Software Framework for Parameter Updating and Finite-Element Response Sensitivity Analysis

The finite-element software framework OpenSees is extended with parameter updating and response sensitivity capabilities to support client applications such as reliability, optimization, and system identification. Using software design patterns, member properties, applied loadings, and nodal coordinates can be identified and repeatedly updated in order to create customized finite-element model updating applications. Parameters are identified using a Chain of Responsibility software pattern, where objects in the finite-element model forward a parameterization request to component objects until the request is handled. All messages to identify and update parameters are passed through a Facade that decouples client applications from the finite-element domain of OpenSees. To support response sensitivity analysis, the Strategy design pattern facilitates multiple approaches to evaluate gradients of the structural response, whereas the Visitor pattern ensures that objects in the finite-element domain make the proper contributions to the equations that govern the response sensitivity. Examples demonstrate the software design and the steps taken by representative finite-element model updating and response sensitivity applications.     

Dynamic Allocation of Ragged Arrays Using C++: Potentiality for Finite-Element Method Software

A ragged array is an irregularly shaped data structure that is an extremely convenient and natural means of implementing storage schemes that exploit the symmetry and sparsity of the different stiffness matrices involved in the finite-element method. Ragged arrays have the potential for improving the programmer’s productivity as well as enhancing code maintainability. Additionally, no performance degradation was detected when ragged arrays were used; the performance of the Gauss elimination procedure, implemented in C++ using ragged arrays, was comparable to the performance of the same procedure implemented in FORTRAN using traditional data structures.     

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.     

Nonlinear Finite-Element Analysis of Posttensioned Concrete Bridge Girders

Posttensioning is an effective method for the construction of different types of bridge girders such as those used in segmentally erected bridges. Available nonlinear analysis programs for bridge girders under severe loading conditions are computationally expensive though. In addition, they neglect important phenomena such as bond-slip, friction, and anchorage losses. The objective of the proposed work is to develop a new nonlinear finite-element program for analysis of posttensioned bridge girders. The new model overcomes most of the difficulties associated with existing models. The model is based on the computationally efficient mixed formulation and considers bond, friction, and anchorage loss effects. The mixed formulation is characterized by its fast convergence, usually with very few finite elements and its robustness even under severe loading conditions. The posttensioning operation is accurately simulated using a phased-analysis technique, in which each stage of the posttensioning operation is simulated through a complete nonlinear analysis procedure. Correlation studies of the proposed model with experimental results of posttensioned specimens are conducted. These studies confirmed the accuracy and efficiency of the newly developed software program, which represents an advancement over existing commercial software packages for evaluating posttensioned bridge girders, in particular those subjected to severe loading conditions.     

Domain-by-Domain Algorithm for Nonlinear Finite-Element Analysis of Structures

Parallel and distributed computers have been shown to provide the necessary computational power to solve large-scale engineering problems. However, in order for this computation style to be effectively used, efficient computational algorithms must be devised. In this work, a domain-by-domain algorithm is developed for the parallel solution of nonlinear structural dynamics problems. In the proposed algorithm, the original structure is partitioned into a number of subdomains. Each subdomain is solved independently and, therefore, concurrently using a traditional direct-solution method. Finally, the solution for the interface degrees of freedom between neighboring subdomains is obtained by enforcing compatibility and equilibrium using an iterative procedure. The nonlinear version of the algorithm involves two iterations: The nonlinear dynamic equilibrium iteration and the interface equilibrium and compatibility iteration. The integration of these two iterations is investigated and two strategies are developed. It is found that the strategy in which the two iterations are isolated is the most efficient. As a demonstration, the fully nonlinear transient analysis of a 20-story model building is carried out. Excellent accuracy in the solution and significant speed up values are obtained.     

Nonlinear Finite-Element Analysis for Highway Bridge Superstructures

The most popular type of bridge in service today is the concrete deck on steel-girder composite bridge. A finite-element model is built to analyze the superstructure of this type of bridge under working load conditions. The deflections along a test bridge are computed by using this method; the results obtained are close to the experimental data. The concrete deck of the bridge is analyzed using nonlinear finite elements, of which the analytical procedure is described in detail. A comparison is also made between this method and the traditional transformed area method.     

Prediction of Damage Behaviors in Asphalt Materials Using a Micromechanical Finite-Element Model and Image Analysis

A study of the micromechanical damage behavior of asphalt concrete is presented. Asphalt concrete is composed of aggregates, mastic cement, and air voids, and its load carrying behavior is strongly related to the local microstructural load transfer between aggregate particles. Numerical simulation of this micromechanical behavior was accomplished by using a finite-element model that incorporated the mechanical load-carrying response between aggregates. The finite-element scheme used a network of special frame elements each with a stiffness matrix developed from an approximate elasticity solution of the stress and displacement field in a cementation layer between particle pairs. Continuum damage mechanics was then incorporated within this solution, leading to the construction of a microdamage model capable of predicting typical global inelastic behavior found in asphalt materials. Using image processing and aggregate fitting techniques, simulation models of indirect tension, and compression samples were generated from surface photographic data of actual laboratory specimens. Model simulation results of the overall sample behavior and evolving microfailure/fracture patterns compared favorably with experimental data collected on these samples.     

Consistent Finite-Element Response Sensitivity Analysis

This paper examines the important issue of response sensitivities of dynamic models of structural systems to both material and (discrete) loading parameters. Plasticity-based finite-element models of structural systems subjected to base excitation such as earthquake loading are considered. The two methods for computing the response sensitivities, namely, (1) discretizing in time the time continuous-spatially discrete response equations and differentiating the resulting time discrete-spatially discrete response equations with respect to sensitivity parameters, and (2) differentiating the time continuous-spatially discrete response equations with respect to sensitivity parameters and discretizing in time the resulting time continuous-spatially discrete response sensitivity equations, are clearly distinguished. The discontinuities in time of the response sensitivities arising due to material state transitions in the plasticity models, and their propagation from the quadrature point level to the global structural response level are discussed using a specific one-dimensional plasticity model. The procedure to obtain the exact sensitivities of the numerical nonlinear finite-element response, including proper capture of their discontinuities, is formalized. Application examples illustrating the concepts are presented at the end.     

Contribution of Nonlinear Finite-Element Analysis to Evaluation of Two Structural Concrete Failures

The failure of two reinforced concrete structures is recounted, one involving a warehouse structure and the other an offshore platform base structure. Design details and factors leading to the collapses are identified and discussed. The structures were subsequently analyzed using nonlinear finite-element analysis procedures, taking into account relevant second-order behavior models. The analyses provided an accurate assessment of the load capacities and failure modes observed, as well as meaningful insights into the underlying behavior mechanisms and factors leading to the failures. This paper supports the view that nonlinear analysis techniques have become useful everyday tools for design office applications, particularly in forensic work, and also gives evidence suggesting that errors in the design of modern structures can be potentially more catastrophic than in the past, and that advanced assessment techniques will assume increased importance as a result.     

New Multidimensional Visualization Technique for Limit-State Surfaces in Nonlinear Finite-Element Reliability Analysis

Structural reliability problems involving the use of advanced finite-element models of real-world structures are usually defined by limit-states expressed as functions (referred to as limit-state functions) of basic random variables used to characterize the pertinent sources of uncertainty. These limit-state functions define hyper-surfaces (referred to as limit-state surfaces) in the high-dimensional spaces of the basic random variables. The hyper-surface topology is of paramount interest, particularly in the failure domain regions with highest probability density. In fact, classical asymptotic reliability methods, such as the first- and second-order reliability method (FORM and SORM), are based on geometric approximations of the limit-state surfaces near the so-called design point(s) (DP). This paper presents a new efficient tool, the multidimensional visualization in the principal planes (MVPP) method, to study the topology of high-dimensional nonlinear limit-state surfaces (LSSs) near their DPs. The MVPP method allows the visualization, in particularly meaningful two-dimensional subspaces denoted as principal planes, of actual high-dimensional nonlinear limit-state surfaces that arise in both time-invariant and time-variant (mean out-crossing rate computation) structural reliability problems. The MVPP method provides, at a computational cost comparable with SORM, valuable insight into the suitability of FORM/SORM approximations of the failure probability for various reliability problems. Several application examples are presented to illustrate the developed MVPP methodology and the value of the information provided by visualization of the LSS.     

Microstructural Finite-Element Analysis of Influence of Localized Strain Distribution on Asphalt Mix Properties

Hot mix asphalt (HMA) is a composite material that consists of mineral aggregates, asphalt binders, and air voids. A finite element model of the HMA microstructure is developed to study the influence of localized strain distribution on the HMA mechanical response. Image analysis techniques are used to capture the HMA microstructure. Due to limitations on the image resolution, the microstructure is divided into two phases: aggregates larger than 0.3 mm and mastic (binder and aggregates smaller than 0.3 mm). A viscoelastic constitutive relationship is used to represent the mastic phase of the HMA microstructure. The mastic viscoelastic properties are obtained from the results of testing asphalt binders in a dynamic shear rheometer and microstructure analysis of idealized mastic. A step-wise finite element procedure is employed in order to account for the influence of the localized high strains on the mastic viscoelastic properties, and HMA mechanical response. The mastic and binder elements of the microstructure are shown to exhibit high strain values within the nonlinear viscoelastic range. The HMA viscoelastic properties are calculated at different strain levels, and the results are compared with experimental data obtained from the frequency sweep shear test.     

Flow Computation and Mass Balance in Galerkin Finite-Element Groundwater Models

In most groundwater modeling studies, quantification of the flow rates at domain and subdomain boundaries is as important as the computation of the groundwater heads. The computation of these flow rates is not a trivial task when a finite-element method is chosen to solve the groundwater equation. Generally, it is believed that finite-element methods do not conserve mass locally. In this paper, a postprocessing technique is developed to compute mass-conserving flow rates at element faces. It postprocesses the groundwater head field obtained by the Galerkin finite-element method, and the calculated flow rates conserve mass locally and globally. The only requirement for the postprocessor to be applicable is the irrotationality of the flow field, i.e., the curl of the Darcy flux should be zero. The accuracy and the mass conservation properties of the new postprocessor are demonstrated using several test problems that include one-, two-, and three-dimensional flow systems in both homogeneous and heterogeneous aquifer conditions.     

Computer-Aided Model Generation for Nonlinear Structural Analysis Using a Structural Component Model Database

This paper presents an approach for efficiently building analytical models for nonlinear analysis. The objective has been achieved by establishing structural component model database by collecting various structural component models addressing various structural details. A common data structure and a relational database schema for storing structural component models were proposed in this study. The proposed structural component model database can serve as a decision supporting system for building nonlinear analytical models manually. In addition, the modeling information stored in this database can be presented in XML document format to be parsed and manipulated by computer system for generating nonlinear analytical model in file automatically. A school building database is used as a case study to show the feasibility of automatic modeling for nonlinear analysis using the proposed structural component database. A semiautomatic model generation system was developed to provide an efficient modeling process, which is in the manner of form filling and option selecting on web-based user interfaces, so that the model builder can focus on making engineering decisions. The modeling details are handled automatically by the proposed system based on user selection and setting.     

Nonlinear Analysis of Masonry Arches Strengthened with Composite Materials

The nonlinear behavior of masonry arches strengthened with externally bonded composite materials is investigated. A finite-element (FE) formulation that is specially tailored for the nonlinear analysis of the strengthened arch is developed. The FE formulation takes into account material nonlinearity of the masonry construction and high-order kinematic relations for the layered element. Implementation of the above concept in the FE framework reduces the general problem to a one-dimensional nonlinear formulation in polar coordinates with a closed-form representation of the elemental Jacobian matrix (tangent stiffness). A numerical study that examines the capabilities of the model and highlights various aspects of the nonlinear behavior of the strengthened masonry arch is presented. Emphasis is placed on the unique effects near irregular points and the nonlinear evolution of these effects through the loading process. A comparison with experimental results and a discussion of the correlating aspects and the ones that designate needs of further study are also presented.     

Seepage from Lined Canal Using Finite-Element Method

The problem of steady-state seepage from a lined canal toward asymmetrical drainages has been solved using the finite-element method, analyzing the effect of canal lining on canal seepage discharge. Studies show that the effectiveness of canal lining in reducing seepage is less when drainage distance is large. With a decrease in the permeability of the canal lining, the canal seepage also decreases; however, the decrease in canal seepage is relatively more when the ratio of lining permeability and subsoil permeability ranges in the region from 2. The decrease in canal seepage is very steep with initial increase in the lining thickness. However, with further increase in the lining thickness, the decrease in canal seepage is not very significant. Therefore, an effective lining permeability must range between 1 and 1 of the subsoil permeability and its thickness must be kept less than 0.2, where h1 is the difference between right drainage water level and canal water level.     

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.     

Model Uncertainty in Finite-Element Analysis: Bayesian Finite Elements

In this paper, probabilistic models for structural analysis are put forward, with particular emphasis on model uncertainty. Context is provided by the finite-element method and the need for probabilistic prediction of structural performance in contemporary engineering. Sources of model uncertainty are identified and modeled. A Bayesian approach is suggested for the assessment of new model parameters within the element formulations. The expressions are formulated by means of numerical “sensors” that influence the model uncertainty, such as element distortion and degree of nonlinearity. An assessment procedure is proposed to identify the sensors that are most suitable to capture model uncertainty. This paper presents the general methodology and specific implementations for a general-purpose structural element. Two numerical examples are presented to demonstrate the methodology and its implications for probabilistic prediction of structural response.     

Finite-Element Analysis of Helical Piers in Frozen Ground

This paper presents a study of the behavior of helical pier foundations in frozen ground. The scope of the work presented includes developing finite-element analysis (FEA) models that simulate the stress-strain relationships in the pier and in the surrounding frozen soil. The paper also presents the results of the analysis models developed. The FEA computer program ANSYS is used to perform the computations that include three phases: The first phase is related to the instantaneous stability of piers in frozen or thawed soil under applied design loads. The second phase is related to the analysis of the pier strength during installation into frozen ground when the piers need to withstand installation torque and axial loads. The third phase is related to the long-term stability and critical loads of piers owing to creep in frozen soil. The most important finding of the analysis is that the load is not distributed into the frozen ground equally by the helixes of a multi-helix pier; instead, the bottom helix transfers most of the load.     

Two-Dimensional Nonlinear Analysis of Long Cables

A simple finite-difference iterative model is presented here for the nonlinear analysis of a long inclined cable due to its self-weight and other concentrated loads in between. The input requires the end coordinates, area of cross section, modulus of elasticity, and initial tension of the cable. If the ends of the cable are subjected to displacements, the tension in the cable varies nonlinearly and the new deformed shape is computed using an iterative procedure. Unlike finite-element methods, initial cable geometry is not required here, and the method automatically computes the initial geometry even with concentrated loads.     

Bridge Structural Condition Assessment Using Systematically Validated Finite-Element Model

The structural condition assessment of highway bridges is largely based on visual observations described by subjective indices, and it is necessary to develop a methodology for an accurate and reliable condition assessment of aging and damaged structures. This paper presents a method using a systematically validated finite-element model for the quantitative condition assessment of a damaged reinforced concrete bridge deck structure, including damage location and extent, residual stiffness evaluation, and load-carrying capacity assessment. In a trial of the method in a cracked bridge beam, the residual stiffness distribution was determined by model updating, thereby locating the damage in the structure. Furthermore, the damage extent was identified through a defined damage index and the residual load-carrying capacity was estimated.