Weakly-Singular Traction and Displacement Boundary Integral Equations and Their Meshless Local Petrov-Galerkin Approaches

The general meshless local Petrov-Galerkin (MLPG) weak forms of the displacement and trac- tion boundary integral equations (BIEs) are presented for solids undergoing small deformations. Using the directly derived non-hyper-singular integral equations for displacement gradients, simple and straight- forward derivations of weakly singular traction BIEs for solids undergoing small deformations are also pre- sented. As a framework for meshless approaches, the MLPG weak forms provide the most general basis for the numerical solution of the non-hyper-singular displacement and traction BIEs. By employing the various types of test functions, several types of MLPG/BIEs are formulated. Numerical examples show that the pre- sent methods are very promising, especially for solving the elastic problems in which the singularities in dis- placements, strains, and stresses are of primary concern.

Synthesis and characterization of BaTiO_3/α-Fe_2O_3 core/shell structure

Multiferroic materials attracted a lot of attention in recent years because of their significant scientific interest and technological applications. The multiferroic core/shell powders have a better connectivity between the phases, resulting in superior dielectric and magneto electric properties. In this study, the influence of preparation condition on structure and properties of BaTiO_3/α-Fe_2 O_3 core/shell composite materials was examined. The five samples were obtained by varying synthesis conditions, such as synthesized method(co-precipitation and sonochemical method) and pH values of solution. XRD and Raman spectroscopy analyses were performed in order to determine phase composition and structural changes within samples. Morphology modifications were examined by SEM and EDS analyses. Finally, effect of structural and microstructural changes on magnetic and electrical properties was detected and explained.