The exact one-dimensional theory for end-loaded fully anisotropic beams ofnarrow rectangular cross section

The exact theory of linearly elastic beams developed by Ladeveze and Ladeve ze and Simmonds is illustrated using the equations of plane stress for a fu lly anisotropic elastic body of rectangular shape. Explicit formulas are gi ven for the cross-sectional material operators that appear in the special S aint-Venant solutions of Ladeveze and Simmonds and in the overall beamlike stress-strain relations between forces and a moment (the generalized stress ) and derivatives of certain one-dimensional displacements and a rotation ( the generalized displacement). A new definition is proposed for built-in bo undary conditions in which the generalized displacement vanishes rather tha n pointwise displacements or geometric averages.