Abstract A balance law for material momentum in shells and plates is proposed. The implications of this the propagation defects, phase transformations, shocks are explored. developments presented using a purely mechanical theory Cosserat (or directed) shell specialized to cases Kirchhoff–Love linearly elastic plate theory. To explore connections literature on delamination adhesion, applied prob...

WE DERIVE FIELD EQUATIONS for a functionally graded plate whose deformations are governed by either the first-order shear deformation theory or the third-order sheardeformation theory. These equations are further simplified for a simply supported polygonal plate. An exact relationship is established between the deflection of the functionally graded plate and that of an equivalent homogeneous Ki...

in this paper, a nonlinear free vibration analysis of thin annular functionally graded (fg) plate integrated with two uniformly distributed actuator layers made of piezoelectric (pzt4) material on the top and bottom surfaces of the annular fg plate is presented based on kirchhoff plate theory. the material properties of the fgm core plate are assumed to be graded in the thickness direction acco...

Abstract We present a new study of linear elasticity for an infinite three-dimensional plate of finite thickness Ω = IR2×(−1, 1). We first caracterize the kernel of the operator of elasticity as polynomials which can be build from the kernel of the classical Kirchhoff-Love model of plate. Using this characterization we get optimal uniform elliptic estimates W , C on the solution as a function o...

The Kirchhoff-Love plate theory is appropriate for analysing thin structures. In a simple form, only one degree of freedom (per node) needed to describe the behaviour plate, thus saving computational cost. Besides, analysis cracked structures important because it related lifetime Therefore, this paper uses extended radial point interpolation method (XRPIM) investigate free vibration plate. XRPI...

We develop a mixed finite-element approximation scheme for Kirchhoff plate theory based on the reformulation of Kirchhoff plate theory of Ortiz and Morris [1]. In this reformulation the moment-equilibrium problem for the rotations is in direct analogy to the problem of incompressible two-dimensional elasticity. This analogy in turn opens the way for the application of diamond approximation sche...

In this paper, micromechanics methods are applied to characterize the damage of plate structures, both Love-Kirchhoff and Reissner-Mindlin plates, due to microcrack distribution. Analytical expressions for effective stiffness of a damaged plate with distributed microcracks are derived for the first time. The results are compared with the results based on continuum damage theory, and it is found...

We present two new recovery-based a posteriori error estimates for the Hellan–Herrmann–Johnson method in Kirchhoff–Love plate theory. The first estimator uses postprocessed deflection and controls \(L^2\) moment discrete \(H^2\) error. second one \(L^2\times H^1\) total utilizes superconvergent field deflection. effectiveness of theoretical results is numerically validated several experiments.