Akash Kumar Gartia

Akash Kumar Gartia is a PhD research scholar in the Department of Mathematics at NIT Rourkela whose work centers on the modelling of differential equations of dynamical problems arising in vibration analysis of advanced functionally graded/nano/metamaterial structures. His research combines mathematical modeling with numerical methods to study the behavior of structural elements and other engineering materials under various complicating effects.

EDUCATION

Ph.D in Mathematics, National Institute of Technology Rourkela (2022-current)

M.Sc. in Mathematics, Central University of Jharkhand (2018-2020)

B.Sc. in Mathematics, Sambalpur University (2015-2018)

RESEARCH, TEACHING, or OTHER INTERESTS

Mathematics, Computational Mathematics, Modeling and Simulation, Numerical Analysis

Scopus Publications

Forward and inverse vibration analysis of prestressed axially functionally graded tapered beams with initial strain estimation for resilient highway bridge systems
Akash Kumar Gartia, S. Chakraverty
International Journal of Mechanics and Materials in Design, 2026
Effect of Variable Size-Dependent Parameters on the Vibration Characteristics of Axially Functionally Graded Electromagnetic Nanobeams
Akash Kumar Gartia, S. Chakraverty
Journal of Vibration Engineering and Technologies, 2026
Effect of Variable Nonlocal Parameter on the Free Vibration of Axially Functionally Graded Nanobeams
Akash Kumar Gartia, S. Chakraverty
Lecture Notes in Networks and Systems, 2026
Coupled effects of axial material gradation and tapered geometry on nanobeam dynamics with uniform square perforations
Akash Kumar Gartia, Ramanath Garai, S. Chakraverty
Acta Mechanica, 2026
Optimizing Shape Functions in the Rayleigh-Ritz Method for Efficient Free Vibration Analysis of Functionally Graded Nanobeams
Akash Kumar Gartia, S. Chakraverty
Mechanics of Solids, 2025
Abstract This study explores the effectiveness of different shape functions in solving the free vibration problem of functionally graded (FG) nanobeams using the Rayleigh-Ritz method. The structural properties of the nanobeam vary continuously through its thickness, following a power law distribution of material volume fractions. The FG nanobeam is modeled using the Euler-Bernoulli beam theory, while small-scale effects are incorporated through Eringen’s nonlocal elasticity theory. Various shape functions are examined within the Rayleigh-Ritz framework to assess their computational efficiency. The primary objective is to identify the optimal shape function for this method. To achieve this, the mass and stiffness matrices are computed, and a generalized eigenvalue problem is formulated to determine the non-dimensional frequency parameter. The study evaluates the convergence behavior and computational time of each shape function to identify the most effective option. The results are validated against existing literature for specific cases, demonstrating the performance of the optimal shape function under different boundary conditions, small-scale parameters, and power law exponents. Additionally, new insights are provided into the vibrational behavior of FG nanobeams across various boundary conditions. This focus on shape function optimization enhances computational methodologies in FG nanobeam vibration analysis.
Advanced Computational Modeling and Mechanical Behavior Analysis of Multi-Directional Functionally Graded Nanostructures: A Comprehensive Review
Akash Kumar Gartia, S. Chakraverty
CMES Computer Modeling in Engineering and Sciences, 2025
This review explores multi-directional functionally graded (MDFG) nanostructures, focusing on their material characteristics, modeling approaches, and mechanical behavior. It starts by classifying different types of functiona... | Find, read and cite all the research you need on Tech Science Press
Analytical Solution for Free Vibration of Multi-Cracked Metal–Ceramic Functionally Graded Nanobeams Resting on Elastic Foundations
Akash Kumar Gartia, Priya Rao, S. Chakraverty
International Journal of Structural Stability and Dynamics, 2025
This study explores the free vibration behavior of multi-cracked functionally graded (FG) nanobeams situated on Winkler–Pasternak elastic foundations. Cracks are modeled as rotational springs, effectively dividing the beam into sub-beams. The present model is formulated for metal–ceramic FG nanobeams composed of two isotropic phases with material properties varying continuously across the thickness based on a power-law distribution. The analysis incorporates Euler–Bernoulli beam theory and Eringen’s nonlocal elasticity theory to capture size-dependent effects. A fourth-order differential equation with constant coefficients is formulated, and an analytical approach is utilized to calculate the frequency parameter values. Validation with existing literature in specific cases confirms the accuracy of the obtained results. The effects of various factors, including the transverse gradient index, nonlocal parameter, Winkler and Pasternak foundation parameters, crack severity, and crack locations, on the first four frequency parameters are investigated. Unlike existing studies, the proposed model allows for any number of cracks (multiple cracks), offering a generalized framework for realistic damage scenarios. This is the first study to analytically address the combined effects of multiple cracks with elastic foundations in FG nanobeams. This framework provides a robust tool for analyzing FG nanobeams with cracks under diverse boundary conditions and material gradations. These findings have significant implications for the design and optimization of nanostructures in aerospace, mechanical, and biomedical applications.
Free Vibration of Bi-Directional Functionally Graded Nanobeams Resting on Winkler–Pasternak Foundations
Akash Kumar Gartia, S. Chakraverty
Journal of Vibration Engineering and Technologies, 2024

RECENT SCHOLAR PUBLICATIONS

Effect of Variable Size-Dependent Parameters on the Vibration Characteristics of Axially Functionally Graded Electromagnetic Nanobeams
AK Gartia, S Chakraverty
Journal of Vibration Engineering & Technologies 14 (3), 115 , 2026
2026
Forward and inverse vibration analysis of prestressed axially functionally graded tapered beams with initial strain estimation for resilient highway bridge systems: AK Gartia …
AK Gartia, S Chakraverty
International Journal of Mechanics and Materials in Design 22 (1), 52 , 2026
2026
Effect of Axial Functional Gradation and Periodic Square Perforations on the Vibration of Nanobeams with Elastic Foundation
R Garai, AK Gartia, S Chakraverty
International Journal of Structural Stability and Dynamics, 2750188 , 2026
2026
Citations: 4
Coupled effects of axial material gradation and tapered geometry on nanobeam dynamics with uniform square perforations: AK Gartia et al.
AK Gartia, R Garai, S Chakraverty
Acta Mechanica, 1-27 , 2026
2026
Citations: 2
Analytical solution for free vibration of multi-cracked metal–ceramic functionally graded nanobeams resting on elastic foundations
AK Gartia, P Rao, S Chakraverty
International Journal of Structural Stability and Dynamics, 2650400 , 2025
2025
Citations: 9
Optimizing shape functions in the rayleigh-ritz method for efficient free vibration analysis of functionally graded nanobeams
AK Gartia, S Chakraverty
Mechanics of Solids 60 (3), 1799-1821 , 2025
2025
Citations: 6
Effect of Variable Nonlocal Parameter on the Free Vibration of Axially Functionally Graded Nanobeams
AK Gartia, S Chakraverty
International Conference on Computational Mathematics and Applications, 293-303 , 2025
2025
Effect of the Size and Total Number of Holes On the Vibration Behaviour of the Non-Homogeneous Perforated Beam Structures
R Garai, AK Gartia, S Chakraverty
2025
Static Analysis of Functionally Graded Nanobeams with Exponential Load under Non-Ideal Boundary Constraints Using Machine Learning Technique
AK Gartia, I Sahu, S Chakraverty
2025
Advanced computational modeling and mechanical behavior analysis of multi-directional functionally graded nanostructures: a comprehensive review
AK Gartia, S Chakraverty
Computer Modeling in Engineering & Sciences 142 (3), 2405 , 2025
2025
Citations: 29
Chebyshev polynomials based Rayleigh–Ritz method for free vibration analysis of axially functionally graded cantilever nanobeam
AK Gartia, S Chakraverty
Advances in modelling and analysis of functionally graded micro-and … , 2024
2024
Citations: 12
Free vibration of Bi-directional functionally graded nanobeams resting on Winkler–Pasternak foundations
AK Gartia, S Chakraverty
Journal of Vibration Engineering & Technologies 12 (Suppl 2), 1929-1945 , 2024
2024
Citations: 35

MOST CITED SCHOLAR PUBLICATIONS

Free vibration of Bi-directional functionally graded nanobeams resting on Winkler–Pasternak foundations
AK Gartia, S Chakraverty
Journal of Vibration Engineering & Technologies 12 (Suppl 2), 1929-1945 , 2024
2024
Citations: 35
Advanced computational modeling and mechanical behavior analysis of multi-directional functionally graded nanostructures: a comprehensive review
AK Gartia, S Chakraverty
Computer Modeling in Engineering & Sciences 142 (3), 2405 , 2025
2025
Citations: 29
Chebyshev polynomials based Rayleigh–Ritz method for free vibration analysis of axially functionally graded cantilever nanobeam
AK Gartia, S Chakraverty
Advances in modelling and analysis of functionally graded micro-and … , 2024
2024
Citations: 12
Analytical solution for free vibration of multi-cracked metal–ceramic functionally graded nanobeams resting on elastic foundations
AK Gartia, P Rao, S Chakraverty
International Journal of Structural Stability and Dynamics, 2650400 , 2025
2025
Citations: 9
Optimizing shape functions in the rayleigh-ritz method for efficient free vibration analysis of functionally graded nanobeams
AK Gartia, S Chakraverty
Mechanics of Solids 60 (3), 1799-1821 , 2025
2025
Citations: 6
Effect of Axial Functional Gradation and Periodic Square Perforations on the Vibration of Nanobeams with Elastic Foundation
R Garai, AK Gartia, S Chakraverty
International Journal of Structural Stability and Dynamics, 2750188 , 2026
2026
Citations: 4
Coupled effects of axial material gradation and tapered geometry on nanobeam dynamics with uniform square perforations: AK Gartia et al.
AK Gartia, R Garai, S Chakraverty
Acta Mechanica, 1-27 , 2026
2026
Citations: 2
Effect of Variable Size-Dependent Parameters on the Vibration Characteristics of Axially Functionally Graded Electromagnetic Nanobeams
AK Gartia, S Chakraverty
Journal of Vibration Engineering & Technologies 14 (3), 115 , 2026
2026
Forward and inverse vibration analysis of prestressed axially functionally graded tapered beams with initial strain estimation for resilient highway bridge systems: AK Gartia …
AK Gartia, S Chakraverty
International Journal of Mechanics and Materials in Design 22 (1), 52 , 2026
2026
Effect of Variable Nonlocal Parameter on the Free Vibration of Axially Functionally Graded Nanobeams
AK Gartia, S Chakraverty
International Conference on Computational Mathematics and Applications, 293-303 , 2025
2025
Effect of the Size and Total Number of Holes On the Vibration Behaviour of the Non-Homogeneous Perforated Beam Structures
R Garai, AK Gartia, S Chakraverty
2025
Static Analysis of Functionally Graded Nanobeams with Exponential Load under Non-Ideal Boundary Constraints Using Machine Learning Technique
AK Gartia, I Sahu, S Chakraverty
2025