Shells with thickness distension

Plane Wave Solutions and Modal Analysis in Higher Order Shear and Normal Deformable Plate Theories

“…and signi"es a pure longitudinal wave with constant displacement through the thickness; these kind of waves, involving in-plane deformations and thickness distension, have been analyzed also by Di Carlo et al [9]. After a certain value of the non dimensional frequency the = waves do not decay anymore.…”

“…Most of the higher order plate theories available in the literature neglect transverse normal strains, those due to Mindlin and Medick [1], Soldatos and Watson [2], Babu and Kant [3], Chao et al [4], Lee and Yu [5], Batra and Vidoli [6], Messina [7], Carrera [8], Di Carlo et al [9] and the Cosserat brothers [10], amongst others, account for them. In general, all these plate theories are derived from the equations of three-dimensional elasticity by expanding the kinetic and the kinematic "elds as a power series in terms of the thickness co-ordinate z, and the plate theory is called higher order if terms involving z) with K*3 are retained in these expansions.…”

Vibrations of thick isotropic plates with higher order shear and normal deformable Plate theories

“…see [1,2]) neglect transverse normal strains, those derived by Mindlin and Medick [3], Soldatos and Watson [4], Babu and Kant [5], Chao et al [6], Lee and Yu [7], Batra and Vidoli [8], Messina [9], Carrera [10], DiCarlo et al [11] and the Cosserat brothers [12], amongst others, consider them. Transverse normal deformations are significant in thick plates and also in laminated plates with laminae having widely different elastic constants.…”

A hybrid stress approach for laminated composite plates within the First-order Shear Deformation Theory

“…The laminated plate is modeled based on the First-order Shear Deformation Theory, viewed as a twodimensional theory deduced from a parent three-dimensional theory (DiCarlo et al, 2001;Podio-Guidugli, 1991, 2007;Teresi and Tiero, 1997). This allows to rationally justify the introduction of the shear correction factors and the use of three-dimensional equilibrium equations for the reconstruction strategy of transverse stresses.…”

“…In fact, within such a framework, the theoretical tools to pass from the two-dimensional plate model to the three-dimensional continuum model are spontaneously available, such as the definition of shear correction factors and the way to reconstruct the transverse stresses. Various papers have been recently published on the rational deduction of plate and shell theories from the three-dimensional elasticity (Bisegna and Sacco, 1997a,b;DiCarlo et al, 2001;Podio-Guidugli, 1991, 2007;Teresi and Tiero, 1997).…”