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On Material Optimization in Continuum Dynamics

  • Konstantin A. Lurie
Chapter
  • 547 Downloads
Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 15)

Abstract

This chapter deals with material optimization in dynamics—the class of problems that necessarily require the involvement of DM to meet the challenges put forth by the temporally changing environment. These problems can be regular and irregular in the sense of Chapter  2. For any particular case, there is no a priori knowledge about the regularity or irregularity of an optimal material layout, so the irregular case should be characterized by a special scenario dictated by the physics accompanying collisions of characteristics. An example of such scenario for the problem of optimal delivery of masses is discussed in detail; it illustrates the way of relaxation of an optimal problem totally different from the homogenization procedure traditionally applicable in statics. Particularly, this result indicates that homogenization in material dynamics is of limited significance compared to its role in statics.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Konstantin A. Lurie
    • 1
  1. 1.Department of Mathematical SciencesWorcester Polytechnic InstituteWorcesterUSA

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