# Mujibur RahmanThe Boeing Company

Mujibur Rahman

Doctor of Philosophy

## About

69

Publications

5,113

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547

Citations

Citations since 2016

Introduction

Mujibur Rahman, Ph.D.,
Lead Structural Analyst,
The Boeing Company

## Publications

Publications (69)

We demonstrate that fractional Laplacian (FL) is the principal characteristic operator of harmonic systems with self-similar interparticle interactions. We show that the FL represents the ‘fractional continuum limit’ of a discrete ‘self-similar Laplacian’
which is obtained by Hamilton's variational principle from a discrete spring model. We deduce...

We analyze the “fractional continuum limit” and its generalization to n dimensions of a self-similar discrete spring model which we introduced recently [21]. Application of Hamilton’s (variational) principle determines in rigorous manner a self-similar and as consequence non-local Laplacian operator. In the fractional continuum limit the discrete s...

We analyse some fundamental problems of linear elasticity in one-dimensional (1D) continua where the material points of the medium interact in a self-similar manner. This continuum with ‘self-similar’ elastic properties is obtained as the continuum limit of a linear chain with self-similar harmonic interactions (harmonic springs) which was introduc...

We analyse some fundamental problems of linear elasticity in one-dimensional (1D) continua where the material points of the medium interact in a self-similar manner. This continuum with 'self-similar' elastic properties is obtained as the continuum limit of a linear chain with self-similar harmonic interactions (harmonic springs) which was introduc...

We employ a self-similar Laplacian in the one-dimensional infinite space and deduce a model for one-dimensional self-similar elasticity. As a consequence of self-similarity this Laplacian assumes the non-local form of a self-adjoint combination of fractional integrals. The linear elastic constitutive law becomes a non-local convolution with the ela...

We analyse some fundamental problems of linear elasticity in one-dimensional (1D) continua where the material points of the medium interact in a self-similar manner. This continuum with 'self-similar' elastic properties is obtained as the continuum limit of a linear chain with self-similar harmonic interactions (harmonic springs) which was introduc...

We analyze a quasi-continuous linear chain with self-similar distribution of
harmonic interparticle springs as recently introduced for one dimension
(Michelitsch et al., Phys. Rev. E 80, 011135 (2009)). We define a continuum
limit for one dimension and generalize it to $n=1,2,3,..$ dimensions of the
physical space. Application of Hamilton's (variat...

This paper is devoted to the analysis of some fundamental problems of linear
elasticity in 1D continua with self-similar interparticle interactions. We
introduce a self-similar continuous field approach where the self-similarity is
reflected by equations of motion which are spatially non-local convolutions
with power-function kernels (fractional in...

The elastic interaction of certain point singularities with a rigid spherical inclusion embedded into an otherwise infinite elastic medium is investigated. The particular singularities considered are point force, force-dipole (with and without moment), centre of dilatation and concentrated moment. In each case, simple, closed form expressions are d...

We develop a general procedure for solving the first and second fundamental problems of the theory of elasticity for cases where boundary conditions are prescribed on a spherical surface, using Love's general solution of the elastostatic equilibrium equations in terms of three scalar harmonic functions. It is shown that this general solution combin...

The article examines the problem of translation and rotation of a nominally (slightly deformed) spherical rigid inclusion embedded into an unbounded elastic medium. To the first order in the small parameter characterizing the boundary perturbation, explicit expressions are deduced for the induced displacement field as well as for the net force and...

In this brief note, we have derived an approximate analytical expression for the Rayleigh wave speed for an isotropic half-space using Lanczos's approximation. This expression is simpler than the exact expressions reported earlier by a number of authors while at the same is very accurate, with an error not exceeding 0.45%. The same approximation ha...

The object of this article is to introduce integral transform of a particular type, called the Hankel transform, and to illustrate the use of this method by means of examples. The treatment is that of a review article and as such is not meant to be exhaustive; its aim is to give a concatenated account of known results rather than present new ones....

The problem investigated in the article concerns that of indentation of a semi-infinite elastic solid by a circular cylinder with a flat base on the assumption that there are heat sources distributed in the interior of the solid. With the thermo-mechanical coupling as well as the frictional forces between the punch and the solid disregarded, the pr...

Consider the elastostatic problem of a transversely isotropic space embedded with an inclusion in the form of a thin rigid sheet with an elliptical opening. The sheet is given an infinitesimal tangential shift along an arbitrary direction in the plane. By means of Fourier transforms, the problem is reduced to a system of coupled two-dimensional int...

We consider the problem of determining the elastic field in an infinite elastic solid induced by an ellipsoidal inclusion with a distribution of eigenstrains. The particular type of distribution considered in the article is characterized by a polynomial in the Cartesian coordinates of the points of the inclusion. Eshelby showed that in such a situa...

The article investigates the elastostatic problem of axial translation of a rigid elliptical disc-inclusion embedded into
an elastic solid. The case of constant translation was previously studied by Kassir and Sih. The present study focuses on
the more general case in which the translation is characterized by an arbitrary-order polynomial in the Ca...

Considered in the present article is the problem of a line load load moving at a constant transonic speed across the surface of an elastic half-space. Solution of the problem is derived here using the method of Fourier transforms.

Explicit expressions are developed, using Dyson's theorem, for the internal and external potentials of an ellipsoid in a three-dimensiona Euclidean space for the case where the volume mass density varies a ijk(x1/a1)i(x2/a2)j(x3/a3)k where l, i, j, k = 0, 1, 2,... and ai(i = 1, 2, 3) are the semi–axes of the ellipsoid. It turns out that the potenti...

The problem investigated herein concerns that of determining the stress-intensity factor (SIF) for a rigid circular disc-inclusion embedded into an infinitely long circular cylinder. The disc is given a constant translation along the direction perpendicular to its plane. An approximate closed-form expression for the SIF is deduced here using the me...

The paper addresses an elastostatic problem concerning an elliptical disk embedded in a transversely isotropic space. The disk is assumed to be absolutely rigid and in perfect contact with the medium. Then, the problem addressed consists of finding the elastic field in the medium when the disk is given a small shift along the direction perpendicula...

The object of the article is to elucidate the application of the singularity method in classical elastodynamics. To this end solutions for higher–order point singularities, e.g. time–harmonic concentrated moment, centre of dilatation, centre of rotatio and force tensor, are derived from the influence tensor by a method usually employed in the theor...

Elasticity solution is given of the problem of a normal force acting on the surface of a transversely isotropic half-space whose free surface is coated with a thin soft film. The force is directed into the half-space. The thin film is modeled as a two-dimensional continuum in the sense of generalized plane stress. By means of Hankel transform, expl...

The article extends Reissner and Sagoci’s classical solution to the problem of a rigid circular punch bonded to a homogeneous, elastic isotropic half-space in which there is an axisymmetrical distribution of buried torsional forces. The surface of the half-space is free from stresses. The punch undergoes rotation due to the action of the internal l...

The paper addresses the problem of contact of an elliptical inclusion in the form of a thin disk, bonded in the interior of a transversely isotropic space. The inclusion is assumed to be absolutely rigid aim in perfect contact with the medium. These different eases of loading are considered, namely, (a) the inclusion is loaded in its plane by a she...

This is a sequel to the first part of the two-part paper, which addresses the problem of contact of a rigid elliptical disk-inclusion bonded in the interior of a transversely isotropic space under three different types of loading, namely (a) the inclusion is loaded in its plane by a shearing force, whose line of action passes through the center of...

The present article elucidates a method that permits the calculation of
the crack-opening volume of a generally non-axisymmetrically loaded
circular crack of tensile mode through its stress intensity factor. It
has been further shown that the derivative of the crack-opening volume
with respect to the crack radius is directly proportional to the mea...

The present paper concerns an interesting phenomenon in linear elastostatics, first discovered by Savin and Rvachev. They observed that there are many solutions in linear elastostatics where factual compatibility is guaranteed not everywhere in the domain. In this article, we present a detailed exposition of these results which seem to have not yet...

The article concerns the problem of bonded contact of a thin, flexible elliptical disk with a transversely isotropic half-space. Three different cases of loading have been considered: (a) the disk is loaded by a transverse force, whose line of action passes through the center of the disk and lies in the plane of the disk; (b) the disk is subjected...

The elastostatic problem of a semi-infinite solid whose surface is reinforced by a thin film and acted upon by an axial ring load is investigated in this paper. Explicit expressions are derived for the surface displacements of the solid.

The paper concerns the problem of determining the stress intensity factor for a circular crack imbedded in an infinitely long cylinder subjected to symmetric normal loading. The cylinder is made of an inhomogeneous material with shear modulus varying with depth as μ = μ0¦z¦n, 0 ≤ n ≤1. Poisson's ratio of the material is assumed to be constant. The...

The present paper elaborates the basic features of application of the plane section method for determining stress intensity factors for cracks in elastic solids with finite geometry. A brief review of the results previously obtained as well as some new results obtained by the author are also presented.

The present article is concerned with finding an integral representation for the product of two first kind Bessel functions, in general, of unequal non-negative integral orders with different arguments, of the form J m+n (r) J n (r 0 ). Products of this kind arise in many problems of mathematical physics, especially in connection with the applicati...

The elastodynamic problem of a rigid punch moving at a constant sub-Rayleigh speed across the surface of an elastic half-space is investigated in the present paper. The unknown contact region is determined as part of solution from the unilateral or Signorini conditions. Numerical results are plotted showing how the eccentricity of the contact ellip...

The axisymmetric problem of determining the dynamic stress intensity factor for a penny-shaped crack in an infinite elastic medium subjected to the action of time-harmonic radial shear body forces is considered in the present paper. The solution of the problem is obtained by superposition of the solutions of two simpler problems. the first of these...

In many sliding systems, the sliding surfaces are not coextensive, so that points on one surface experience alternating periods of contact and separation. This intermittent process can be expected to influence the sliding speed at which the system is susceptible to frictionally-induced thermoelastic instability (TEI). This question is explored in t...

The present paper is concerned with the problem of determining dynamic SIF of a penny-shaped crack in an infinite elastic medium, which is subjected to the action of time-harmonic axial body forces, placed symmetrically with respect to the crack plane. The solution of the problem is obtained by superposition of the solutions of two simpler problems...

Peer Reviewed http://deepblue.lib.umich.edu/bitstream/2027.42/42781/1/10704_2004_Article_BF00033725.pdf

Some axially symmetric singular solutions are derived for an elastic space subjected to the action of time-dependent body
forces. These singular solutions may also be defined as the axisymmetric elastodynamic Green's functions. They correspond
to the cases where a unit concentrated force (time-harmonic or transient) is uniformly distributed along c...

The numerical expression for the speed CR at which Rayleigh waves can propagate over the surface of an isotropic linear elastic half-space was presented. The speed CR was shown to be a root of a given equation from which a cubic equation in m was derived. The objective of this paper was to develop the closed-form solutions of the cubic equation and...

The present paper is concerned with finding an effective polynomial solution to a class of dual integral equations which arise in many mixed boundary value problems in the theory of elasticity. The dual integral equations are first transformed into a Fredholm integration equation of the second kind via an auxiliary function, which is next reduced t...

The problem of determining dynamic SIF for a penny-shaped crack embedded in an infinite elastic medium in which time-harmonic torsional body forces are available is investigated in the present paper. The solution of the title problem is obtained by superposition of the solutions of two simpler problems. The first problem corresponds to the unpertur...

## Projects

Project (1)

The project will be devoted to a review of different methods and methodologies for LCF lifing of SC & DS type of materials used in gas turbine technology.