Convergence studies for the static analysis of thin plates resting on Pasternak foundations is performed. The are discretized using two different finite elements, formulations which based Kirchhoff and Reissner-Mindlin plate theories. shear locking problem arises when full integration used in element implementation theory eliminated with selective integration. foundation accounted by adding par...

In this paper, we will consider the modelling of problems in linear elasticity on thin plates by the models of Kirchhoff–Love and Reissner– Mindlin. A fundamental investigation for the Kirchhoff plate goes back to Morgenstern [Herleitung der Plattentheorie aus der dreidimensionalen Elastizitätstheorie. Arch. Rational Mech. Anal. 4, 145–152 (1959)] and is based on the two-energies principle of P...

The thermal buckling response of square plates with variable angle tows under simply supported conditions is modeled numerically. path tow as a function lateral location. classical lamination theory utilizes fiber paths to calculate loads and stiffness matrices. Using Kirchhoff plate finite element theory, the global material matrix geometric are obtained. By using these matrices, eigenvalues o...

Based on Lagrange and Hermite interpolation two novel versions of weak form quadrature element are proposed for a non-classical Euler-Bernoulli beam theory. By extending these concept two new plate elements are formulated using Lagrange-Lagrange and mixed Lagrange-Hermite interpolations for a non-classical Kirchhoff plate theory. The non-classical theories are governed by sixth order partial di...

The Kirchhoff-Love plate model is a widely used in the analysis of thin elastic plates. It is well known that Kirchhoff-Love solutions can be viewed as certain limits of displacements and stresses for elastic plates where the thickness tends to zero. In this paper, we consider the problem from a different point of view and derive computable upper bounds of the difference between the exact three...

The modelization of bending plates with through the thickness cracks is investigated. We consider the Kirchhoff-Love plate model which is valid for very thin plates. We apply the eXtended Finite Element Method (XFEM) strategy: enrichment of the finite element space with the asymptotic bending and with the discontinuity across the crack. We present two variants and their numerical validations an...

A cohesive zone modeling (CZM) approach with a bilinear traction-separation relation is used to study the peeling of a thin overhanging plate from the edge of an incompressible elastomeric layer bonded firmly to a stationary rigid base. The deformations are approximated as plane strain and the materials are assumed to be linearly elastic, homogeneous, and isotropic. Furthermore, governing equat...

This study presents critical buckling of functionally graded soft ferromagnetic porous (FGFP) rectangular plates, under magnetic field with simply supported boundary condition. Equilibrium and stability equations of a porous rectangular plate in transverse magnetic field are derived. The geometrical nonlinearities are considered in the Love-Kirchhoff hypothesis sense. The formulations are compa...

In this paper, we prove a Carleman estimate for a Kirchhoff plate equation and apply the Carleman estimate to inverse problems of determining spatially varying two Lamé coefficients and the mass density by a finite number of boundary observations. Our main results are Lipschitz stability estimates for the inverse problems under suitable conditions of initial values and boundary val-