Micropolar and Director Theories of Plates

摘要

After discussing the relationship between general theories based on dipolar displacement and micropolar displacement and the relations of these to a theory with a simple dipolar displacement (i.e., full displacement gradient), the remainder of the paper is concerned with linear theories of elastic plates in the presence of micropolar and director displacements. Using a method of asymptotic expansion, plate equations are derived from the three-dimensional equations of both the linearized theory of micropolar elasticity and the linearized theory of directors for an elastic body. The equations resulting from the latter derivation completely agree with those obtained previously for an elastic Cosserat plate. (Author)