Seminar by Prof. Dr. Pham Chi Vinh

On November 11, 2024, the lectures from Prof. Dr. Pham Chi Vinh takes place on the 5th Floor of the Library with detailed content as follows:

Prof. Dr. Pham Chi Vinh presents about "On the well-posedness of Eringen’s non-local elasticity for harmonic plane wave problems"

Abstract:

In this work, we establish a criterion for well-posedness of Eringen’s nonlocal elasticity theory for problems of harmonic plane waves in domains with non-empty boundaries, and introduce a novel method for solving well-posed problems. The criterion for well-posedness says that for problems of harmonic plane waves, Eringen’s non-local elasticity theory is well-posed when the constitutive boundary conditions contain all equilibrium boundary conditions, otherwise it is ill-posed in the sense of no solutions. With this well-posedness criterion, it is easy to check whether a non-local harmonic plane wave problem is well-posed or not. If it is a well-posed problem, its solution will be found by employing the novel method. It has been shown that Eringen’s method, which has been used widely to solve problems of nonlocal harmonic plane waves, does not give their correct solutions. Therefore, it must be replaced by the novel method. As an application of the criterion for well-posedness and the novel method, two well-posed problems of harmonic plane waves are considered including Rayleigh waves and SH waves propagating in traction-free non-local isotropic elastic half-spaces. Exact solutions of these problems have been obtained including explicit expressions of displacements, local and non-local stresses and dispersion equations.