John F. Abel

Yield surface applications in nonlinear steel frame analysis

An efficient procedure for modeling inelastic behavior in three-dimensional beam-column finite elements is presented. Plastic hinge formation, the interaction of element forces at a hinge, and elastic unloading are taken into account. A single-equation, stress-resultant yield surface has been developed to model the plastification of light and medium weight American wide-flange steel sections under a combination of axial force and bending about both principal axes. The techniques discussed have been incorporated in a three-dimensional static nonlinear analysis program capable of treating both geometrical and material nonlinearities. The results of several numerical examples are presented.

An interactive computer graphics approach to surface representation

An interactive computer graphics method has been developed for the rapid generation of arbitrary shaped three-dimensional surfaces. The method is a synthesis of spline theory and algorithms, an interactive means for man-machine communication, and software for static or dynamic graphics display. The basic technique employed is a modified lofting method in which sectional curves are represented by uniform B-splines and the surface is interpolated between sections by Cardinal splines. Among the features of this method are algorithm, which enable interactive modification of the B-spline representation of the sectional curves. At all stages of the process, the spatial information is graphically displayed to the user. Complex surfaces can be created by the combination of a number of shapes that have been separately generated and automatically joined. The system has been successfully interfaced to a variety of analytical routines for structural, medical and graphical applications.

Initial equilibrium solution methods for cable reinforced membranes part I-formulations

Abstract This paper describes the initial equilibrium problem for tension structures and presents a variety of methods for solving it. Two least squares techniques are presented in which the prestress distribution in the reference configuration is the problem unknown and the reference shape is explicitly defined by the designer. The existing force density method is shown to be a special case of the new assumed geometric stiffness method where both the reference shape and prestress distribution are unknowns in the solution. The iterative smoothing technique allows the designer to solve for the shape of the reference configuration in terms of an assumed prestress distribution. Also, an extension of the nonlinear displacement analysis method is presented which is based on a special slip formulation which accounts for relative movement between membranes and other structural components. Finally, the possibility of a combined solution process is discussed.

Recursive spectral algorithms for automatic domain partitioning in parallel finite element analysis

Abstract Recently, several domain partitioning algorithms have been proposed to effect load-balancing among processors in parallel finite element analysis. The recursive spectral bisection (RSB) algorithm [1] has been shown to be effective. However, the bisection nature of the RSB results in partitions of an integer power of two, which is too restrictive for computing environments consisting of an arbitrary number of processors. This paper presents two recursive spectral partitioning algorithms, both of which generalize the RSB algorithm for an arbitrary number of partitions. These algorithms are based on a graph partitioning approach which includes spectral techniques and graph representation of finite element meshes. The ‘algebraic connectivity vector’ is introduced as a parameter to assess the quality of the partitioning results. Both node-based and element-based partitioning strategies are discussed. The spectral algorithms are also evaluated and compared for coarse-grained partitioning using different types of structures modelled by 1-D, 2-D and 3-D finite elements.

Inelastic analyses of a 17-story steel framed building damaged during Northridge

A series of two- and three-dimensional static and dynamic inelastic frame analyses are performed for a 17-story steel moment frame building damaged by the 1994 Northridge earthquake. The primary objectives of the study are to: (1) exercise state-of-the-art inelastic static and dynamic analyses for the evaluation and design of steel buildings; (2) establish to what degree frame analyses can be used to predict the types of brittle connection damage that occurred during the Northridge earthquake; and (3) investigate the reliability of the analyses and the influence of modeling parameters on computed performance indices. In general, this study shows that calculated interstory drift ratios and curvature demands obtained from inelastic time history analyses correlate reasonably well with the pattern of connection damage observed in the building. However, there is significant scatter in the computed deformation demands that are strongly dependent on the degree to which three-dimensional torsion, secondary structural elements and strength/stiffness degradation (associated with connection fractures) are modeled in the analyses. Further, comparisons of static and dynamic analyses indicate that for this building static pushover analyses do not capture higher vibration modes that are significant.

Intersection of parametric surfaces by means of look-up tables

When primitive parametric surfaces are combined and modified inferactively to form complex intersecting surfaces, it becomes important to find the curves of intersection. One must distinguish between finding the shape of the intersection curve, which might only be useful for display, and finding an accurate mathematical representation of the curve. The latter is important for any meaningful geometric modeling, analysis, design, or manufacture involving the intersection. The intersection curve between parametric surfaces is important in such computer-aided design and manufacturing (CAD/CAM) functions as shape design, analysis of groins, design of fillets, and computation of numerically controlled tooling paths. The algorithm presented here provides an adequately accurate mathematical representation of the intersection curve. It also provides a database to simplify such operations as hidden-surface removal, surface rendering, profile identification, and interference or clearance computations. Further, the algorithm facilitates creating and changing a finite element mesh in the intersection region.

Parallel processing for transient nonlinear structural dynamics of three-dimensional framed structures using domain decomposition

Abstract A strategy is presented for the solution of the fully nonlinear transient structural dynamics problem in a coarse-grained parallel processing environment. Emphasis is placed on the analysis of three-dimensional framed structures subjected to arbitrary dynamic loading and, in particular, steel building frames subject to earthquake loading. Concerns include long-duration dynamic loading, geometric and material nonlinearity, and the wide distribution of vibrational frequencies found in frame models. The implicit domain decomposition method described employs substructuring techniques and then a preconditioned conjugate gradient algorithm for the iterative solution of the reduced set of unknowns along the substructure interfaces. Substructuring is shown to provide a natural preconditioner for effective parallel iterative solution.

EVALUATION OF AUTOMATIC DOMAIN PARTITIONING ALGORITHMS FOR PARALLEL FINITE ELEMENT ANALYSIS

SUMMARY This paper studies and compares the domain partitioning algorithms presented by Farhat,1 Al-Nasra and Nguyen,2 Malone,3 and Simon4/Hsieh et al.5,6 for load balancing in parallel finite element analysis. Both the strengths and weaknesses of these algorithms are discussed. Some possible improvements to the partitioning algorithms are also suggested and studied. A new approach for evaluating domain partitioning algorithms is described. Direct numerical comparisons among the considered partitioning algorithms are then conducted using this suggested approach with both regular and irregular finite element meshes of di⁄erent order and dimensionality. The test problems used in the comparative studies along with the results obtained provide a set of benchmark examples for other researchers to evaluate both new and existing partitioning algorithms. In addition, interactive graphics tools used in this work to facilitate the evaluation and comparative studies are presented.

Material and geometric nonlinear dynamic analysis of steel frames using computer graphics

Abstract A promising analytical model for nonlinear dynamic analysis of steel frames is described. This approach is based on an updated Lagrangian formulation in conjunction with force-space, concentrated plasticity. Kinematic strain hardening behavior is modelled by the bounding-surface concept. The analysis is implemented in a highly interactive, adaptive fashion using computer graphics and a super-minicomputer. Several examples illustrate the effectiveness of the analysis strategy described.

Initial equilibrium solution methods for cable reinforced membranes part II-implementation

Abstract This paper describes a portion of an interactive computer graphics design system which is devoted to the solution of the initial equilibrium problem for membrane structures. Real-time vector graphics displays are used to speed the preparation and display of structural data. A variety of solution methods is available to the designer to be used either individually or in combination. Examples of the use of each solution method and combined methods are included.