Engr. Charles Chinwuba IKE | Enugu State University of Science and Technology (original) (raw)

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Papers by Engr. Charles Chinwuba IKE

Journal of mechanical engineering, automation and control systems, Feb 22, 2024

Maǧallaẗ al-handasaẗ wa-al-tiknūlūǧiyā, Dec 2, 2023

Journal of engineering and thermal sciences, Mar 16, 2024

Maǧallaẗ al-handasaẗ wa-al-tiknūlūǧiyā, Nov 18, 2023

Mathematical models in engineering, Dec 29, 2023

Applied and Computational Mechanics, 2019

In this work, the Mellin transform method was used to obtain solutions for the stress field compo... more In this work, the Mellin transform method was used to obtain solutions for the stress field components in two dimensional (2D) elasticity problems in terms of plane polar coordinates. the Mellin transformation was applied to the biharmonic stress compatibility equation expressed in terms of the Airy stress potential function, and the boundary value problem transformed to an algebraic problem which was solved to obtain the Mellin transformed Airy stress potential function. The Mellin transform was similarly used to obtain the Mellin transformed stress field components. The use of Mellin transform inversion formula yielded the solutions to the 2D elasticity problem in the physical space domain variables. Specific illustration was considered of the solution by using the Mellin transform method for the Flamant problem and the Mellin transform solutions found to agree with solutions from the literature.

International Journal of Scientific & Technology Research, 2020

The Fourier cosine transform method was used in this work to obtain general solutions for stresse... more The Fourier cosine transform method was used in this work to obtain general solutions for stresses and displacement fields in homogeneous, isotropic linear elastic soil of semi-infinite extent due to a point load applied vertically at the origin of the half plane. A stress-based formulation was used. Boussinesq-Papkovich potential functions were used to express the displacement components, strains, and stresses. Fourier cosine transformation of the biharmonic stress compatibility equation was done to obtain suitable bounded stress functions for the problem. Stresses were similarly expressed in the Fourier cosine transform space variable, by Fourier cosine transformation. Enforcement of stress boundary conditions were used to obtain the unknown constants of the stress functions. Inversion of the Fourier cosine transforms of the stresses yielded the general expressions for the stress fields in the physical domain two dimensional Cartesian variables. The strain fields were obtained usi...

Civil Engineering and Architecture, 2021

Mathematical Modelling in Civil Engineering, 2018

The Fourier sine transform method was implemented in this study to obtain general solutions for s... more The Fourier sine transform method was implemented in this study to obtain general solutions for stress and displacement fields in homogeneous, isotropic, linear elastic soil of semi-infinite extent subject to a point load applied tangentially at a point considered the origin of the half plane. The study adopted a stress based formulation of the elasticity problem. Fourier transformation of the biharmonic stress compatibility equation was done to obtain bounded stress functions for the elastic half plane problem. Stresses and boundary conditions expressed in terms of the Boussinesq-Papkovich potential functions were transformed using Fourier sine transforms. Boundary conditions were used to obtain the unknown constants of the stress functions for the Cerrutti problem considered; and the complete determination of the stress fields in the Fourier transform space. Inversion of the Fourier sine transforms for the stresses yielded the general expressions for the stresses in the physical d...

In this work, the least squares weighted residual method is used to solve the two-dimensional (2D... more In this work, the least squares weighted residual method is used to solve the two-dimensional (2D) elasticity problem of a rectangular plate of in-plane dimensions 2a 2b subjected to parabolic edge tensile loads applied at the two edges x = a. The problem is expressed using Beltrami–Michell stress formulation. Airy’s stress function method is applied to the stress compatibility equation, and the problem is expressed as a boundary value problem (BVP) represented by a non-homogeneous biharmonic equation. Airy’s stress functions are chosen in terms of one and three unknown parameters and coordinate functions that satisfy both the domain equations and the boundary conditions on the loaded edges. Least squares weighted residual integral formulations of the problems are solved to determine the unknown parameters and thus the Airy stress function. The normal and shear stress fields are determined for the one-parameter and the three-parameter coordinate functions. The solutions for the stre...

In this study, stress and displacement functions of the three-dimensional theory of elasticity fo... more In this study, stress and displacement functions of the three-dimensional theory of elasticity for homogeneous isotropic bodies are derived from first principles from the differential equations of equilibrium, the generalized stress – strain laws and the geometric relations of strain and displacement. It is found that the stress and displacement functions must be biharmonic functions. The derived functions are used to solve the elasticity problem of finding stresses and displacement fields in a thick circular plate with clamped edges for the case of uniformly distributed transverse load over the plate domain. Superposition of second to sixth order Legendre polynomials which are biharmonic functions are used in the thick circular plate problem as the stress function with the unknown constants as the parameters to be determined. Use of the stresses and displacement fields derived in terms of the stress and displacement function yielded the stress fields and displacement fields in term...

Advances in Modelling and Analysis A, 2019

Latin American Journal of Solids and Structures, 2019

International Journal of Innovative Technology and Exploring Engineering, 2019

The partial differential equations (PDE) of equilibrium governing the natural vibrations of concr... more The partial differential equations (PDE) of equilibrium governing the natural vibrations of concrete gravity dams were derived in this work such that the fluid structure interactions were accounted for. The displacement formulation is a system of two coupled PDE in two unknown displacement components. For seismic ground motion assumed to be horizontal harmonic motion whose amplitude and period are known, the system of two coupled PDEs were solved subject to the boundary conditions using the method of undetermined parameters. In applying the method of undetermined parameters to the PDE, displacement shape functions constructed to satisfy the displacement boundary conditions were used in assuming the trial dynamic displacement fields in terms of two unknown parameters that were determined by substitution into the governing equations. Conditions for the trial dynamic displacement fields to be solutions to the governing PDE were sought by solving the resulting system of equations. The p...

Mathematical Modelling of Engineering Problems, 2021

The Fourier integral method was used in this work to determine the stress fields in a two dimensi... more The Fourier integral method was used in this work to determine the stress fields in a two dimensional (2D) elastic soil mass of semi-infinite extent subject to line and strip loads of uniform intensity acting on the boundary. The two dimensional plane strain problem was formulated using stress-based method. The Fourier integral was used to transform the biharmonic stress compatibility equation to a fourth order linear ordinary differential equation (ODE) in terms of the stress function. The ODE was solved subject to the boundedness condition to obtain the bounded stress function. Cartesian stress components were obtained using the Love stress functions. Application of the stress boundary conditions for the case of line load of uniform intensity and the cases of uniformly distributed load on a strip of finite width gave the respective unknown constants of the Love stress functions; and hence the complete determination of the Cartesian stress components for the two cases considered. I...

The elastic buckling problem of moderately thick plates, presented as a classical problem of the ... more The elastic buckling problem of moderately thick plates, presented as a classical problem of the mathematical theory of elasticity is solved in this work using the Laplace transform method. The governing equation solved was a fourth order ordinary differential equation (ODE) and solutions were obtained for various end support conditions, namely fixedfixed ends, fixed-pinned ends, pinned-fixed ends and pinnedpinned ends. Application of the Laplace transformation to the governing domain equation simplified the ODE to an algebraic equation in the Laplace transform space. Inversion yielded the general solution in the physical domain space in terms of the initial values of the buckled deflection and its derivatives. Boundary conditions for the considered end support conditions were then used on the general solution, reducing the problem to algebraic eigenvalue problem represented by a system of homogeneous equations. The condition for nontrivial solution was used to obtain the characteri...

In this paper, the Trefftz potential function method has been used to solve the three dimensional... more In this paper, the Trefftz potential function method has been used to solve the three dimensional problem of elasticity for a point load P acting at the origin on the boundary of a linear elastic homogeneous soil mass of semi-infinite extent. The Trefftz potential function method simplified the problem to finding a harmonic function that satisfies the loading boundary condition. The functions were used together with the geometric and constitutive relations to obtain the stress and displacement fields. The solutions obtained for stress fields and displacement fields were the same as those obtained by Boussinesq.