Articles written in Sadhana

    • A generalized quarter car modelling approach with frame flexibility and other nonlocal effects


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      Quarter-car models are popular, simple, unidirectional in kinematics and enable quicker computation than full-car models. However, they do not account for three other wheels and their suspensions, nor for the frame’s flexibility, mass distribution and damping. Here we propose a generalized quarter-car modelling approach, incorporating both the frame as well as other-wheel ground contacts. Our approach is linear, uses Laplace transforms, involves vertical motions of key points of interest and has intermediate complexity with improved realism. Our model uses baseline suspension parameters and responses to step force inputs at suspensionattachment locations on the frame. Subsequently, new suspension parameters and unsprung mass compliance parameters can be incorporated, for which relevant formulas are given. The final expression for the transfer function, between ground displacement and body point response, is approximated using model orderreduction. A simple Matlab code is provided that enables quick parametric studies. Finally, a parametric study and wheel hop analysis are performed for a realistic numerical example. Frequency and time domain responses obtained show clearly the effects of other wheels, which are outside the scope of usual quarter-car models. The displacements obtained from our model are compared against those of the usual quarter-car model and show ways in which predictions of the quarter-car model include errors that can be reduced in our approach. In summary, our approach has intermediate complexity between that of a full-car model and a quarter-car model, and offers corresponding intermediate detail and realism.

    • An engineering-design oriented exploration of human excellence in throwing


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      Humans are fast throwers, and their bodies differ correspondingly from those of other hominids. One might ask why humans evolved to throw fast while others did not; whether the design of a fast thrower is unique or special and whether indeed humans remain fast within broader comparison sets of non-hominidthrowers. As a non-hominid comparison set, we consider a random population of five-link robots with simplified joint angle and torque constraints. We generate 20,000 such robot models and sequentially optimize their throwing motion. Since good initial guesses are needed for each optimization, the robots are first arranged in distance-minimizing sequences in design parameter space. Each robot’s optimal throw then serves as an initial guess for the next one in sequence. Multiple traversals of these sequences, and random perturbations, are used toavoid local optima. Subsequently, regression models are used to predict throwing performance as a function of robot design parameters. From these regression models, the dominant heuristic predictor of fast throwing is found to be a long and light last link. Direct optimization of the robot design leads to much faster throwers, also with long and light last links. In striking contrast, the human arm has two equally long intermediate links of significant mass. Nevertheless, a somewhat human-like arm within the same robot set is found to be a good thrower. On combining several throwing criteria to obtain a single figure of merit, the human-like arm lies in the 96th percentile of the population. Since our human-like arm is a crude approximation of an actual human arm, we suggest that fast throwing by human-like robot arms is not inherently difficult from a mechanical point ofview.

    • Variability in large-sample postbuckling behavior of two small thin walled structures


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      In thin shell buckling, geometric imperfections are important contributors to observed scatter in experimentally determined postbuckling behavior. Buckling experiments with large shells are difficult and expensive to conduct, and hence the sample sizes of buckling tests reported in the literature are generally small.To study statistical variability of buckling loads for a large number of notionally identical thin shells, we have carried out 100 buckling experiments each for two thin shell geometries. One shell geometry is a dome-like shell with a flat base (a bowl), and the other is a truncated cone with a flat base (a tumbler). The test shells are industrially produced, inexpensive, made of stainless steel, and easily available in India as utensils for domestic use. We provide detailed geometric and material characterization of these thin shell specimens. These shells were compressed axially between rigid plates. Buckling for both shell geometries was elastoplastic in nature. The experimental buckling load–displacement curves of 100 specimens for the bowl show variability in buckling loads by a factor of two, and stable postbuckling response. The corresponding curves for 100 specimens of the tumbler show variations of as much as a factor 5, with many snap-throughs, and unstable postbuckling response for larger compressions. We present two sets of axisymmetric elastoplastic finite element simulations of the tumbler, with both (a) tractions directly applied on a predetermined region and (b) through contact with a rigid plate. The latter set of simulations show approximately twice as much sensitivity to geometrical imperfections. Our results may guide new assessments of factors of safety in buckling, as laid downin design codes, when there is a chance of such interactions between contact loading and geometry.

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