An isogeometric Galerkin approach for analysing the free vibrations of piezoelectric shells is presented. The shell kinematics specialized to infinitesimal deformations and follow Kirchhoff–Love hypothesis. Both geometry physical fields are discretized using Catmull–Clark subdivision bases. This provides required C 1 $$ {C}^1 -continuous discretization theory. crystalline structure materials de...

A rectangular isotropic two-layer plate of an irregular structure is considered, the edges which are freely supported, and a constant temperature maintained on them. Two-dimensional Kirchhoff-type thermoelasticity equations two-dimensional heat written for inhomogeneous material were used to study stresses in plate. Using method double trigonometric series spatial variables Laplace integral tra...

The capacitance of the circular parallel plate capacitor is calculated by expanding the solution to the Love integral equation into a Fourier cosine series. Previously, this kind of expansion has been carried out numerically, resulting in accuracy problems at small plate separations. We show that this bottleneck can be alleviated, by calculating all expansion integrals analytically in terms of ...

In this paper, the bending waves propagating along the edge of a semi-infinite Kirchhoff plate resting on a two-parameter Pasternak elastic foundation are studied. Two geometries of the foundation are considered: either it is infinite or it is semi-infinite with the edges of the plate and of the foundation coinciding. Dispersion relations along with phase and group velocity expressions are obta...

We propose a new discontinuous Galerkin (dG) method for geometrically nonlinear Kirchhoff plate model large isometric bending deformations. The minimization problem is nonconvex due to the isometry constraint. present practical discrete gradient flow that decreases energy and computes minimizers satisfy prescribed defect. prove [Formula: see text]-convergence of energies global minimizers. docu...

The aim of this paper is to analyze a piecewise linear finite element method to approximate the buckling and the vibration problems of a thin plate. The method is based on a conforming discretization of a bending moment formulation for the Kirchhoff-Love model. The analysis restricts to simply connected polygonal clamped plates, not necessarily convex. The method is proved to converge with opti...

We employ surface differential calculus to derive models for Kirchhoff plates including in-plane membrane deformations. We also extend our formulation to structures of plates. For solving the resulting set of partial differential equations, we employ a finite element method based on elements that are continuous for the displacements and discontinuous for the rotations, using C0-elements for the...

We study the bending of a thin plate, stiffened with a thin elastic layer, of thickness δ. We describe the complete construction of an asymptotic expansion with respect to δ of the solution of the Kirchhoff-Love model and give optimal estimates for the remainder. We identify approximate boundary conditions, which take into account the effect of the stiffener at various orders. Thanks to the too...

The accuracy and physical significance of the classical Rayleigh-Sommerfeld and Kirchhoff diffraction integrals are assessed in the context of Sommerfeld's rigorous theory of half-plane diffraction and Maxwell's equations. It is shown that the Rayleigh-Sommerfeld integrals are in satisfactory agreement with Sommerfeld's theory in most of the positive near zone, except at sub-wavelength distance...

The effects of selected membrane, plate and flat shell finite element formulations on optimal topologies are numerically investigated. Two different membrane components are considered. The first is a standard 4-node bilinear quadrilateral, and the other is a 4-node element accounting for in-plane (drilling) rotations. Plate elements selected for evaluation include discrete Kirchhoff quadrilater...