Abstract:

The objective of this lecture is to present an overview of the author?s recent research on nonlocal elasticity and modified couple stress/strain gradient theories in formulating the governing equations of functionally graded material beams and plates. In addition to Eringen?s nonlocal elasticity (1972), two different nonlinear gradient elasticity theories that account for (a) geometric nonlinearity and (b) microstructure-dependent size effects are revisited to establish the connection between the two theories (Reddy and Srinivasa, 2014). The first theory is based on modified couple stress theory of Mindlin (1963) and Yang et al. (2000) and the second one is based on Srinivasa?Reddy gradient elasticity theory (2013). The modified couple stress theory includes a material length scale parameter that can capture the size effect in a material. The Srinivasa?Reddy (2013) theory contains, as a special case, the first one. These two theories are used to derive the governing equations of beams and plates. The research reported herein was carried out while the author was supported by MURI09 grant FA-9550-09-1-0686 from Air Force Office of Scientific Research and NSF Grant CMMI-CMMI-1000790.