Publications

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The Third International Workshop on Jointed Structures was held from August 16th to 17th, 2012, in Chicago Illinois, following the ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Thirty two researchers from both the United States and international locations convened to discuss the recent progress of mechanical joints related research and associated efforts in addition to developing a roadmap for the challenges to be addressed over the next five to ten years. These proceedings from the workshop include the minutes of the discussions and follow up from the 2009 workshop [1], presentations, and outcomes of the workshop. Specifically, twelve challenges were formulated from the discussions at the workshop, which focus on developing a better understanding of uncertainty and variability in jointed structures, incorporating high fidelity models of joints in simulations that are tractable/efficient, motivating a new generation of researchers and funding agents as to the importance of joint mechanics research, and developing new insights into the physical phenomena that give rise to energy dissipation in jointed structures. The ultimate goal of these research efforts is to develop a predictive model of joint mechanics.

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Random vibration under preload is important in multiple endeavors, including those involving launch and re-entry. There are some methods in the literature to begin to address this problem, but there is nothing that accommodates the existence of preloads and the necessity of making probabilistic statements about the stress levels likely to be encountered. An approach to achieve to this goal is presented along with several simple illustrations.

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Development of mathematical models for built-up struc-tures, particularly those with many interfaces, is still primitive. This limitation is particularly evident when complex loads and load histories are considered, an example of which is random vibration. Two steps in simplifying this problem are explored here. First, the system response is approximated as that of the super-position of numerous decoupled modes, the coordinates of which evolve according to a constitutive model designed to capture the nonlinearity of the structure. Second, because among the cat-egories of load for which dynamic analysis on nonlinear struc-tures is particularly difficult is that of random loads and the re-sulting random vibration, and given the previous approximation, it is natural to apply the method of stochastic equivalent lin-earization to the governing equation of each mode. Both of these approximations are explored for the case where the nonlinear behavior of the interfaces is represented by a Masing-Prandtl-Ishlinskii-Iwan model employing a Palmov kernel. Copyright © 2013 by ASME.

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A systematic approach to defining margin in a manner that incorporates statistical information and accommodates data uncertainty, but does not require assumptions about specific forms of the tails of distributions is developed. This approach extends to calculations underlying validation assessment and quantitatively conservative predictions.

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Iwan models have had some exposure recently in modeling the nonlinear response of individual joints. This popularity can be ascribed to their mathematical simplicity, their versatility, and their ability to capture the important responses of mechanical joints under unidirectional loads. There is a lot of history to this category of model. Masing explored kinematic hardening of metals with a model consisting of ten Jenkins elements in series. Soon after, Prandtl explored the behavior of a continuous distribution of such elements. Ishlinskii explored the mathematical structure of such continuous distributions. Much more recently, Iwan demonstrated practical application of such models in capturing various sorts of metal plasticity. Among the features that make such models interesting is a simple relationship between the asymptotic nature of the integral kernel at small values and the power-law relation between force amplitude and dissipation per cycle in harmonic loading. Iwan provided several differential equations for deducing the kernel from force-displacement relations. Segalman and Starr devised methods for deducing kernels from force-displacement curves of arbitrary Masing models. This is illustrated to generate a BPII model equivalent to the Ramberg-Osgood plasticity model. The Segalman-Starr relationship is used to find relationships among several other plasticity models. Copyright © 2012 by ASME.

Solutions for analytical models of systems with nonlinear constraints have focused on exact methods for satisfying the constraint conditions. Exact methods often require that the constraint can be expressed in a piecewise-linear manner, and result in a series of mapping equations from one linear regime of the constraint to the next. Due to the complexity of these methods, exact methods are often limited to analyzing a small number of constraints for practical reasons. This paper proposes a new method for analyzing continuous systems with arbitrary nonlinear constraints by approximately satisfying the constraint conditions. Instead of dividing the constraints into multiple linear regimes, a discontinuous basis function is used to supplement the system's linear basis functions. As a result, precise contact times are not needed, enabling this method to be more computationally efficient than exact methods. While the discontinuous basis functions are continuous in displacement, their derivatives contain discontinuities that allow for the nonlinear forces to be accounted for with the assumption that the nonlinear constraints are able to be modeled in a discrete manner. Since each nonlinear constraint requires only one associated discontinuous basis function, this method is easily expanded to handle large numbers of constraints. In order to illustrate the application of this method, an example with a pinned-pinned beam is presented. © 2011 by ASME.

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Correctly incorporating the influence of mechanical joints in built-up mechanical systems is a critical element for model development for structural dynamics predictions. Quality experimental data are often difficult to obtain and is rarely sufficient to determine fully parameters for relevant mathematical models. On the other hand, fine-mesh finite element (FMFE) modeling facilitates innumerable numerical experiments at modest cost. Detailed FMFE analysis of built-up structures with frictional interfaces reproduces trends among problem parameters found experimentally, but there are qualitative differences. Those differences are currently ascribed to the very approximate nature of the friction model available in most finite element codes. Though numerical simulations are insufficient to produce qualitatively correct behavior of joints, some relations, developed here through observations of a multitude of numerical experiments, suggest interesting relationships among joint properties measured under different loading conditions. These relationships can be generalized into forms consistent with data from physical experiments. One such relationship, developed here, expresses the rate of energy dissipation per cycle within the joint under various combinations of extensional and clamping load in terms of dissipation under other load conditions. The use of this relationship - though not exact - is demonstrated for the purpose of extrapolating a representative set of experimental data to span the range of variability observed from real data. © 2011 American Society of Mechanical Engineers.

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