boundary integral equation
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Author(s):  
Ekaterina Titova ◽  
Dmitri Alexandrov

Abstract The boundary integral method is developed for unsteady solid/liquid interfaces propagating into undercooled binary liquids with convection. A single integrodifferential equation for the interface function is derived using the Green function technique. In the limiting cases, the obtained unsteady convective boundary integral equation (CBIE) transforms into a previously developed theory. This integral is simplified for the steady-state growth in arbitrary curvilinear coordinates when the solid/liquid interface is isothermal (isoconcentration). Finally, we evaluate the boundary integral for a binary melt with a forced flow and analyze how the melt undercooling depends on P\'eclet and Reynolds numbers.


Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 38
Author(s):  
Mikhail V. Golub ◽  
Olga V. Doroshenko

The widespread of composite structures demands efficient numerical methods for the simulation dynamic behaviour of elastic laminates with interface delaminations with interacting faces. An advanced boundary integral equation method employing the Hankel transform of Green’s matrices is proposed for modelling wave scattering and analysis of the eigenfrequencies of interface circular partially closed delaminations between dissimilar media. A more general case of partially closed circular delamination is introduced using the spring boundary conditions with non-uniform spring stiffness distribution. The unknown crack opening displacement is expanded as Fourier series with respect to the angular coordinate and in terms of associated Legendre polynomials of the first kind via the radial coordinate. The problem is decomposed into a system of boundary integral equations and solved using the Bubnov-Galerkin method. The boundary integral equation method is compared with the meshless method and the published works for a homogeneous space with a circular open crack. The results of the numerical analysis showing the efficiency and the convergence of the method are demonstrated. The proposed method might be useful for damage identification employing the information on the eigenfrequencies estimated experimentally. Also, it can be extended for multi-layered composites with imperfect contact between sub-layers and multiple circular delaminations.


2021 ◽  
Vol 17 (2) ◽  
pp. 146-153
Author(s):  
Nur Hazwani Aqilah Abdul Wahid ◽  
Ali Hassan Mohamed Murid ◽  
Mukhiddin I. Muminov

The Ahlfors map is a mapping function that maps a multiply connected region onto a unit disk. This paper presents a new boundary integral equation related to the Ahlfors map of a bounded multiply connected region. The boundary integral equation is constructed from a boundary relationship satisfied by the Ahlfors map of a multiply connected region.


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