Narrow Results

A class of mixed boundary value problems (BVPs) arising in the study of scattering of surface water waves by the edges of floating structures comprising of elastic plates, with or without cracks, is examined for their solutions. It is observed that the simplest possible method of solution of such BVPs is the one that involves solution of an over-determined system of Linear Algebraic Equations. Such over-determined systems of equations are best solved by the method of least squares. Numerical results for useful practical quantities such as the "reflection" and "transmission" coefficients are obtained for one of the problems considered here.

The harmonic Dirichlet problem in a planar domain with smooth cracks of an arbitrary shape is considered in case, when the solution is not continuous at the ends the cracks. The well–posed formulation of the problem is given, theorems on existence and uniqueness of a classical solution are proved, the integral representation for a solution is obtained. With the help of the integral representation, the properties of the solution are studied. It is proved that a weak solution of the Dirichlet problem in question does not exist typically, though the classical solution exists.

The numerical and analytical methods are hardly used to solve the cracks problems for foam metal materials. Only experiments currently are used for the crack tensile and compression, as well as the cracks study of them. The finite element analysis is used to solve the problems of the crack tips, based on the similarity of the TG model and DP model. The results of the crack tips under the two conditions of the plane stress and plane strain for single notched side tension specimen are presented.

Irregular transfer of traction easily caused cracks at the hook tongue component in freight couplers when they were in hard working conditions, which has a great impact on freight security. In order to investigate how much the stress influences the damage on hook body component, finite element models of Type 13B and Type 17 assemblies was proposed to calculate the stress distribution. The results of FEM are highly consistent with the actual destruction in working conditions, making it possible to solve such issues in engineering practice.