Najib N. Abboud

SOME PRACTICAL APPLICATIONS OF THE USE OF SCALE INDEPENDENT ELEMENTS FOR DYNAMIC ANALYSIS OF VIBRATING SYSTEMS

Abstract Discrete deterministic methods such as finite elements offer great flexibility in analyzing the dynamic response of vibrating systems. However, these methods can easily grow beyond available computer resources as frequencies of interest grow higher. In this paper we present a new approach for the frequency domain dynamic analysis of structures. A theory is developed for the analysis of systems which are uniform along a single coordinate axis, but otherwise arbitrary in geometry and material composition. This approach, termed the scale independent element, is shown to be an accurate, efficient and general method for the analysis of vibrating systems. This technique extends the applicability of discrete deterministic finite element based modeling to higher frequencies and is capable of bridging the gap to frequency regimes where statistical energy methods become applicable.

Anatomy of a Disaster: A Structural Investigation of the World Trade Center Collapses

The purpose of this study is to analyze the damage to the structure of each of the WTC Twin Towers due to the high speed impacts of the Boeing 767 airplanes and subsequent fires such as to elucidate why the Twin Towers stood for as long as they did, and why they ultimately collapsed. The Boeing 767 airplane attacks on WTC 1 and WTC 2 caused immediate and significant structural damage to the towers: In each case, exterior columns were severed and the floor system at the point of impact was damaged. The airplanes broke up during the impact and the resulting projectiles and fragments proceeded to inflict further damage to the core. Much of the impact damage to the exterior walls of the towers was evident. However, damage to the interior was not visible and cannot be quantified on the basis of the physical evidence. Dynamic nonlinear explicit finite element FLEX simulations coupled with independently validated airplane crash models were leveraged to understand and assess the structural states of damage to the tower interiors that could not be observed; this includes the degradation or loss of the load carrying capacity of columns and floor assemblies as well as the stripping of fireproofing from structural members. The impact damage to the structure was substantial but so were the reserve capacity and redundancy of the structure. Iterative analyses of the load redistribution in the impact damaged towers clearly indicate that the that the outer tube structure was very effective in developing Vierendeel action around the severed exterior columns and that the outrigger hat truss provided a substantial redundant load path away from the damaged core columns. Although not specifically designed for this purpose, the hat trusses served to delay the eventual collapse of the towers. These analyses also indicate that the damage to the corner of the core in WTC 2 left it in a state more vulnerable to subsequent thermal loads compared to WTC 1. This eccentric damage, more than the height of the airplane impact, resulted in a shorter time to collapse for WTC 2, considering that the fire environments in both towers were not meaningfully different. Further degradation or loss of the load carrying capacity of columns stripped of fireproofing by direct debris impact and heated by fire is shown to be the cause of each collapse. The examination of smoke flow from each building indicates that there were no floor collapses subsequent to the initial impact throughout the fire [1] and our 1 Chief Technology Officer, Weidlinger Associates Inc., 375 Hudson Street, New York, NY 10014. Phone: 212.367.3000. Email: abboud@wai.com. 2 Chairman, Weidlinger Associates Inc., 375 Hudson Street, New York, NY 10014. Phone: 212.367.3000. Email: levy@wai.com. 3 Weidlinger Associates, Inc., 4410 El Camino Real, Los Altos, CA 94022. Phone: 650.949.3010 4 Weidlinger Associates, Inc, 2525 Michigan Avenue, Santa Monica, CA 90404. Phone: 310.998.9154

Ship Impact Study: Analytical Approaches and Finite Element Modeling

The current paper presents the results of a ship impact study conducted using various analytical approaches available in the literature with the results obtained from detailed finite element analysis. Considering a typical container vessel impacting a rigid wall with an initial speed of 10 knots, the study investigates the forces imparted on the struck obstacle, the energy dissipated through inelastic deformation, penetration, local deformation patterns, and local failure of the ship elements. The main objective of the paper is to study the accuracy and generality of the predictions of the vessel collision forces, obtained by means of analytical closed-form solutions, in reference to detailed finite element analyses. The results show that significant discrepancies between simplified analytical approaches and detailed finite element analyses can occur, depending on the specific impact scenarios under consideration.

Stress resultant based elasto-viscoplastic thick shell model

The current paper presents enhancement introduced to the elasto-viscoplastic shell formulation, which serves as a theoretical base for the finite element code EPSA (Elasto-Plastic Shell Analysis) [1–3]. The shell equations used in EPSA are modified to account for transverse shear deformation, which is important in the analysis of thick plates and shells, as well as composite laminates. Transverse shear forces calculated from transverse shear strains are introduced into a rate-dependent yield function, which is similar to Iliushins yield surface expressed in terms of stress resultants and stress couples [12]. The hardening rule defined by Bieniek and Funaro [4], which allows for representation of the Bauschinger effect on a moment-curvature plane, was previously adopted in EPSA and is used here in the same form. Viscoplastic strain rates are calculated, taking into account the transverse shears. Only non-layered shells are considered in this work.

INVESTIGATION OF SHIP IMPACT SCENARIOS AND MITIGATION MEASURES

Ship impact is an important loading scenario for analysis and design of bridges, oil platforms, and other marine structures. Ships collision is also a very important design consideration for ship hulls. Designing structures to resist both accidental and intentional ship impact requires characterization of the impact loading history. Standard design practice relies on simplified methods to determine the impact loads, which typically consider only speed and mass of the vessel. However, ship impact is a complicated non-linear structural dynamic event that depends not just on the size and mass of the vessel, but also local stiffening pattern, location and function of the bulkheads, possible ice-strengthening classification, draft, presence of the bulbous bow, and many other factors. Neglecting these factors can lead to overestimation or underestimation of the loads, depending on a specific scenario. The discrepancies between simplified load estimates and detailed finite element analyses are investigated in this paper.Copyright

Characterization of the Pressure Wave Emitted From Implosion of Submerged Cylindrical Shell Structures

Buckling of submerged cylindrical shells is a sudden and rapid implosion which emits a high pressure pulse that may be damaging to nearby structures. The characteristics of this pressure pulse are dictated by various parameters defining the shell structure such as the length to diameter ratio, shell thickness, material, and the existence and configuration of internal stiffeners. This study examines, through the use of high fidelity coupled fluid-structure finite element computations, the impact of various structural parameters on the resulting pressure wave emanating from the implosion. The results demonstrate that certain structural configurations produce pressure waves with higher peak pressure and impulse thereby enhancing the potential for damage to nearby structures.Copyright

Impact Mitigation for Buried Structures: Demolition of the New Haven Veterans Memorial Coliseum

We present an overview of the analysis and design of mitigation schemes for buried structures subjected to impact loading, with a focus on the hazard evaluation to underground utilities from the demolition by implosion of the Veterans Memorial Coliseum in New Haven, CT. We discuss the analytical and numerical investigations validated by field testing conducted prior to the implosion and leading to the design of the mitigation schemes aimed at protecting the utilities buried under ground. All the designed and constructed mitigation schemes proved successful during the January 2007 implosion of the Veterans Memorial Coliseum.