On the Asymptotic Nature of Approximate Models of Beams, Plates, and Shells

By using test examples, results obtained for the approximate models of beams, plates, and shells based on the Bernoulli-Kirchhoff-Love and Timoshenko-Reissner kinematical hypotheses are compared with asymptotic solutions to the 3D equations of elasticity theory for narrow areas. Static and free vibration problems for bodies made of linearly elastic orthotropic materials are studied. The main attention is paid to the cases in which the material stiffness in the tangential directions is much larger than that in the transversal direction.