modelling of crack propagation by finite element method under mixed mode conditions is of prime importance in fracture mechanics. this paper describes an application of finite element method to the analysis of mixed mode crack growth in linear elastic fracture mechanics. crack growth process is simulated by an incremental crack-extension analysis based on the maximum principal stress criterion,...

a two-dimensional (2d) single particle model for the copolymerization of propylene-ethylene with heterogeneous ziegler-natta catalyst is developed. the model accounts for the effects of the initial shape of the catalyst and carck/ pore patterns on the copolymer composition, polymerization rate and the average molecular weight properties. the spherical and oblate ellipsoidal shapes of catalyst p...

this research work is devoted to the development of a mathematical model for the simulation of the flow of polymeric melts through the die region of extruders. a set of governing equations are solved using finite element method. standard galerkin technique is used in conjunction with the mixed scheme to solve the flow equation. due to the non-linear nature of global equations, the picard iterat...

Vorticity-stream function method and MAC algorithm are adopted to systemically compare the finite volume method (FVM) and finite difference method (FDM) in this paper. Two typical problems—lid-driven flow and natural convection flow in a square cavity—are taken as examples to compare and analyze the calculation performances of FVM and FDMwith variant mesh densities, discrete forms, and treatmen...

In this paper we present a stable hybrid scheme for viscous problems. The hybrid method combines the unstructured finite volume method with high-order finite difference methods in complex geometries. The coupling procedure between the two numerical methods is based on energy estimates and stable interface conditions are constructed. Numerical calculations show that the hybrid method is efficien...

Abstract. An analog of Taylor’s formula, which arises by substituting the classical derivative by a divided difference operator of Askey-Wilson type, is developed here. As an application, a generalization of the binomial theorem is obtained. Besides, this method becomes quite useful to obtain summation formulas of basic hypergeometric series. New proofs of several well-known summation formulas ...

Abstract. An analogue of Taylor’s formula, which arises by substituting the classical derivative by a divided difference operator of Askey-Wilson type, is developed here. We study the convergence of the associated Taylor series. Our results complement a recent work by Ismail and Stanton. Quite surprisingly, in some cases the Taylor polynomials converge to a function which differs from the origi...