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THE FIRST AND THE SECOND FUNDAMENTAL PROBLEMS FOR AN ELASTIC INFINITE PLATE WITH HOLES
El-Bary, Alaa Abd. 한국전산응용수학회 2001 The Korean journal of computational & applied math Vol.8 No.3
Complex variable methods are used to solve the first and the second fundamental problems for infinite plate with two holes having arbitrary shapes which are conformally mapped on the domain outside of the unit circle by means of rational mapping function. Some applications are investigated and some special cases are derived AMS Mathematics Subject Classification : 45E05, 45E10
Ibrahim Abbas,M. Saif AlDien,Mawahib Elamin,Alaa El-Bary Techno-Press 2024 Coupled systems mechanics Vol.13 No.1
This study seeks to develop analytical solutions for the biothermoelastic model without accounting for energy dissipation. These solutions are then applied to estimate the temperature changes induced by external heating sources by integrating relevant empirical data characterizing the biological tissue of interest. The distributions of temperature, displacement, and strain were obtained by utilizing the eigenvalues approach with the Laplace transforms and numerical inverse transforms method. The impacts of the rate of blood perfusion and the metabolic activity parameter on thermoelastic behaviors were discussed specifically. The temperature, displacement, and thermal strain results are visually represented through graphical representations.
Aatef D. Hobiny,Ibrahim A. Abbas,C Alaa A. El-Bary 국제구조공학회 2023 Steel and Composite Structures, An International J Vol.48 No.6
In this article, we explore the issue concerning semiconductors half-space comprised of materials with varying thermal conductivity. The problem is within the framework of the generalized thermoelastic model under one thermal relaxation time. The half-boundary space's plane is considered to be traction free and is subjected to a thermal shock. The material is supposed to have a temperature-dependent thermal conductivity. The numerical solutions to the problem are achieved using the finite element approach. To find the analytical solution to the linear problem, the eigenvalue approach is used with the Laplace transform. Neglecting the new parameter allows for comparisons between numerical findings and analytical solutions. This facilitates an examination of the physical quantities in the numerical solutions, ensuring the accuracy of the proposed approach.