 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 13427 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8178
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| In English (Mech. Solids): | | 5249 |
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| N.K. Lamba, V.R. Manthena, and K.C. Deshmukh, "Thermal Effects under Memory Responses of a Thin Rectangular Plate Structure During Laser Heating," Mech. Solids. 60 (6), 5056-5072 (2025) |
| Year |
2025 |
Volume |
60 |
Number |
6 |
Pages |
5056-5072 |
| DOI |
10.1134/S0025654425602654 |
| Title |
Thermal Effects under Memory Responses of a Thin Rectangular Plate Structure During Laser Heating |
| Author(s) |
N.K. Lamba (Department of Mathematics, Shri Lemdeo Patil Mahavidyalaya, Mandhal, Nagpur, India, navneetkumarlamba@gmail.com)
V.R. Manthena (Department of Mathematics, Priyadarshini J. L. College of Engineering, Nagpur, India, vkmanthena@gmail.com)
K.C. Deshmukh (Department of Mathematics, R.T.M. Nagpur University, Nagpur, India, kcdeshmukh2000@rediffmail.com) |
| Abstract |
Recent breakthroughs in memory-dependent and fractional-order formulations address
fundamental inadequacies in classical theory. Fractional derivatives capture hereditary effects and
spatial nonlocality, but memory-dependent derivatives (MDDs) allow more flexibility and interpretability by integrating kernel-defined delay mechanisms. To assist engineers and scientists in designing
next-generation thermal systems, this effort aims to provide a robust and proven framework that incorporates a solid structure using memory-dependent derivatives (MDDs). Many studies have been conducted so far that have used a cylindrical-shaped structure for thermal investigations, but there is still
a tremendous opportunity to modify the structural design by using a rectangular-shaped plate, which
is capable and significant for the advancement of the research and is critical for contemporary design
issues in infrastructure, nuclear, and aerospace engineering. This confirmed framework can only be
potentially observed by creating a more precise modeling of the heat transfer equation in the light of a
circular laser beam moving heat source with uniform distribution utilizing MDDs for a thin rectangular plate structure. The desired solution to the heat transfer equation (HTE) is found by applying the
Laplace transformation to memory derivatives and the Fourier transform method to spatial variables.
The effects of thermal stress on the plate are also assessed using the ensuing moments and forces.
The temperature, deflection, and stress function results are visually shown for various time-delay
parameters, kernel function options, laser-moving heat sources with varied laser powers, and scan
speeds. The computing investigation examines a plate with copper-based material characteristics.
Finally, the proposed mathematical modeling employing MDDs is revolutionizing heat transfer in
materials exposed to laser pulses, especially in industries where precision, speed, and thermal control
are critical. |
| Keywords |
Memory dependent derivatives, rectangular structure, thermal bending moment, laser heating, thermal stresses |
| Received |
26 May 2025 | Revised |
20 August 2025 | Accepted |
22 August 2025 |
| Link to Fulltext |
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