Soumen Shaw - Academia.edu (original) (raw)

Papers by Soumen Shaw

In this note, an improved Regula falsi (IRF) method based on the classical Regula falsi (RF) meth... more In this note, an improved Regula falsi (IRF) method based on the classical Regula falsi (RF) method is proposed. The method is verified on a number of test examples and numerical results. The proposed method has faster convergence rate with respect to the classical Regula falsi method.

The European Physical Journal Plus, Nov 14, 2023

WSEAS transactions on applied and theoretical mechanics, Apr 17, 2024

The present article deals with the thermoelastic behavior of a nonhomogeneous isotropic material.... more The present article deals with the thermoelastic behavior of a nonhomogeneous isotropic material. This study is carried out in the context of an advanced thermoelastic model involving a higher order memory dependent derivative (MDD) with dual time delay terms. The thermoelastic interactions and evolved stresses into the medium are analyzed subject to external mechanical load as well as laser-type heat source. It is observed that the material moduli of the medium have a significant impact on its thermodynamic behavior. The analytical expression of the field functions is obtained in the integral transform domain. To know the nature of the field functions in the spacetime domain, a discretized form of the inverse integral transformations is applied and depicted graphically for various kernel functions and empirical constants.

Computational Mathematics and Mathematical Physics, Jun 30, 2023

The present article deals with a thermodynamic analysis of laser treatment on human skin. Replaci... more The present article deals with a thermodynamic analysis of laser treatment on human skin. Replacing Pennes model of thermodynamics, a well defined memory dependent hyperbolic type thermoelastic heat conduction model is adopted. In order to analyse the thermal shock experienced by the skin layers, a bi-layer skin containing two main layers: epidermis and dermis, is considered. An instantaneous point heat source and a non-Gaussian laser pulse are applied on the skin surface to analyse the thermal memory response into the skin-layers. Two different types of laser beams are considered to validate the thermoelastic observations with the optical results.

Computational Mathematics and Mathematical Physics, Feb 1, 2023

Computational Mathematics and Mathematical Physics

International Journal of Thermophysics, 2021

The main objective of the present paper is to propose a new boundary element modeling technique f... more The main objective of the present paper is to propose a new boundary element modeling technique for simulation and optimization of three-temperature micropolar magneto-thermoviscoelastic problems in anisotropic porous smart structures, where we implemented the genetic algorithm (GA), as a method of optimization based on the free form deformation (FFD) methodology to improve the performance of our proposed technique. Two numerical examples are presented herein, in order to prove that the proposed technique is able to optimize the shape of the domains with minimum computational effort. A nonuniform rational B-spline curve (NURBS) has been introduced to define the optimum boundary where it decreases the number of control points and offers a new degree of versatility in the design of various different shapes. The profiles of the items considered shall be represented by the FFD methodology. The location vectors of the FFD control points are known to be the genes, and then the chromosomes for the profiles are determined by the gene sequence. The population is made up of several chromosomes individuals, where the fitness functions of individuals are assessed using BEM. The numerical results are depicted graphical forms to show the effects of viscosity and magnetic fields on the three temperatures, displacement components, microrotation components, pore pressure, electric potential, and thermal stress components. The validity, accuracy, and computational efficiency of the proposed BEM technique were demonstrated by comparing our BEM-obtained results with the corresponding results of normal mode analysis method (NMAM), finite difference method (FDM), and finite element method (FEM).

Journal of Engineering Physics and Thermophysics, 2012

ABSTRACT This paper deals with the problem of electromagnetic effect on the propagation of Raylei... more ABSTRACT This paper deals with the problem of electromagnetic effect on the propagation of Rayleigh surface waves in a homogeneous, isotropic, thermally-conducting microstretch elastic half-space. In this context, the generalized theory of thermoelasticity is considered. The governing equations for the Rayleigh surface waves in the cases of insulated as well as isothermal boundaries are derived. In the presence of the magnetic effect, the analytical expressions for the displacement, microrotation, microstretch, and temperature changes are obtained. The changes in the phase velocity, microrotation, and path of particles for aluminum epoxy material are presented graphically.

Journal of Engineering Physics and Thermophysics, 2015

The generalized theory of thermodiffusion is applied to study the propagation of plane harmonic w... more The generalized theory of thermodiffusion is applied to study the propagation of plane harmonic waves in an infinitely long isotropic micropolar plate. The present analysis also includes both the thermal and mass diffusive relaxation times, as well as the coupling of the thermal diffusion with microrotation of the material. To determine the effect of the presence of thermal as well as mass diffusion on the phase velocity of the wave propagation, two potential functions are used, and more general dispersive relations are obtained for symmetric and antisymmetric modes. The results for the cases of thermoelasticity, micropolar thermoelasticity, and thermodiffusive elasticity are derived. The changes in the phase velocity, attenuation coefficient, and the specific loss factor with the wave number are shown graphically.

Journal of Engineering Physics and Thermophysics, 2015

The generalized theory of thermoelasticity is applied to study the propagation of plane harmonic ... more The generalized theory of thermoelasticity is applied to study the propagation of plane harmonic waves in an infinitely long, isotropic, micropolar plate in the presence of a uniform magnetic field. The present analysis also includes the thermal relaxation time, electric displacement current, and the coupling of heat transfer and microrotation of the material. To determine the effect of the presence of thermal as well as magnetic fields on the phase velocity, two potential functions are used, and more general dispersive relations are obtained for symmetric and antisymmetric modes. The results for the cases of coupled thermoelasticity, magnetoelasticity, micropolar thermoelasticity, and classical micropolar elasticity as special cases are derived. The changes in the phase velocity and attenuation coefficient with the wave number are shown graphically.

Encyclopedia of Forensic Sciences, 2000

In this paper we introduce a new generalized Fourier series and a Fourier-type integral transform... more In this paper we introduce a new generalized Fourier series and a Fourier-type integral transform. We derive the complex inversion formula, convolution theorem and generalized product theorem. We also attempt to generalize the convolution of two functions and the Dirac-delta function. In the last section we extend our idea to a generalized double Fourier series and transform which can be further extended to n-Fourier series and transform.

Enlightened by the asymptotic behavior of the thin wall structured body, the present study deals ... more Enlightened by the asymptotic behavior of the thin wall structured body, the present study deals with the novel Legendre polynomials to investigate the dynamic behavior of an isotropic thin cylindrical shell by using asymptotic approach under cylindrical symmetry. It is found that the motion in n-th mode of the cylinder does not depend on higher or lower modes and variants of each mode satisfies same set of equations. Here we set some special assumption to make the problem simple and make an attempt to give an analytic expression of radial vibration when a semi-infinite cylinder of large radius is subjected to large longitudinal stimuli. Excellent analytical expressions are demonstrated by using the Duhamel’s principle for non-homogeneous differential equations and due to the presence of Legendre Polynomials, and cylindrical symmetry also. Key-Words: Radial and longitudinal vibration; asymptotic approach; cylindrical shell; cylindrical symmetry; linear classical theory.

In this note, an improved Newton-Raphson (INR) method based on the classical Newton-Raphson (N-R)... more In this note, an improved Newton-Raphson (INR) method based on the classical Newton-Raphson (N-R) method is proposed for solving simultaneous nonlinear equations (SNEs). An implicit function theorem and a resulting modified Newton Raphson method for roots of the functions between finite dimensional spaces is being analyzed without assuming non-singularity of the Jacobian at the initial approximation. The proposed method has faster convergence rate with respect to the other modified Newton’s method for solving SNEs.

A new simple well-behaved definition of the fractional derivative termed as conformable fractiona... more A new simple well-behaved definition of the fractional derivative termed as conformable fractional derivative and introducing a geometrical approach of fractional derivatives, non-integral order initial value problems are an attempt to solve in this article. Based on the geometrical interpretation of the fractional derivatives, the solution curve is approximated numerically. Two special phenomena are employed for concave upward and downward curves. In order to obtain the solution of fractional order differential equation (FDE) with the integer-order initial condition, some new criteria on fractional derivatives are proposed.

WSEAS TRANSACTIONS ON CIRCUITS AND SYSTEMS

The present paper deals with the memory response on thermal disturbances emanating from a cylindr... more The present paper deals with the memory response on thermal disturbances emanating from a cylindrical cavity in an unbounded thermoelastic solid. Here we have theoretically demonstrated the memory response of thermal disturbances in the generalized magneto-thermo-elastic materials. Firstly, the characteristics of thermoelastic disturbances originated from the cavity in an unbounded elastic solid under the light of generalized magnetothermoelasticity theory with memory dependent derivatives (MDD). For numerical computation, cylindrical-polar coordinate system with radial symmetry subjected to two different types of heat sources into the cavity are considered. An integral transform method and, while in inverse transformation, an efficient and pragmatic NILT (Numerical Inverse Laplace Transform) is adopted. Finally, parameter studies are performed to evaluate the effect of the kernel function and time delay. For thermal wave the results show appreciable differences with those in the us...

International Journal for Computational Methods in Engineering Science and Mechanics

The European Physical Journal Plus

In this note, an improved Regula falsi (IRF) method based on the classical Regula falsi (RF) meth... more In this note, an improved Regula falsi (IRF) method based on the classical Regula falsi (RF) method is proposed. The method is verified on a number of test examples and numerical results. The proposed method has faster convergence rate with respect to the classical Regula falsi method.

The European Physical Journal Plus, Nov 14, 2023

WSEAS transactions on applied and theoretical mechanics, Apr 17, 2024

The present article deals with the thermoelastic behavior of a nonhomogeneous isotropic material.... more The present article deals with the thermoelastic behavior of a nonhomogeneous isotropic material. This study is carried out in the context of an advanced thermoelastic model involving a higher order memory dependent derivative (MDD) with dual time delay terms. The thermoelastic interactions and evolved stresses into the medium are analyzed subject to external mechanical load as well as laser-type heat source. It is observed that the material moduli of the medium have a significant impact on its thermodynamic behavior. The analytical expression of the field functions is obtained in the integral transform domain. To know the nature of the field functions in the spacetime domain, a discretized form of the inverse integral transformations is applied and depicted graphically for various kernel functions and empirical constants.

Computational Mathematics and Mathematical Physics, Jun 30, 2023

The present article deals with a thermodynamic analysis of laser treatment on human skin. Replaci... more The present article deals with a thermodynamic analysis of laser treatment on human skin. Replacing Pennes model of thermodynamics, a well defined memory dependent hyperbolic type thermoelastic heat conduction model is adopted. In order to analyse the thermal shock experienced by the skin layers, a bi-layer skin containing two main layers: epidermis and dermis, is considered. An instantaneous point heat source and a non-Gaussian laser pulse are applied on the skin surface to analyse the thermal memory response into the skin-layers. Two different types of laser beams are considered to validate the thermoelastic observations with the optical results.

Computational Mathematics and Mathematical Physics, Feb 1, 2023

Computational Mathematics and Mathematical Physics

International Journal of Thermophysics, 2021

The main objective of the present paper is to propose a new boundary element modeling technique f... more The main objective of the present paper is to propose a new boundary element modeling technique for simulation and optimization of three-temperature micropolar magneto-thermoviscoelastic problems in anisotropic porous smart structures, where we implemented the genetic algorithm (GA), as a method of optimization based on the free form deformation (FFD) methodology to improve the performance of our proposed technique. Two numerical examples are presented herein, in order to prove that the proposed technique is able to optimize the shape of the domains with minimum computational effort. A nonuniform rational B-spline curve (NURBS) has been introduced to define the optimum boundary where it decreases the number of control points and offers a new degree of versatility in the design of various different shapes. The profiles of the items considered shall be represented by the FFD methodology. The location vectors of the FFD control points are known to be the genes, and then the chromosomes for the profiles are determined by the gene sequence. The population is made up of several chromosomes individuals, where the fitness functions of individuals are assessed using BEM. The numerical results are depicted graphical forms to show the effects of viscosity and magnetic fields on the three temperatures, displacement components, microrotation components, pore pressure, electric potential, and thermal stress components. The validity, accuracy, and computational efficiency of the proposed BEM technique were demonstrated by comparing our BEM-obtained results with the corresponding results of normal mode analysis method (NMAM), finite difference method (FDM), and finite element method (FEM).

Journal of Engineering Physics and Thermophysics, 2012

ABSTRACT This paper deals with the problem of electromagnetic effect on the propagation of Raylei... more ABSTRACT This paper deals with the problem of electromagnetic effect on the propagation of Rayleigh surface waves in a homogeneous, isotropic, thermally-conducting microstretch elastic half-space. In this context, the generalized theory of thermoelasticity is considered. The governing equations for the Rayleigh surface waves in the cases of insulated as well as isothermal boundaries are derived. In the presence of the magnetic effect, the analytical expressions for the displacement, microrotation, microstretch, and temperature changes are obtained. The changes in the phase velocity, microrotation, and path of particles for aluminum epoxy material are presented graphically.

Journal of Engineering Physics and Thermophysics, 2015

The generalized theory of thermodiffusion is applied to study the propagation of plane harmonic w... more The generalized theory of thermodiffusion is applied to study the propagation of plane harmonic waves in an infinitely long isotropic micropolar plate. The present analysis also includes both the thermal and mass diffusive relaxation times, as well as the coupling of the thermal diffusion with microrotation of the material. To determine the effect of the presence of thermal as well as mass diffusion on the phase velocity of the wave propagation, two potential functions are used, and more general dispersive relations are obtained for symmetric and antisymmetric modes. The results for the cases of thermoelasticity, micropolar thermoelasticity, and thermodiffusive elasticity are derived. The changes in the phase velocity, attenuation coefficient, and the specific loss factor with the wave number are shown graphically.

Journal of Engineering Physics and Thermophysics, 2015

The generalized theory of thermoelasticity is applied to study the propagation of plane harmonic ... more The generalized theory of thermoelasticity is applied to study the propagation of plane harmonic waves in an infinitely long, isotropic, micropolar plate in the presence of a uniform magnetic field. The present analysis also includes the thermal relaxation time, electric displacement current, and the coupling of heat transfer and microrotation of the material. To determine the effect of the presence of thermal as well as magnetic fields on the phase velocity, two potential functions are used, and more general dispersive relations are obtained for symmetric and antisymmetric modes. The results for the cases of coupled thermoelasticity, magnetoelasticity, micropolar thermoelasticity, and classical micropolar elasticity as special cases are derived. The changes in the phase velocity and attenuation coefficient with the wave number are shown graphically.

Encyclopedia of Forensic Sciences, 2000

In this paper we introduce a new generalized Fourier series and a Fourier-type integral transform... more In this paper we introduce a new generalized Fourier series and a Fourier-type integral transform. We derive the complex inversion formula, convolution theorem and generalized product theorem. We also attempt to generalize the convolution of two functions and the Dirac-delta function. In the last section we extend our idea to a generalized double Fourier series and transform which can be further extended to n-Fourier series and transform.

Enlightened by the asymptotic behavior of the thin wall structured body, the present study deals ... more Enlightened by the asymptotic behavior of the thin wall structured body, the present study deals with the novel Legendre polynomials to investigate the dynamic behavior of an isotropic thin cylindrical shell by using asymptotic approach under cylindrical symmetry. It is found that the motion in n-th mode of the cylinder does not depend on higher or lower modes and variants of each mode satisfies same set of equations. Here we set some special assumption to make the problem simple and make an attempt to give an analytic expression of radial vibration when a semi-infinite cylinder of large radius is subjected to large longitudinal stimuli. Excellent analytical expressions are demonstrated by using the Duhamel’s principle for non-homogeneous differential equations and due to the presence of Legendre Polynomials, and cylindrical symmetry also. Key-Words: Radial and longitudinal vibration; asymptotic approach; cylindrical shell; cylindrical symmetry; linear classical theory.

In this note, an improved Newton-Raphson (INR) method based on the classical Newton-Raphson (N-R)... more In this note, an improved Newton-Raphson (INR) method based on the classical Newton-Raphson (N-R) method is proposed for solving simultaneous nonlinear equations (SNEs). An implicit function theorem and a resulting modified Newton Raphson method for roots of the functions between finite dimensional spaces is being analyzed without assuming non-singularity of the Jacobian at the initial approximation. The proposed method has faster convergence rate with respect to the other modified Newton’s method for solving SNEs.

A new simple well-behaved definition of the fractional derivative termed as conformable fractiona... more A new simple well-behaved definition of the fractional derivative termed as conformable fractional derivative and introducing a geometrical approach of fractional derivatives, non-integral order initial value problems are an attempt to solve in this article. Based on the geometrical interpretation of the fractional derivatives, the solution curve is approximated numerically. Two special phenomena are employed for concave upward and downward curves. In order to obtain the solution of fractional order differential equation (FDE) with the integer-order initial condition, some new criteria on fractional derivatives are proposed.

WSEAS TRANSACTIONS ON CIRCUITS AND SYSTEMS

The present paper deals with the memory response on thermal disturbances emanating from a cylindr... more The present paper deals with the memory response on thermal disturbances emanating from a cylindrical cavity in an unbounded thermoelastic solid. Here we have theoretically demonstrated the memory response of thermal disturbances in the generalized magneto-thermo-elastic materials. Firstly, the characteristics of thermoelastic disturbances originated from the cavity in an unbounded elastic solid under the light of generalized magnetothermoelasticity theory with memory dependent derivatives (MDD). For numerical computation, cylindrical-polar coordinate system with radial symmetry subjected to two different types of heat sources into the cavity are considered. An integral transform method and, while in inverse transformation, an efficient and pragmatic NILT (Numerical Inverse Laplace Transform) is adopted. Finally, parameter studies are performed to evaluate the effect of the kernel function and time delay. For thermal wave the results show appreciable differences with those in the us...

International Journal for Computational Methods in Engineering Science and Mechanics

The European Physical Journal Plus