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...

This paper deals with local buckling analysis of rectangular functionally graded material plates using finite strip method and based on classical plate theory. The modulus of elasticity of the plate is assumed to vary according to a power-law distribution in terms of the volume fractions of the constituents. The principle of minimum total potential energy is employed to obtain stiffness and sta...

Bending analysis of FGM plates under uniform and sinusoidal loaded result in forth order partial differential equation. In this paper the analytical solution is based on the extended Kantorovich iterative procedure. The differential equations for the iterative procedure is derived using the Galerkin method. The solution was develope based on the classical plate’s theory (CLPT). The reliability ...

the nonlocal nonlinear buckling of a double layer graphene sheet (dlgs) covered by zinc oxide (zno) piezoelectric layers is investigated in this study. the surrounding circumstances of the system are considered as a pasternak foundation including spring constants and a shear layer. graphene sheets are subjected to longitudinal magnetic field and biaxial forces. on the other hand, the zno piezoe...

This paper addresses the influence of boundary conditions and small-scale effect on the free vibration of nano-plates using molecular dynamics (MD) and nonlocal elasticity theory. Based on the MD simulations, Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) is used to obtain fundamental frequencies of single layered graphene sheets (SLGSs) which modeled in this paper as the mo...

In this article, classical plate theory (CPT) is reformulated using the nonlocal differential constitutive relations of Eringen to develop an equivalent continuum model for orthotropic triangular nanoplates. The equations of motion are derived and the Galerkin’s approach in conjunction with the area coordinates is used as a basis for the solution. Nonlocal theories are employed to bring out the...

Flexural wave speeds on beams or plates depend upon the bending stiffnesses which differ by the well-known factor (1 - nu2). A quantitative analysis of a plate of finite lateral width displays the plate-to-beam transition, and permits asymptotic analysis that shows the leading order dependence on the width. Orthotropic plates are analyzed using both the Kirchhoff and Kirchhoff-Rayleigh theories...

In this paper, transfinite element method is used to analyze the two dimensional thermoelasticity problems. A comparison is made between the thermoelastic analysis results of the classical theory and theories with one or two relaxation times (i.e. L-S and G-L theories), for the half space problem. Governing equations are transformed to Laplace domain and then, node variables are calculated by t...

Plate-type structural members are commonly used in engineering applications like aircraft, ships nuclear reactors etc. These structural members often have cracks arising from manufacture or from material defects or stress concentrations. Designing a structure against fracture in service involves consideration of strength of the structure as a function of crack size, dimension and the applied lo...