Seminar khoa học của GS.TS Phạm Chí Vĩnh

Vào 14h00, ngày 11/11/2024 Viện IAST tổ chức buổi trao đổi học thuật tại Phòng họp Lầu 5 Thư viện với nội dung chi tiết như sau: 

GS.TS Phạm Chí Vĩnh trình bày về "On the well-posedness of Eringen’s non-local elasticity for harmonic plane wave problems"
Tóm tắt: 

  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.