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.     

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.     

Transient Dynamic Nonlinear Analysis Using MIMD Computer Architectures

This paper presents research on the use of homogeneous parallel and heterogeneous distributed computers for finite-element analysis of transient dynamic problems using a message passing interface. The appropriate computer architectures are discussed, and this review is the basis for the development of a new definition of computational efficiency for heterogeneously distributed finite-element analysis. A code for the transient nonlinear analysis of reinforced concrete plates is profiled. It is demonstrated that although the code is efficient for homogeneous computing systems a new message passing procedure must be developed for heterogeneously distributed systems. A new algorithm is developed and tested on a heterogeneous system of workstations.     

Sensitivity Statistics of 3D Structures under Parametric Uncertainty

Determination of sensitivity gradient is a major prerequisite for structural optimization, reliability assessment, and parameter identification. As the conventional deterministic sensitivity analysis cannot provide complete information, stochastic analysis is needed to tackle the uncertainties in structural parameters. This study focuses on the utility of the stochastic finite-element method for random response sensitivity analysis. The stochastic modeling of a random parameter is based on a commonly used 2D local averaging method generalized for a 3D case. The Choleski decomposition technique is then employed for digital simulation. The Neumann expansion based finite-element simulation method is extended for stochastic sensitivity analysis. This technique leads to a considerable saving of computational time. Example problems are used to compare the accuracy of this method to the direct Monte Carlo simulation and perturbation method in terms of varying stochasticity and efficiency in CPU time.     

Parallel Computing Techniques for Sensitivity Analysis in Optimum Structural Design

Among different activities of the optimum structural design using the gradient-based optimization approaches, design sensitivity analysis is the most time-consuming computational process. By introducing parallel computing techniques for sensitivity computation, significant speedup has been obtained in optimum structural design. Computation of design sensitivities is characteristically uncoupled, thus opening the door to parallelization. In this paper, two types of approaches viz. single-level and multilevel parallelisms are pursued for design sensitivities. The design sensitivities are computed using analytical and finite-difference methods. Numerical studies show that the performance of the parallel algorithms for design sensitivities on message passing systems is very good. Good speedups have been achieved in parallel multilevel sensitivity calculation. The parallel algorithms for design sensitivity analysis have been implemented on message passing parallel systems within the software platform of Parallel Computer Adaptive Language.     

Parameter Sensitivity and Importance Measures in Nonlinear Finite Element Reliability Analysis

Finite element reliability methods allow the analyst to define material, load, and geometry parameters as random variables to represent uncertainties in these model parameters. Approximate probabilistic analysis methods produce estimates of the response variance/covariances, probabilities of exceeding specified structural performance thresholds, and parameter importance measures. A necessary ingredient for such analysis is consistent, efficient, and accurate algorithms for computing finite element response sensitivities. In this paper, unified response sensitivity equations with respect to material, load, and geometry parameters are developed for the time- and space-discretized finite element model. The sensitivities with respect to nodal coordinates and global shape parameters in the presence of material and geometric nonlinearities represent an extension of previous work. Practical computer implementation issues are emphasized. The equations are implemented in the comprehensive, open-source, object-oriented finite element software OpenSees. Importance measures from reliability analysis, employing the sensitivity results, are presented to enable the investigation of the relative importance of uncertainty in the parameters of a finite element model. Two example applications demonstrate that the variability in nodal coordinates of a structure can be a significant source of uncertainty along with that in key material and load parameters.     

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.     

Development of Finite-Element Modeling Approach for Lateral Load Analysis of Dry-Glazed Curtain Walls

This paper presents a finite-element modeling option to provide an analytical approach for a seismic analysis of dry-glazed curtain-wall systems. In this modeling approach, Ansys finite-element software was used to model the glass panel, aluminum glazing frame, perimeter rubber gaskets, rubber setting and side blocks, glass-to-frame clearances, and glass-to-frame contact once the clearance was overcome by in-plane drift. The results of the finite-element modeling of the curtain-wall system were compared with full-scale laboratory test results. The effect of some of the parameters such as gasket friction and aspect ratio were evaluated. The study showed that finite-element modeling is a viable approach for analytical evaluation of curtain walls. The modeling can function to predict the drift associated with glass-panel cracking. Further refinement of the modeling approach developed can increase the accuracy of the prediction.     

Combined Finite- and Boundary-Element Analysis of the Effects of Tunneling on Single Piles

An efficient and practical method of analysis to predict the effects of tunneling on existing single pile foundations is described. The method involves a combination of the finite- and boundary-element (FAB) methods, with free-field ground movements predicted by the finite-element method and the response of an embedded pile to these ground movements predicted by the boundary-element method. The method allows prediction of the full three-dimensional (3D) response of the pile as tunnel excavation proceeds towards the pile and away from it. Very good agreement is obtained between predictions of the pile response obtained by the FAB method and a 3D finite-element analysis which specifically includes the pile in the finite-element mesh. The vastly superior computational efficiency of the FAB method over the full 3D finite element approach is also illustrated.     

Identification of a Distribution of Stiffness Reduction in Reinforced Concrete Slab Bridges Subjected to Moving Loads

The method for identifying arbitrary stiffness reduction in damaged reinforced concrete slab bridges under moving loads is proposed and dynamic signals measured at several points are used as response data to reflect the properties of the moving loads sensitivity. In particular, the change in stiffness in each element before and after damage, based on the system identification method, is described and discussed by using a modified bivariate Gaussian distribution function. The proposed method in this work is more feasible than the conventional element-based damage detection method from the computational efficiency because the procedure of finite-element analysis coupled with microgenetic algorithm using six unknown parameters irrespective of the number of elements are considered. The validity of the technique is numerically verified using a set of dynamic data obtained from a simulation of the actual bridge modeled with a three-dimensional solid element. The numerical calculations show that the proposed technique is a feasible and practical method that can prove the exact location of a damaged region as well as inspect the complex distribution of deteriorated stiffness, although there is a modeling error between actual bridge results and numerical model results as well as a measurement error like uncertain noise in the response data.     

Finite-Element Model Updating for the Kap Shui Mun Cable-Stayed Bridge

This paper presents the implementation of the finite-element model updating for the Kap Shui Mun Bridge, a 430 m main span double-deck cable-stayed bridge in Hong Kong. The dynamic characteristics of the bridge have been studied through both three-dimensional finite-element prediction and field vibration measurement previously. In this paper, the developed finite-element model is updated based on the field measured dynamic properties. A comprehensive sensitivity study to demonstrate the effects of various structural parameters (including the connections and boundary conditions) on the modes of concern is first performed, according to which a set of structural parameters are then selected for adjustment. The finite-element model is updated in an iterative fashion so as to minimize the differences between the predicted and the measured natural frequencies. The final updated finite-element model for the Kap Shui Mun Bridge is able to produce natural frequencies in good agreement with the measured ones, and can be helpful for a more precise dynamic response prediction.     

Reliability-Based Optimum Design of Glulam Cable-Stayed Footbridges

This work presents a procedure for finding the reliability-based optimum design of cable-stayed bridges. The minimization problem is stated as the minimization of stresses, displacements, reliability, and bridge cost. A finite-element approach is used for structural analysis. It includes a direct analytic sensitivity analysis module, which provides the structural behavior responses to changes in the design variables. An equivalent multicriteria approach is used to solve the nondifferential, nonlinear optimization problem, turning the original problem into sequential minimization of unconstrained convex scalar functions, from which a Pareto optimum is obtained. Examples are given illustrating the procedure.     

Flutter and Buffeting Analysis.?I: Finite-Element and RPE Solution

A finite-element formulation is developed for analyzing flutter instability and buffeting response of long-span bridges and their interaction. The flutter derivatives, instead of the indicial functions used by previous researchers, are applied in the random parametric excitation (RPE) analysis. This application makes finite-element formulation possible and results in much less computational effort in RPE analysis than those of previous analyses. With the finite-element program developed in the present study, as many modes as desired can be easily included in the flutter and buffeting analyses. Users have the choice of RPE or eigenvalue method for flutter analysis and RPE or spectral method for buffeting analysis.     

New Fast Convolution Algorithm in Boundary-Element Methods for Two- and Three-Dimensional Linear Soil Consolidation Analysis

Over the last 25?years, the time domain boundary element formulations for the linear consolidation theory of Biot involving fully coupled governing differential equations of flow through porous media and those of elastic deformation of porous skeleton have been fully developed and implemented for both single-region and multiregion two-dimensional plane strain, axisymmetric and three-dimensional problems. However, this storage-based convolution method used in those developments was not found to be suitable for solving large practical problems because of the substantial computer disk space requirements. In order to find a better alternative, an accurate integration-based scheme was developed by the present writers and co-workers, in which, the storage was eliminated by accurately recalculating the summation (involved in the time convolution) of the right-hand side at each step during the time marching process. Although this work was not published in any literature, by using this type of approach, solving large scale problems became possible in an accurate manner, but the computational cost was significantly high, and there was a further need to develop a more practical and efficient time stepping algorithm. In the present work, an efficient and simplified integration-based fast convolution algorithm for two- and three-dimensional soil consolidation analysis has been subsequently developed. In this new algorithm, all of the time convolution steps have been calculated by assuming an equivalent spatial and temporal averaged value of the variables over each element to represent the total effect. The number of Gauss points used has been calculated in an efficient manner based on time-embedded distance criteria to accurately capture the past effects. The efficiency and accuracy of this newly developed fast convolution algorithm are compared with the accurate integration-based convolution approach and also with the analytical and other available solutions. Examples of applications involving two- and three-dimensional practical soil consolidation problems are presented to demonstrate the usefulness of the developed algorithm.     

Thermal analysis of the arc welding process: Part I. General solutions

An analytical solution for the temperature-rise distribution in arc welding of short workpieces is developed based on the classical Jaeger’s moving heat-source theory to predict the transient thermal response. It, thus, complements the pioneering work of Rosenthal and his colleagues (and others who extended that work), which addresses quasi-stationary moving heat-source problems. The arc beam is considered as a moving plane (disc) heat source with a pseudo-Gaussian distribution of heat intensity, based on the work of Goldak et al. It is a general solution (both transient and quasi-steady state) in that it can determine the temperature-rise distribution in and around the arc beam heat source, as well as the width and depth of the melt pool (MP) and the heat-affected zone (HAZ) in welding short lengths, where quasi-stationary conditions may not have been established. A comparative study is made of the analytical approach of the transient analysis presented here with the finite-element modeling of arc welding by Tekriwal and Mazumder. The analytical model developed can determine the time required for reaching quasi-steady state and solve the equation for the temperature distribution, be it transient or quasi-steady state. It can also calculate the temperature on the surface as well as with respect to the depth at all points, including those very close to the heat source. While some agreement was found between the results of the analytical work and those of the finite-element method (FEM) model, there were differences identified due to differences in the methods of approach, the selection of the boundary conditions, the need to consider image heat sources, and the effect of variable thermal properties with temperature. The analysis presented here is exact, and the solution can be obtained quickly and in an inexpensive way compared to the FEM. The analysis also facilitates optimization of process parameters for good welding practice.     

Stability Analysis of Composite Plates with Through-the-Width Delamination

In this paper, the compressive bucking and postbuckling behavior of composite laminates with through-the-width delamination are investigated. The analytical method is based on the first-order shear deformation theory, and its formulation is developed on the basis of the Rayleigh-Ritz approximation technique by the implementation of the polynomial series, which has been used for the first time in the case of the mixed mode of buckling. Both local buckling of the delaminated sublaminate and global buckling of the whole plate are investigated. Also, the contact among sublaminates is taken into account. The three-dimensional finite-element analysis is performed by using ANSYS5.4 general-purpose commercial software just to compare the finite-element method results with those obtained by the analytical model. It is noted that the significance and contribution of the current paper lies in the fact that for a rather complicated problem, very good results are obtained by using a fairly small number of degrees of freedom through the application of complete polynomial series.     

Finite Element Response Sensitivity Analysis of Steel-Concrete Composite Beams with Deformable Shear Connection

The behavior of steel-concrete composite beams is strongly influenced by the type of shear connection between the steel beam and the concrete slab. For accurate analytical predictions, the structural model must account for the interlayer slip between these two components. In numerous engineering applications (e.g., in the fields of structural optimization, structural reliability analysis, and finite element model updating), accurate response sensitivity calculations are needed as much as the corresponding response simulation results. This paper focuses on a procedure for response sensitivity analysis of steel-concrete composite structures using displacement-based locking-free frame elements including deformable shear connection with fiber discretization of the cross section. Realistic cyclic uniaxial constitutive laws are adopted for the steel and concrete materials as well as for the shear connection. The finite element response sensitivity analysis is performed according to the direct differentiation method. The concrete and shear connection material models as well as the static condensation procedure at the element level are extended for response sensitivity computations. Two steel-concrete composite structures for which experimental test results are available in the literature are used as realistic testbeds for response and response sensitivity analysis. These benchmark structures consist of a nonsymmetric, two-span continuous beam subjected to monotonic loading and a frame subassemblage under cyclic loading. The new analytical derivations for response sensitivity calculations and their computer implementation are validated through forward finite difference analysis based on the two benchmark examples considered. Selected sensitivity analysis results are shown for validation purposes and for quantifying the effect and relative importance of the various material parameters in regards to the nonlinear monotonic and cyclic response of the testbed structures.     

Unified Modeling of Fluid or Granular Flows on Dam-Break Case

The stopping process of debris-flow pulses is a complex phenomenon that expresses both the characteristics of a non-Newtonian fluid when it flows and those of a soil when it comes to a stop. In order to capture this phenomenon, we have developed a model based on a Navier-Stokes approach with a constitutive law including a Drucker-Prager yield criterion. The latter permits us to continuously describe the passage of granular material from the flowing (viscous) to the stopped (viscoplastic) status. In addition to being easy to implement, this approach has the advantage of being straightforwardly expandable to full three-dimensional modeling. In order to evaluate this approach, we have implemented it using finite elements. This implementation uses a Galerkin finite-element approximation with a least-squares stabilization procedure. The free surface is treated by means of a level-set approach to cope with the complex geometry of a flowing pulse. The rheological model and the free-surface treatment are tested in an analytical problem and in a dam-break test.     

Spatial Stability of Nonsymmetric Thin-Walled Curved Beams. I: Analytical Approach

An improved formulation for spatial stability of thin-walled curved beams with nonsymmetric cross sections is presented based on the displacement field considering both constant curvature effects and the second-order terms of finite-semitangential rotations. By introducing Vlasov's assumptions and invoking the inextensibility condition, the total potential energy is derived from the principle of linearized virtual work for a continuum. In this formulation, all displacement parameters and the warping function are defined at the centroid axis so that the coupled terms of bending and torsion are added to the elastic strain energy. Also, the potential energy due to initial stress resultants is consistently derived corresponding to the semitangential rotation and moment. Analytical solutions are newly derived for in-plane and lateral-torsional buckling of monosymmetric thin-walled curved beams subjected to pure bending or uniform compression with simply supported conditions. In a companion paper, finite-element procedures for spatial buckling analysis of thin-walled circular curved beams under arbitrary boundary conditions are developed by using thin-walled straight and curved beam elements with nonsymmetric sections. Numerical examples are presented to demonstrate the accuracy and the practical usefulness of the analytical and numerical solutions.     

Roebling Suspension Bridge. I: Finite-Element Model and Free Vibration Response

This first part of a two-part paper on the John A. Roebling suspension bridge (1867) across the Ohio River is an analytical investigation, whereas Part II focuses on the experimental investigation of the bridge. The primary objectives of the investigation are to assess the bridge’s load-carrying capacity and compare this capacity with current standards of safety. Dynamics-based evaluation is used, which requires combining finite-element bridge analysis and field testing. A 3D finite-element model is developed to represent the bridge and to establish its deformed equilibrium configuration due to dead loading. Starting from the deformed configuration, a modal analysis is performed to provide the frequencies and mode shapes. Transverse vibration modes dominate the low-frequency response. It is demonstrated that cable stress stiffening plays an important role in both the static and dynamic responses of the bridge. Inclusion of large deflection behavior is shown to have a limited effect on the member forces and bridge deflections. Parametric studies are performed using the developed finite-element model. The outcome of the investigation is to provide structural information that will assist in the preservation of the historic John A. Roebling suspension bridge, though the developed methodology could be applied to a wide range of cable-supported bridges.