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• Open Access

ARTICLE

On Solving Linear and Nonlinear Sixth-Order Two Point Boundary Value Problems Via an Elegant Harmonic Numbers Operational Matrix of Derivatives

W.M. Abd- Elhameed1,2
CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.3, pp. 159-185, 2014, DOI:10.3970/cmes.2014.101.159
Abstract This paper is concerned with developing two new algorithms for direct solutions of linear and nonlinear sixth-order two point boundary value problems. These algorithms are based on the application of the two spectral methods namely, collocation and Petrov-Galerkin methods. The suggested algorithms are completely new and they depend on introducing a novel operational matrix of derivatives which is expressed in terms of the well-known harmonic numbers. The basic idea for the suggested algorithms rely on reducing the linear or nonlinear sixth-order boundary value problem governed by its boundary conditions to a system of linear or nonlinear algebraic equations which can… More >

• Open Access

ARTICLE

Time-Domain BEM Analysis for Three-dimensional Elastodynamic Problems with Initial Conditions

Yuan Li1, Jianming Zhang1,2, Guizhong Xie1, Xingshuai Zheng1, Shuaiping Guo1
CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.3, pp. 187-206, 2014, DOI:10.3970/cmes.2014.101.187
Abstract In this paper, a time-domain boundary element method formulation for the analysis of three-dimensional elastodynamic problems with arbitrary, non-null initial conditions is presented. The formulation is based on the convolution quadrature method, by which the numerical stability is improved significantly. In order to take into account the non-null initial conditions in this formulation, a general method is developed to replace the initial conditions by equivalent pseudo-forces based on the pseudo-force method. The original governing equation is transformed into a new one subjected to null initial conditions. In the numerical examples, longitudinal vibrations of a free beam and a cantilevered beam… More >

• Open Access

ARTICLE

Dynamic Response of Borehole in Poroelastic Medium with Disturbed Zone

W. Kaewjuea1, T. Senjuntichai2, R.K.N.D. Rajapakse3
CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.3, pp. 207-228, 2014, DOI:10.3970/cmes.2014.101.207
Abstract Dynamic response of an infinite cylindrical borehole in a poroelastic medium with an excavation disturbed zone is investigated in this paper. The borehole is subjected to axisymmetric time-harmonic loads and fluid sources applied to its surface, which is either fully permeable or impermeable. The governing equations based on Biot’s poroelastodynamics theory are solved by using two scalar potentials and two vector potentials. The general solutions are then derived through the application of Fourier integral transform with respect to the vertical coordinate. An exact stiffness matrix scheme is established from the derived general solutions to include the excavation disturbed zone. Boundary… More >