On minimum compliance problems of thin elastic plates of varying thickness
Sławomir Adam Czarnecki , Tomasz Denis Lewiński
AbstractThe paper deals with two minimum compliance problems of variable thickness plates subject to an in-plane loading or to a transverse loading. The first of this problem (called also the variable thickness sheet problem) is reduced to the locking material problem in its stress-based setting, thus interrelating the stress-based formulation by Allaire (2002) with the kinematic formulation of Golay and Seppecher (Eur J Mech A Solids 20:631-644, 2001). The second problem concerning the Kirchhoff plates of varying thickness is reduced to a non-convex problem in which the integrand of the minimized functional is the square root of the norm of the density energy expressed in terms of the bending moments. This proves that the problem cannot be interpreted as a problem of equilibrium of a locking material. Both formulations discussed need the numerical treatment in which stresses (bending moments) are the main unknowns.
|Journal series||Structural and Multidisciplinary Optimization, ISSN 1615-147X|
|Publication size in sheets||0.7|
|Keywords in English||design problem, locking materials, Minimum compliance, Optimum design of plates, Plates of varying thickness, shape optimization, topology, variable thickness|
|ASJC Classification||; ; ; ;|
|Score|| = 30.0, 12-06-2020, ArticleFromJournal|
= 35.0, 12-06-2020, ArticleFromJournal
|Publication indicators||= 4; = 8; = 13.0; : 2013 = 2.327; : 2013 = 1.696 (2) - 2013=2.061 (5)|
|Citation count*||13 (2020-09-08)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.