In the present paper, the buckling problem of rectangular functionally graded (FG) plate with arbitrary edge supports is investigated. The present analysis is based on the classical plate theory (CPT) and large deformation is assumed for deriving stability equations. The plate is subjected to bi-axial compression loading. Mechanical properties of FG plate are assumed to vary continuously along ...

This paper is the first in a series devoted to the approximation theory of the p-version of the finite element method in three dimensions. In this paper, we introduce the Jacobi-weighted Besov and Sobolev spaces in the three-dimensional setting and analyze the approximability of functions in the framework of these spaces. In particular, the Jacobi-weighted Besov and Sobolev spaces with three di...

In the current research work, the problem of fracture mechanics in a plate with a central hole under tensile loading is studied. The stress intensity factors are calculated for a finite plate containing two symmetrical hole-edge cracks. The problem is solved by two different methods, namely the finite element method and the FRANC software analysis. At first the finite element method is used and...

Rapid development of engineering activities expands through a variety of rock engineering processes such as drilling, blasting, mining and mineral processing. These activities require rock dynamic fracture mechanics method to characterize the rock behavior. Dynamic fracture toughness is an important parameter for the analysis of engineering structures under dynamic loading. Several experimental...

We propose a new algorithm for adaptive finite element methods (AFEMs) based on smoothing iterations (S-AFEM), linear, second-order, elliptic partial differential equations (PDEs). The is inspired by the ascending phase of V-cycle multigrid method: we replace accurate algebraic solutions in intermediate cycles classical AFEM with application prolongation step, followed smoother. Even though the...

In this paper, edge crack problems under mechanical loads have been analysed using extended finite element method (XFEM) as it has proved to be a competent method for handling problems with discontinuities. The XFEM provides a versatile technique to model discontinuities in the solution domain without re-meshing or conformal mesh. The stress intensity factors (SIF) have been calculated by domai...

A new way of modelling and solving partial differential equations is derived. While the finite element (FE) methodology is based on the integration over finite elements, this novel approach utilizes edges (finite lines) instead, which results in a finite line integration (FLIM). We present how the FE-computations over elements (areas or volumes) can be rewritten for the stiffness matrix based o...

This paper is devoted to a rigorous mathematical foundation for the convergence properties of strain-smoothed element (SSE) method. The SSE method has demonstrated improved behaviors compared other strain smoothing methods through various numerical examples; however, there been no theoretical evidence behavior. A unique feature construction smoothed fields within elements by fully unifying stra...