Handling of Constraints in Finite-Element Response Sensitivity Analysis

In this paper, the direct differentiation method (DDM) for finite-element (FE) response sensitivity analysis is extended to linear and nonlinear FE models with multi-point constraints (MPCs). The analytical developments are provided for three different constraint handling methods, namely: (1) the transformation equation method; (2) the Lagrange multiplier method; and (3) the penalty function method. Two nonlinear benchmark applications are presented: (1) a two-dimensional soil-foundation-structure interaction system and (2) a three-dimensional, one-bay by one-bay, three-story reinforced concrete building with floor slabs modeled as rigid diaphragms, both subjected to seismic excitation. Time histories of response parameters and their sensitivities to material constitutive parameters are computed and discussed, with emphasis on the relative importance of these parameters in affecting the structural response. The DDM-based response sensitivity results are compared with corresponding forward finite difference analysis results, thus validating the formulation presented and its computer implementation. The developments presented in this paper close an important gap between FE response-only analysis and FE response sensitivity analysis through the DDM, extending the latter to applications requiring response sensitivities of FE models with MPCs. These applications include structural optimization, structural reliability analysis, and finite-element model updating.     

Estimating Work Zone Road User Cost for Alternative Contracting Methods in Highway Construction Projects

Highway construction often causes an additional road user cost (RUC) to motorists due to traffic flow interruption and congestion in work zones. Consequently, facility owners, such as the Florida Department of Transportation (FDOT), are often interested in using alternative contracting methods such as A+B contracting to expedite construction. Although many of these contracting methods rely on the RUC to determine incentives or disincentives, no standard method for RUC calculation is available to FDOT district engineers. In addition, existing methods are neither practical nor user-friendly for determining incentives or disincentives. This study intends to develop a RUC calculation procedure for the FDOT that focuses on using data that are easily accessible to FDOT district engineers, such as drawings and maintenance of traffic plans. The procedure is developed based on traffic analysis methods published in the Highway Capacity Manual, previous studies on user benefit analysis and work zones, and empirical data specific to Florida. Case studies are used to illustrate the procedure and to compare it with two other existing models, the Arizona model and the queue and user cost evaluation of work zone model, through correlation analysis, comparison of calculation assumptions, and data input analysis. This study shows that the suggested procedure produces consistent RUC estimates.     

Influence of Spatial Variability on Slope Reliability Using 2-D Random Fields

The paper investigates the probability of failure of slopes using both traditional and more advanced probabilistic analysis tools. The advanced method, called the random finite-element method, uses elastoplasticity in a finite-element model combined with random field theory in a Monte-Carlo framework. The traditional method, called the first-order reliability method, computes a reliability index which is the shortest distance (in units of directional equivalent standard deviations) from the equivalent mean-value point to the limit state surface and estimates the probability of failure from the reliability index. Numerical results show that simplified probabilistic analyses in which spatial variability of soil properties is not properly accounted for, can lead to unconservative estimates of the probability of failure if the coefficient of variation of the shear strength parameters exceeds a critical value. The influences of slope inclination, factor of safety (based on mean strength values), and cross correlation between strength parameters on this critical value have been investigated by parametric studies in this paper. The results indicate when probabilistic approaches, which do not model spatial variation, may lead to unconservative estimates of slope failure probability and when more advanced probabilistic methods are warranted.     

Multicomponent diffusion simulation based on finite elements

A numerical model is presented to treat multicomponent, multiphase diffusion problems. Unlike other recent approaches that are based on the finite-difference method, analytical solutions, or particular thermodynamic models, a general procedure based on the finite-element technique is applied. The suggested formalism is based on the solution of the integral statement of the generalized diffusion equation. This treatment allows for a simple implementation of particular boundary conditions and can easily be extended from a one- to a multidimensional analysis. A brief overview of the formal representation of multicomponent diffusion coefficients, as suggested by Andersson and Agren, is given. The finite-element diffusivity matrices are evaluated for a one-dimensional bar and a two-dimensional triangular element. The model is applied to some classical examples in diffusion simulation in both one and two dimensions. The results are compared to available analytical solutions or experimental data.     

Mixed Finite Element for Three-Dimensional Nonlinear Dynamic Analysis of Rectangular Concrete-Filled Steel Tube Beam-Columns

A beam finite-element formulation following Euler-Bernoulli beam theory is presented for geometrically and materially nonlinear analysis of rectangular concrete-filled steel tube (RCFT) beam-columns. The formulation is geared for conducting transient dynamic analysis of composite steel/concrete frame structures. The element stiffness and internal forces were derived through adopting a mixed finite-element approach based on the Hellinger-Reissner variational principle. The load transfer between the steel and concrete constitutive materials was provided through steel and concrete interface via friction and interlocking. Six extra translational degrees-of-freedom (DOFs) were added to the conventional 12 DOF beam element to quantify the differential displacement between the two media. The formulation was verified for a range of geometrically nonlinear test problems and geometrically and materially nonlinear RCFT experimental test specimens from the literature. Strong correlation and convergence characteristics were achieved compared to the published results.     

Failure of Web-Flange Junction in Postbuckled Pultruded I-Beams

A numerical procedure for analyzing a common and catastrophic failure mode in pultruded composite material I-beams is presented in this paper. Pultruded wide-flange profiles (often referred to as I-beams) exhibit a number of different failure modes when loaded in flexure or axial compression. The particular failure mode of interest to this paper is that due to the local separation of the flange from the web of the profile following local buckling of the flange. A node-separation technique is used to simulate the progressive failure of the joint between the flange and the web of the wide-flange beam in the postbuckled regime. The procedure has been implemented in NIKE3D, a multipurpose nonlinear implicit finite-element code. The fundamentals of the separation algorithm and the mechanics of the implementation in NIKE3D are described. The results of simulations using the proposed procedure are compared with experimental observations.     

Numerical Analysis of Geomaterials within Theory of Porous Media

It is widely accepted that the mechanical behavior of saturated geomaterials is largely governed by the interaction of the solid skeleton with the fluids present in the pore structure. This interaction is particularly strong in quasi-static and dynamic problems and may lead to the catastrophic loss of strength known as liquefaction, which frequently occurs under earthquake loading. In this work, numerical simulations of saturated granular deposits under transient loads are presented to illustrate the performance of a u-p-U finite-element method formulation and the versatility of the numerical implementation. Closed-form solutions based on both a Biot formulation and modern theories of mixtures are compared with numerical results. In addition, centrifuge experimental results are correlated with numerical simulations. A companion paper presents the details of the theoretical formulation and the numerical implementation within the finite-element method.     

Performance Evaluation of FRP Bridge Deck Component under Torsion

Torsional response of fiber-reinforced polymeric (FRP) composites is more complex than conventional materials. Therefore, understanding torsional response of FRP components along with shear behavior leads to development of safe and accurate design specifications. Experimental data of multicellular FRP bridge deck components have been compared with simplified theoretical model studies focused on torsional rigidity, equivalent in-plane shear modulus, in-plane shear strain, and joint efficiency. Simplified classical lamination theory (SCLT) is used to predict torsional rigidity. Results from SCLT, experimental data, and finite-element analysis validate proposed methodology to find torsional rigidity. Data on torsional rigidity and equivalent in-plane shear modulus correlated (less than 12%) with results from SCLT and finite-element analysis. In-plane shear strain based on SCLT is also concordant with test results. In an FRP deck system with 100% joint efficiency, the two-dimensional effect (plate action) on torsional rigidity results in a 20% higher rigidity when compared to a beam model. However, if a refined model has only 80% joint efficiency, then plate action results in a 6% difference from the beam model. In addition, service load design criteria for FRP decks under shear must not excess 16% of the ultimate strain by accounting for environmental and aging effects.     

Methods and Object-Oriented Software for FE Reliability and Sensitivity Analysis with Application to a Bridge Structure

This paper addresses the growing demand for finite-element software with capabilities to incorporate uncertainty in the input parameters. Reliability and response sensitivity algorithms are implemented in the general-purpose finite-element software OpenSees, which employs an object-oriented programming approach to achieve a sustainable software with focus on maintainability and extensibility. The product is a comprehensive and freely available library of software tools for finite-element reliability and response sensitivity analysis. A numerical example involving a detailed model of a highway bridge with inelastic material behavior and 320 random variables is presented to demonstrate features of the methodology and the software. Importance vectors are employed to rank the input parameters according to their relative influence on the structural reliability. The required response sensitivities are obtained by an extensive implementation of the direct differentiation method.     

Thermodynamic Consistent Formulations of Viscoplastic Deformations in FCC Metals

A general consistent thermodynamic framework for small strain thermoviscoplastic deformations of face-centered cubic (FCC) metals is presented in this study. An appropriate and consistent Helmholtz free energy definition is incorporated, after considering the strain rate effect imbedded through the hardening definition, in deriving the proposed three-dimensional kinematical model. Microstructural physically based thermal and athermal yield function definitions (von Mises type) are utilized in this work for dynamic and static deformations of FCC metals. A length scale parameter introduced implicitly through the viscosity parameter is related to the waiting time of dislocations at an obstacle. The role of material dependence in setting the character of the governing equations is illustrated in the context of a simple uniaxial tensile problem in order to check the effectiveness and the performance of the proposed framework and its finite-element implementation. Results obtained for OFHC copper at low and high strain rates and temperatures show, generally, good comparisons with experimental results.     

Zigzag Sublaminate Model for Nonlinear Analysis of Laminated Panels

A geometrically nonlinear first-order zigzag sublaminate theory and finite-element model are presented that account for moderately large displacements and moderate rotations using a total Lagrangian formulation. The model contains special laminated plate bending kinematics but is cast in the form of a 3D eight-noded brick finite-element topology with five engineering degrees of freedom per node—three translations and two rotations. This permits discretization through the thickness of a laminate to obtain higher accuracy of displacements and stresses when required. The accuracy of the present model is demonstrated by comparing its structural response predictions with results from previous experimental investigations and with numerical tests using a commercial finite-element code.     

Mesomechanical Model for Numerical Study of Two-Dimensional Triaxially Braided Composite

A mesoscale three-dimensional finite-element model is set up to model two-dimensional triaxially braided composites. Unit cell scheme is used to take into account braiding architecture as well as mechanical behavior of fiber tows, matrix, and fiber tow interface. A 0°/±60° braiding configuration has been studied. A failure criterion and progressive damage evolution model taking into account fiber tow and tow interface has been applied to theoretically predict interlaminar and intralaminar failure mode. Straight-sided specimen testing has been carried out in both axial and transverse direction. Results obtained in the tests as well as finite-element approaches are discussed. This paper also discusses the main feature of the model through an extensive parameter study. Overall, by comparison of experiment and model results, the applicability of the developed model is assessed and the failure process is investigated; furthermore, conducted parameter study enhances the strength of the model, which lies in the correlation of model parameters and identification of damage modes with experimental data on the overall stress strain curves.     

Reliability Analysis of Suspension Bridges against Fatigue Failure from the Gusting of Wind

A fatigue reliability analysis of suspension bridges due to the gustiness of the wind velocity is presented by combining overall concepts of bridge aerodynamics, fatigue analysis, and reliability analysis. For this purpose, the fluctuating response of the bridge deck is obtained for buffeting force using a finite-element method and a spectral analysis in frequency domain. Annual cumulative fatigue damage is calculated using Palmgren–Miner’s rule, stress-fatigue curve approach and different forms of distribution for stress range. In order to evaluate the reliability, both first-order second-moment (FOSM) method and full distribution procedure (assuming Weibull distribution for fatigue life) are used to evaluate the fatigue reliability. Probabilities of fatigue failure of the Thomas Bridge and the Golden Gate Bridge for a number of important parametric variations are obtained in order to make some general observations on the fatigue reliability of suspension bridges. The results of the study show that the FOSM method predicts a higher value of the probability of fatigue failure as compared to the full distribution method. Further, the distribution of stress range used in the analysis has a significant effect on the calculated probability of fatigue failure in suspension bridges.     

Numerical Implementation of Polymer Viscoplastic Equations for High Strain-Rate Composite Models

For polymer matrix composites subjected to large strain rates, it is important to correctly characterize the nonlinear and strain-rate dependent response of polymers. Viscoplastic constitutive material models have been developed to account for the effects of hydrostatic effects and inelastic strains in polymer materials. The effective implementation of such viscoplastic models is important for development of composite models geared toward practical applications. Goldberg’s polymer model numerical implementation into a commercial finite-element code constitutes the main objective of this paper. Special attention is given to the use of effective algorithms for solving the model nonlinear rate dependent viscoplastic equations. Existent experimental data are used to verify the accuracy and robustness of the computational polymer model. A phenomenological fiber model and a simplified iso-strain mixture theory used to obtain the resultant stresses in the composite by averaging the stresses of the individual constituents are also defined. The validation of the simplified mixture theory for the composite model will be presented later on.     

Performance Evaluation of FRP Composite Deck Considering for Local Deformation Effects

We examine here the replacement of a deteriorated concrete deck in the historic Hawthorne Street Bridge in Covington, Va. with a lightweight fiber-reinforced polymer (FRP) deck system (adhesively bonded pultruded tube and plate assembly) to increase the load rating of the bridge. To explore construction feasibility, serviceability, and durability of the proposed deck system, a two-bay section (9.45 by 6.7?m) of the bridge has been constructed and tested under different probable loading scenarios. Experimental results show that the response of the deck is linear elastic with no evidence of deterioration at service load level (HS-20). From global behavior of the bridge superstructure (experimental data and finite- element analysis), degree of composite action, and load distribution factors are determined. The lowest failure load (93.6?kips or 418.1?kN) is about 4.5 times the design load (21.3?kips or 94?kN), including dynamic allowance at HS-20. The failure mode is consistent in all loading conditions and observed to be localized under the loading patch at the top plate and top flange of the tube. In addition to global performance, local deformation behavior is also investigated using finite-element simulation. Local analysis suggests that local effects are significant and should be incorporated in design criteria. Based on parametric studies on geometric (thickness of deck components) and material variables (the degree of orthotropy in pultruded tube), a proposed framework for the sizing and material selection of cellular FRP decks is presented for future development of design guidelines for composite deck structures.     

General Formulation of Two Kinematic Hardening Constitutive Models with a Smooth Elastoplastic Transition

Two new constitutive models formulated within the framework of kinematic hardening plasticity are presented and their implementation into a finite-element program is described. The models are extensions of two existing constitutive models for reconstituted clays and introduce a number of kinematic surfaces within the modified CAM clay bounding surface. The new key feature of the models is a hardening modulus which results in a smooth variation of stiffness with strain, from the high elastic value, within the first kinematic surface, to the value on the bounding surface. Other features include a mathematical formulation of the models in general stress space to facilitate their implementation into a finite-element program, a variety of shapes of the yield and plastic potential surfaces in the deviatoric plane, and the novel concept of changing the active yield surface, which is necessary for the consistent formulation and implementation of the models into a finite-element code. The models are shown to have the ability to reproduce realistically the observed nonlinear prefailure behavior of overconsolidated clays in the small strain range.     

Probabilistic Slope Stability Analysis by Finite Elements

In this paper we investigate the probability of failure of a cohesive slope using both simple and more advanced probabilistic analysis tools. The influence of local averaging on the probability of failure of a test problem is thoroughly investigated. In the simple approach, classical slope stability analysis techniques are used, and the shear strength is treated as a single random variable. The advanced method, called the random finite-element method (RFEM), uses elastoplasticity combined with random field theory. The RFEM method is shown to offer many advantages over traditional probabilistic slope stability techniques, because it enables slope failure to develop naturally by “seeking out” the most critical mechanism. Of particular importance in this work is the conclusion that simplified probabilistic analysis, in which spatial variability is ignored by assuming perfect correlation, can lead to unconservative estimates of the probability of failure. This contradicts the findings of other investigators who used classical slope stability analysis tools.     

Response of RC Beams Strengthened with CFRP Laminates and Subjected to a High Rate of Loading

Results are presented of an experimental program undertaken to investigate the effects of strain rate on the behavior of reinforced concrete (RC) beams strengthened with carbon fiber-reinforced polymer (CFRP) laminates. Nine 3-m RC concrete beams, one unstrengthened, four strengthened with S-type CFRP laminates, and four strengthened with R-type laminates, were loaded under four different loading schedules. The stroke rates ranged from 0.0167 mm∕s (slow rate of loading) to 36 mm∕s (fast rate of loading). This induced a strain rate in the CFRP of 2.96 με∕s (slow rate) to 6,930 με∕s (fast rate). Some beams were subjected to either 1 or 12 cycles of loading prior to a fast rate of loading to failure. The rapidly loaded beams showed an increase of approximately 5% in capacity, stiffness, and energy absorption. Ductility and the mode of failure were not directly affected by the change in loading rate. Precycled beams performed similarly to the beams loaded monotonically to failure but showed a 10% increase in service stiffness and a 10% loss in energy absorption. A finite-element, layered analysis is presented to predict the moment-curvature response of CFRP strengthened RC beams. The model includes the effects of strain rate and correlates well with the experimental data.     

Numerical Model for Tracing the Response of FRP-Strengthened RC Beams Exposed to Fire

This paper presents the development of a numerical model for evaluating the performance of fiber-reinforced polymer (FRP)-strengthened RC beams under fire conditions. The model is based on a macroscopic finite-element approach and utilizes moment-curvature relationships to trace the response of insulated FRP-strengthened RC beams from linear elastic stage to collapse under any given fire exposure and loading scenarios. In the analysis, high temperature properties of constitutive materials, load and restraint conditions, material and geometric nonlinearity are accounted for, and a realistic failure criterion is applied to evaluate the failure of the beams. The model is validated against fire test data on FRP-strengthened RC beams and is applied to study the effect of FRP-strengthening, insulation scheme, and failure criterion on the fire response of FRP-strengthened RC beams. Results from the analysis indicate that FRP-strengthened RC beams should be protected with supplemental fire insulation to satisfy fire resistance requirements. A case study is presented to illustrate the application of the model for optimizing the fire insulation scheme to achieve required fire resistance in FRP-strengthened concrete beams.     

Probabilistic Analysis of Coupled Soil Consolidation

Coupled Biot consolidation theory was combined with the random finite-element method to investigate the consolidation behavior of soil deposits with spatially variable properties in one-dimensional (1D) and two-dimensional (2D) spaces. The coefficient of volume compressibility (mv) and the soil permeability (k) are assumed to be lognormally distributed random variables. The random fields of mv and k are generated by the local average subdivision method which fully takes account of spatial correlation, local averaging, and cross correlations. The generated random variables are mapped onto a finite-element mesh and Monte Carlo finite-element simulations follow. The results of parametric studies are presented, which describe the effect of the standard deviation, spatial correlation length, and cross correlation coefficient on output statistics relating to the overall “equivalent” coefficient of consolidation. It is shown that the average degree of consolidation defined by excess pore pressure and settlement are different in heterogeneous soils. The dimensional effect on the soil consolidation behaviors is also investigated by comparing the 1D and 2D results.