was performed on specimens with different overall heights and different number of stiffeners. A nonlinear three-dimensional FE model was developed using ANSYS program. The efficiency of the nonlinear FE model was verified and a parametric analysis was performed considering variation of number of stiffeners, values of web depth-to-thickness ratio, flange-to-thickness ratio, and slenderness ratio. The load carrying capacity of steel columns with large web-to-thickness ratio is noticeably enhanced up to 34% by increasing number of web stiffeners. Initial imperfection during fabrication should be well controlled and should be carefully considered in the FE modelling. Post local buckling strength of the sections is more sensitive to web width–thickness ratio than flange width–thickness ratio.

Failure analysis of a welded steel pipe at Kullar fault crossing

Abstract The seismic response of a 2200-mm-diameter welded steel pipe at strike slip Kullar fault crossing in Izmit, Kocaeli during 1999 Kocaeli earthquake is investigated. The pipe was crossing the fault-line with an angle of 55° and suffered leaks due to 3.0 m of right lateral movement of fault, which imposed compressive axial strain in the pipe. The backfill material of the trench was native soil which was non-homogenous (soft and stiff clay) with respect to fault line-soft material on the North side, stiff material on the South side. Field observations revealed two major wrinkles with finger width cracks and a minor wrinkle on the soft soil side of the fault. Large plastic strains and local folding were observed at wrinkles due to compressive strains. The case is known as one of the best documented fault crossing examples. The failure behavior of the Thames water pipe during 1999 Kocaeli earthquake is simulated by utilizing a 3D nonlinear continuum FE model. The numerical model considers contact surface at soil pipe interface and performs large deformation analyses of the pipe. The locations of wrinkles as well as axial displacements/rotations demands due to fault rupture are predicted. It is observed that once wrinkle initiates, strain in the pipe away from the wrinkle reduces after initial local buckling and additional shortening of the pipeline tends to accumulate at the wrinkle causing large plastic strains and rotation demands associated with fault rupture, an observation consistent with field observations and 2005 ALA guidelines.