New Elzaki Integral Transformation Application on Studying the Bending Elastic Beams According to the Euler-Bernoulli Beam Theory
Keywords:
Elastic beam bending, Elzaki integral transformation, Clamped beams, Simply supported beams, Clamped beams at one edge and free at the other edgeAbstract
In recent years, several integral transformations have been presented and applied to solving some ordinary and partial differential equations, as well as to solving integral equations that represent some diverse problems in mathematics, physics, engineering, statistics, biological sciences, and medical sciences. This research aims to solve problems in engineering mechanics, particularly in linear elasticity theory, using the Elzaki integral transformation. The steps are similar to those used in solving problems with the use of Laplace integral transformation. The exact solutions of the elastic beam bending problem, which is represented by a differential equation according to the well-known Euler-Bernoulli theory when the beam is subjected to various boundary conditions. It was concluded that the Laplace transform can be applied analogously to the Laplace transform in finding solutions of differential equations under the specified boundary conditions.
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