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Title:Design optimization for 2-D granular media with dissipation
Author(s):Salazar De Troya, Miguel Angel
Department / Program:Mechanical Sci & Engineering
Discipline:Mechanical Engineering
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):sensitivity analysis
discrete adjoint
granular media
adaptive time step
explicit algorithm
Abstract:We propose an optimization scheme for the tailored dynamic response through a two-dimensional packing of spherical beads. Our goal is to minimize or maximize the reaction force at the desired bead contacts. Two design approaches are presented: introducing interstitial beads and prescribing initial plastic compression in the system. Using the intruders presence or lack thereof as the design variable is a discrete optimization problem. It is necessary to make the problem tractable by convexifying the design space. The intruders presence (or non-presence) are replaced by their volume fraction. A penalty term in the cost function is used to recover the discrete design representation wherein the volume fraction converges to 0,1 values. Constraints on the design space limit the total number of intruders, which is related to the total packing weight. Designs obtained from both the elastic and the elasto-plastic material response are compared. In our second approach, we prescribe the initial plastic compression of the contact law in the beads which alters their stiffnesses. To do this the contact law is shifted by the amount of initial plastic compression and to ensure that all the beads are tightly packed, an upper bound on the initial plastic compression is imposed to limit the amount of plastic deformation between the beads. To evaluate the response, we perform a transient analysis using an explicit Runge-Kutta algorith with an adaptive time step scheme. Residual plasticity is modeled using an empirical one dimensional law that describes the history dependent contact interaction between the beads. A constitutive equation is required to evolve the state variables, i.e. the bead’s plastic deformation and large displacements are considered. Sensitivities are calculated using an adjoint method for the coupled transient analysis.
Issue Date:2015-05-01
Rights Information:Copyright 2015 Miguel Angel Salazar De Troya
Date Available in IDEALS:2015-07-22
Date Deposited:May 2015

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