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.     

Microtasking, Macrotasking, and Autotasking for Structural Optimization

Various multitasking approaches are investigated for optimization of large space structures. Judicious combination of microtasking, macrotasking, and autotasking is explored with the goal of achieving a vectorized and multitasked algorithm for optimization of a large structure with maximum speedup performance. Speedup results are presented and compared for three space truss structures, with 526, 1,046, and 3,126 members. The processing time required for optimization of large structures increases exponentially with the size of the structure (number of design variables). Example 3 of this paper has 3,126 members and 2,226 displacement degrees of freedom. Development of efficient concurrent algorithms utilizing the unique architecture and capabilities of high‐performance computers results in substantial reduction in the overall execution time.     

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.     

Statistical Sensitivity Analysis of Lattice Space Structures

This paper presents a statistical sensitivity analysis for shape distortions of space structures. The approach is based on a statistical shape‐distortion analysis on the structural errors and an adjoint method of sensitivity analysis. The statistical shape‐distortion analysis allows the stochastic errors to be represented by member‐length tolerances. The sensitivity analysis is performed to predict the effects of member‐length errors for lattice space antennas on the surface accuracy. The formulas presented in this paper give an effective approach to predict the effects of member‐length errors on the shape distortions, to obtain effective structural elements to correct the shape distortions, and to design tolerance errors of the structural elements. Numerical examples for statically determinate and indeterminate two‐dimensional truss beams have been demonstrated to identify the members contributing most to the errors. These results show that the errors of the longitudinal elements of the structure are important for designing accurate truss structures. Moreover, the validity and effectiveness of the present approach have been investigated.     

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.     

High‐Performance Computing in Structural Mechanics and Engineering

Recent advances in computer hardware and software have made multiprocessing a viable and attractive technology. This paper reviews high‐performance computing methods in structural mechanics and engineering through the use of a new generation of multiprocessor computers. The paper presents an overview of vector pipelining, performance metrics for parallel and vector computers, programming languages, and general programming considerations. Recent developments in the application of concurrent processing techniques to the solution of structural mechanics and engineering problems are reviewed, with special emphasis on linear structural analysis, nonlinear structural analysis, transient structural analysis, dynamics of multibody flexible systems, and structural optimization.     

Parallel Algorithms for Integrated Structural/Control Optimization

Optimization of combined structural and control systems is a complex problem requiring an inordinate amount of computer‐processing time, especially the solution of the eigenvalue problem of a general unsymmetric square real matrix with complex eigenvalues and eigenvectors, which is frequently used in such problem. The few algorithms presented in the literature thus far have been applied to small structures with a few members and controllers only. Parallel processing on new‐generation multiprocessor computers provides an opportunity to solve large‐scale problems. In this paper, the integrated structural and control optimization problem is formulated by including constraints on displacements, stresses, and closed‐loop eigenvalues and the corresponding damping factors. Then, parallel algorithms are presented for integrated optimization of structures on shared‐memory multiprocessors such as the Cray YMP 8/864 supercomputer. In particular, parallel algorithms are presented for the solution of complex eigenvalue problems encountered in structural control problems using the method of matrix iteration for dominant eigenvalue(s). The solution is divided into two parts. The first part is the iteration for dominant eigenvalue(s) and the corresponding eigenvector(s) and the second part is the reduction of the matrix to obtain the smaller eigenvalue(s) and the corresponding eigenvector(s).     

Optimization of Space Trusses on Vector Multiprocessor

Mathematical optimization of space trusses in a vector/parallel processing environment is the subject of this paper. Parallel processing is achieved through microtasking and the use of the CRAY CFT77 compiler directives. Speedup results are presented for four space‐truss examples. It is concluded that the speedup due to microtasking is improved substantially with an increase in the size of the problem.     

Object-Oriented Modeling of Structural Analysis and Design with Application to Damping Device Configuration

This paper presents an object-oriented (OO) software framework for computer-aided structural analysis and design research, where different structural analysis methods and design procedures need to be implemented and investigated. The framework is designed with four basic modules: structure, load, analysis, and design. Each module includes a set of cooperating interfaces and classes. Through the predefined interfaces, the framework provides architecture for many structural design applications. A variety of similar entities, such as different design applications, design procedures, and analysis methods, can be built on this architecture by implementing the necessary interfaces. The clearly defined interactions between the modules accommodate the future extensions within the modules. The final OO design of the framework can be communicated by many well-known design patterns, and it is described by unified modeling language. The framework is then customized to the application for optimizing the configuration of energy dissipation devices in a given structure. By implementing a few interfaces, this paper illustrates how this OO framework accommodates changes, and how reusability and extensibility can be achieved.     

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.     

Augmented Lagrangian Genetic Algorithm for Structural Optimization

This paper presents a robust hybrid genetic algorithm for optimization of space structures using the augmented Lagrangian method. An attractive characteristic of genetic algorithm is that there is no line search and the problem of computation of derivatives of the objective function and constraints is avoided. This feature of genetic algorithms is maintained in the hybrid genetic algorithm presented in this paper. Compared with the penalty function‐based genetic algorithm, only a few additional simple function evaluations are needed in the new algorithm. Furthermore, the trial and error approach for the starting penalty function coefficient and the process of arbitrary adjustments are avoided. There is no need to perform extensive numerical experiments to find a suitable value for the penalty function coefficient for each type or class of optimization problem. The algorithm is general and can be applied to a broad class of optimization problems.     

Version and Configuration Model for Structural Design Objects: Design and Implementation

This paper presents the design and implementation of a version and configuration model (VCM) for structural design objects. The VCM is developed to capture the incremental, evolutionary, multipath and iterative nature of the structural design process. Specifically, this model: (1) defines representational frameworks for representing the versions and configurations of design objects; (2) suggests sets of manipulation operations for creating and tracking the versions and configurations of design objects across the different representational frameworks; and (3) presents a prototype implementation scheme of a version manager, that is based on the representational frameworks and the manipulation operations of the proposed VCM. A case study of reinforced concrete T-beam is presented together with its prototype implementation using Object Pascal as a proof of concept. This is to describe the elements of the model, validate its effectiveness and demonstrate its viability. It is concluded that the VCM and its implementation is a valuable and necessary ingredient for developing a truly integrated structural engineering design system.     

Concurrent Optimization of Large Structures. II: Applications

In a companion paper, we presented algorithms and procedures for concurrent optimization of framed structures on shared‐memory multiprocessor computers. Implementation of the algorithms and applications are presented in this paper. The efficiency and versatility of the algorithms are assessed by presenting four examples. Speed‐ups and work‐load‐balance issues at various steps of the optimization process are considered and discussed. The efficiency of the parallel‐processing algorithms increases with the size of the structure, thus making them particularly suitable for optimization of large structures such as space stations.     

Concurrent Optimization of Large Structures. I: Algorithms

Parallel algorithms are presented for optimization of structures on shared‐memory multiprocessor computers. Structures subjected to multiple loading cases with limitations on nodal displacements, element stresses, and member sizes are optimized using the optimality‐criteria approach in a concurrent‐processing environment. Emphasis is directed toward parallelizing each computational step of the solution process. Parallel algorithms are developed to assure the best concurrent performance and speed‐up within each step. A substructuring algorithm is used to achieve the best work‐load balance during the solution of the generalized displacements. Concurrency is achieved through the use of the notion of cheap concurrency and the concept of threads. (A companion paper demonstrates the efficiency of the parallel algorithms through optimization of several truss and frame problems on an Encore Multimax shared‐memory computer for a variable number of processors.) The algorithms are particularly suitable for optimization of large structures such as space stations.     

Three-Dimensional Field-Scale Coupled Thermo-Hydro-Mechanical Modeling: Parallel Computing Implementation

An approach for the simulation of three-dimensional field-scale coupled thermo-hydro-mechanical problems is presented, including the implementation of parallel computation algorithms. The approach is designed to allow three-dimensional large-scale coupled simulations to be undertaken in reduced time. Owing to progress in computer technology, existing parallel implementations have been found to be ineffective, with the time taken for communication dominating any reduction in time gained by splitting computation across processors. After analysis of the behavior of the solver and the architecture of multicore, nodal, parallel computers, modification of the parallel algorithm using a novel hybrid message passing interface/open multiprocessing (MPI/OpenMP) method was implemented and found to yield significant improvements by reducing the amount of communication required. This finding reflects recent enhancements of current high-performance computing architectures. An increase in performance of 500% over existing parallel implementations on current processors was achieved for the solver. An example problem involving the Prototype Repository experiment undertaken by the Swedish Nuclear Fuel and Waste Management Co. [Svensk K?rnbr?nslehantering AB (SKB)] in ?sp?, Sweden, has been presented to demonstrate situations in which parallel computation is invaluable because of the complex, highly coupled nature of the problem.     

Optimum Design of Cantilever Retaining Walls Using Target Reliability Approach

In this paper, an approach for reliability-based design optimization of reinforced concrete cantilever retaining wall is described. A parametric study is conducted to assess the effect of uncertainties in design parameters on the probability of failure of cantilever retaining walls. In total, ten modes of failure are considered, viz. overturning of the wall about its toe, sliding of the wall on its base, eccentricity, bearing capacity failure below the base slab, and shear and moment failure in the toe slab, heel slab, and stem. The analysis is performed by treating backfill and foundation soil properties, geometric properties of wall, and reinforcement and concrete properties as random variables. These results are used to develop a set of reliability-based design charts for different coefficients of variation of friction angle of backfill soil (5 and 10%) and targeting reliability index (βt) in the range of 3–3.2 for all failure modes. A comparative study is also presented, which shows that optimized sections have less areas of cross section compared to those obtained from specifications on dimensioning of retaining walls available in literature.     

Concurrent Genetic Algorithms for Optimization of Large Structures

In a recent article, the writers presented an augmented Lagrangian genetic algorithm for optimization of structures. The optimization of large structures such as high‐rise building structures and space stations with several hundred members by the hybrid genetic algorithm requires the creation of thousands of strings in the population and the corresponding large number of structural analyses. In this paper, the writers extend their previous work by presenting two concurrent augmented Lagrangian genetic algorithms for optimization of large structures utilizing the multiprocessing capabilities of high‐performance computers such as the Cray Y‐MP 8/864 supercomputer. Efficiency of the algorithms has been investigated by applying them to four space structures including two high‐rise building structures. It is observed that the performance of both algorithms improves with the size of the structure, making them particularly suitable for optimization of large structures. A maximum parallel processing speed of 7.7 is achieved for a 35‐story tower (with 1,262 elements and 936 degrees of freedom), using eight processors.     

Stream Sockets versus Web Services for High-Performance and Secure Structural Analysis in Internet Environments

The increased growth of internet use in the last several years has opened up new possibilities for structural engineering analysis, moving from personal computer oriented software to client–server distributed software. In this paper two client–server applications for structural engineering based on stream sockets and on web services are presented. These two technologies have been chosen to compare, in terms of performance and complexity, new internet protocols with traditional ways of implementing client–server applications. Moreover, special care has been taken in the security aspects as the internet has become much more susceptible to breaches of security. Therefore, two new applications based on the same technologies have been created that guarantee a secure use of structural software. Also, two different client applications are presented to emphasize the versatility and power of internet distributed technology—one as a stand-alone application and the other as an integrated commercial computer-aided design program.     

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.     

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.