Publications

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An LDRD funded approach to development of reduced order models for systems with local nonlinearities is presented. This method is particularly useful for problems of structural dynamics, but has potential application in other fields. The key elements of this approach are (1) employment of eigen modes of a reference linear system, (2) incorporation of basis functions with an appropriate discontinuity at the location of the nonlinearity. Galerkin solution using the above combination of basis functions appears to capture the dynamics of the system with a small basis set. For problems involving small amplitude dynamics, the addition of discontinuous (joint) modes appears to capture the nonlinear mechanics correctly while preserving the modal form of the predictions. For problems involving large amplitude dynamics of realistic joint models (macro-slip), the use of appropriate joint modes along with sufficient basis eigen modes to capture the frequencies of the system greatly enhances convergence, though the modal nature the result is lost. Also observed is that when joint modes are used in conjunction with a small number of elastic eigen modes in problems of macro-slip of realistic joint models, the resulting predictions are very similar to those of the full solution when seen through a low pass filter. This has significance both in terms of greatly reducing the number of degrees of freedom of the problem and in terms of facilitating the use of much larger time steps.

Structural assemblies often include bolted connections that are a primary mechanism for energy dissipation and nonlinear response at elevated load levels. Typically these connections are idealized within a structural dynamics finite element model as linear elastic springs. The spring stiffness is generally tuned to reproduce modal test data taken on a prototype. In conventional practice, modal test data is also used to estimate nominal values of modal damping that could be used in applications with load amplitudes comparable to those employed in the modal tests. Although this simplification of joint mechanics provides a convenient modeling approach with the advantages of reduced complexity and solution requirements, it often leads to poor predicted responses for load regimes associated with nonlinear system behavior. In this document we present an alternative approach using the concept of a "whole-joint" or "whole-interface" model [1]. We discuss the nature of the constitutive model, the manner in which model parameters are deduced, and comparison of structural dynamic prediction with results for experimental hardware subjected to a series of transient excitations beginning at low levels and increasing to levels that produced macro-slip in the joint. Further comparison is performed with a traditional "tuned" linear model. The ability of the whole-interface model to predict the onset of macro-slip as well as the vast improvement of the response levels in relation to those given by the linear model is made evident. Additionally, comparison between prediction and high amplitude experiments suggests areas for further work.

The constitutive behavior of mechanical joints is largely responsible for the energy dissipation and vibration damping in built-up structures. For reasons arising from the dramatically different length scales associated with those dissipative mechanisms and the length scales characteristic of the overall structure, this physics cannot be captured through direct numerical simulation (DNS) of the contact mechanics within a structural dynamics analysis. The difficulties of DNS manifest themselves either in terms of Courant times that are orders of magnitude smaller than that necessary for structural dynamics analysis or as intractable conditioning problems. The only practical method for accommodating the nonlinear nature of joint mechanisms within structural dynamic analysis is through constitutive models employing degrees of freedom natural to the scale of structural dynamics. In this way, development of constitutive models for joint response is a prerequisite for a predictive structural dynamics capability. A four-parameter model, built on a framework developed by Iwan, is used to reproduce the qualitative and quantitative properties of lap-type joints. In the development presented here, the parameters are deduced by matching joint stiffness under low load, the force necessary to initiate macroslip, and experimental values of energy dissipation in harmonic loading. All the necessary experiments can be performed on real hardware or virtually via fine-resolution, nonlinear quasistatic finite elements. The resulting constitutive model can then be used to predict the force/displacement results from arbitrary load histories. copyright © 2005 by ASME.

The presence of mechanical joints--typified by the lap joint--in otherwise linear structures has been accommodated in structural dynamics via ad hoc methods for a century. The methods range from tuning linear models to approximate non-linear behavior in restricted load ranges to various methods which introduce joint dissipation in a post-processing stage. Other methods, employing constitutive models for the joints are being developed and their routine use is on the horizon.

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The generalized momentum balance (GMB) methods, explored chiefly by Shabana and his co-workers, treat slap or collision in linear structures as sequences of impulses, thereby maintaining the linearity of the structures throughout. Further, such linear analysis is facilitated by modal representation of the structures. These methods are discussed here and extended. Simulations on a simple two-rod problem demonstrate how this modal impulse approximation affects the system both directly after each impulse as well as over the entire collision. Furthermore, these simulations illustrate how the GMB results differ from the exact solution and how mitigation of these artifacts is achieved. Another modal method discussed in this paper is the idea of imposing piecewise constant forces over short, yet finite, time intervals during contact. The derivation of this method is substantially different than that of the GMB method, yet the numerical results show similar behavior, adding credence to both models. Finally, a novel method combining these two approaches is introduced. The new method produces physically reasonable results that are numerically very close to the exact solution of the collision of two rods. This approach avoids most of the non physical, numerical artifacts of interpenetration or chatter present in the first two methods.

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The Lubkin solution for two spheres pressed together and then subjected to a monotonically increasing axial couple is examined numerically. The Deresiewicz asymptotic solution is compared to the full solution and its utility is evaluated. Alternative approximations for the Lubkin solution are suggested and compared. One approximation is a Pade rational function which matches the analytic solution over all rotations. The other is an exponential approximation that reproduces the asymptotic values of the analytic solution at infinitesimal and infinite rotations. Finally, finite element solutions for the Lubkin problem are compared with the exact and approximate solutions.

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The constitutive behavior of mechanical joints is largely responsible for the energy dissipation and vibration damping in weapons systems. For reasons arising from the dramatically different length scales associated with those dissipative mechanisms and the length scales characteristic of the overall structure, this physics cannot be captured adequately through direct simulation of the contact mechanics within a structural dynamics analysis. The only practical method for accommodating the nonlinear nature of joint mechanisms within structural dynamic analysis is through constitutive models employing degrees of freedom natural to the scale of structural dynamics. This document discusses a road-map for developing such constitutive models.

The constitutive behavior of mechanical joints is largely responsible for the energy dissipation and vibration damping in weapons systems. For reasons arising from the dramatically different length scales associated with those dissipative mechanisms and the length scales characteristic of the overall structure, this physics cannot be captured through direct numerical simulation (DNS) of the contact mechanics within a structural dynamics analysis. The difficulties of DNS manifest themselves either in terms of Courant times that are orders of magnitude smaller than that necessary for structural dynamics analysis or as intractable conditioning problems. The only practical method for accommodating the nonlinear nature of joint mechanisms within structural dynamic analysis is through constitutive models employing degrees of freedom natural to the scale of structural dynamics. In this way, development of constitutive models for joint response is a prerequisite for a predictive structural dynamics capability. A four-parameter model, built on a framework developed by Iwan, is used to reproduce the qualitative and quantitative properties of lap-type joints. In the development presented here, the parameters are deduced by matching experimental values of energy dissipation in harmonic loading and values of the force necessary to initiate macro-slip. (These experiments can be performed on real hardware or virtually via fine-resolution, nonlinear quasi-static finite elements.) The resulting constitutive model can then be used to predict the force/displacement results from arbitrary load histories.

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The structural dynamics modeling of engineering structures must accommodate the energy dissipation due to microslip in mechanical joints. Given the nature of current hardware and software environments, this will require the development of constitutive models for joints that both adequately reproduce the important physics and lend themselves to efficient computational processes. The exploration of the properties of mechanical joints--either through fine resolution finite element modeling or through experiment--is itself an area of research, but some qualitative behavior appears to be established. The work presented here is the presentation of a formulation of idealized elements due to Iwan, that appears capable of reproducing the important joint properties as they are now understood. Further, methods for selecting parameters for that model by joining the results from experiments in regimes of small and large load are developed. The significance of this work is that a reduced order model is presented that is capable of reproducing the important qualitative properties of mechanical joints using only a small number of parameters.

Frictional energy dissipation in joints is an issue of long-standing interest in the effort to predict damping of built up structures. Even obtaining a qualitative understanding of how energy dissipation depends on applied loads has not yet been accomplished. Goodman[l] postulated that in harmonic loading, the energy dissipation per cycle would go as the cube of the amplitude of loading. Though experiment does support a power-law relationship, the exponent tends to be lower than Goodman predicted. Recent calculations discussed here suggest that the cause of that deviation has to with reshaping of the contact patch over each loading period.

The von Mises stress is often used as the metric for evaluating design margins, particularly for structures made of ductile materials. While computing the von Mises stress distribution in a structural system due to a deterministic load condition may be straightforward, difficulties arise when considering random vibration environments. As a result, alternate methods are used in practice. One such method involves resolving the random vibration environment to an equivalent static load. This technique, however, is only appropriate for a very small class of problems and can easily be used incorrectly. Monte Carlo sampling of numerical realizations that reproduce the second order statistics of the input is another method used to address this problem. This technique proves computationally inefficient and provides no insight as to the character of the distribution of von Mises stress. This tutorial describes a new methodology to investigate the design reliability of structural systems in a random vibration environment. The method provides analytic expressions for root mean square (RMS) von Mises stress and for the probability distributions of von Mises stress which can be evaluated efficiently and with good numerical precision. Further, this new approach has the important advantage of providing the asymptotic properties of the probability distribution. A brief overview of the theoretical development of the methodology is presented, followed by detailed instructions on how to implement the technique on engineering applications. As an example, the method is applied to a complex finite element model of a Global Positioning Satellite (GPS) system. This tutorial presents an efficient and accurate methodology for correctly applying the von Mises stress criterion to complex computational models. The von Mises criterion is the traditional method for determination of structural reliability issues in industry.

Salinas provides a massively parallel implementation of structural dynamics finite element analysis, required for high fidelity, validated models used in modal, vibration, static and shock analysis of weapons systems. This document provides a users guide to the input for Salinas. Details of input specifications for the different solution types, output options, element types and parameters are included. The appendices contain detailed examples, and instructions for running the software on parallel platforms.

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I have recently become involved in the ABET certification process under the new system - ABET 2000. This system relies heavily on concepts of Total Quality Management (TQM). It encourages each institution to define its objectives in terms of its own mission and then create a coherent program based on it. The prescribed steps in setting up the new system at an engineering institution are: o identification of constituencies G definition of mission. It is expected that the department's mission will be consistent with that of the overall institution, but containing some higher resolution language appropriate to that particular discipline of the engineering profession. o statement of objectives consistent with the mission 3G~~\vED " enumeration of desired, and preferably measurable, outcomes of the process that would ~ `=. verify satisfaction of the objectives. ~~~ 07 !398 o establish performance standards for each outcome. o creation of appropriate feedback loops to assure that the objectives are still consistent with Q$YT1 the mission, that the outcomes remain consistent with the objectives, and that the curriculum and the teaching result in those outcomes. It is my assertion that once the institution verbalizes a mission, enumerated objectives naturally flow from that mission. (We shall try to demonstrate by example.) Further, if the mission uses the word "engineer", one would expect that word also to appear in at least one of the objectives. The objective of producing engineers of any sort must -by decree - involve the presence of the ABET criteria in the outcomes list. In other words, successful satisfaction of the ABET items a-k are a necessary subset of the measure of success in producing engineers. o We shall produce bachelor level engineers whose training in the core topics of chemical (or electrical, or mechanical) engineering is recognized to be among the best in the nation. o We shall provide an opportunity for our students to gain a significant exposure to biomedical topics and the integration of those topics with chemical (electrical or mechanical) engineering. o We shall provide unique opportunities for our students to work with clinicians and researchers in hospitals and other medical institutions. combined criteria a-k of ABET and 1-6 of AICHE (or IEEE or ASME) in some sensible manner. Here I have just estimated the number of distinct criteria that would be extracted from the AICHE paragraphs. These criteria are necessarily included because of the objective to producing chemical (electrical or mechanical) engineers. every student who desires an internship or independent study at a medical institution will be placed. a majority of our students will take either the FE exam or the M-CAT exam. demonstrating a commitment to professionalism and to life-long learning. a majority of our students will go on to graduate school or other post-graduate school. (I do not assert that this sort of outcome is appropriate to all excellent schools. In the case of this hypothetical school though, this outcome might be a reasonable expectation.) medical schools will rank our school as among the best from which to admit