Exact Solution of the Elastica with Transverse Shear Effects - Zalmanovici, Adrian Marcel; Rebello da Fonseca Brasil, Reyolando Manoel Lopes; Balthazar, Jose Manoel [UNESP] (World Scientific Publ Co Pte Ltd, 2014)
A new derivation of Euler's Elastica with transverse shear effects included is presented. The elastic potential energy of bending and transverse shear is set up. The work of the axial compression force is determined. The equation of equilibrium is derived using the variation of the total potential. Using substitution of variables an exact solution is derived. The equation is transcendental and does not have a closed form solution. It is evaluated in a dimensionless form by using a numerical procedure. Finally, numerical examples of laminates made of composite material (fiber reinforced) and sandwich panels are provided.
Keywords: Postbuckling; transverse shear; elastica; composite beam