A Hermite interpolation element-free Galerkin method for piezoelectric materials

Piezoelectric materials have played an important role in industry due to a number of beneficial properties. However, most numerical methods for the piezoelectric materials need mesh, in which the mesh generation and remeshing are prominent difficulties. This paper proposes a Hermite interpolation element-free Galerkin method (HIEFGM) for piezoelectric materials, where the Hermite approximate approach and interpolation element-free Galerkin method (IEFGM) are combined. Based on the constitutive equation, geometric equation, and Galerkin integral weak form, the HIEFGM formulation for piezoelectric materials is established. In the proposed method, the problem domain is discretized by many nodes rather than the meshes, so the pre-processing of numerical computation is simplified. Furthermore, a new approximation technique based on the moving least squares method and Hermite approximate approach is used to derive the approximation function of field quantities. The derived approximation function has the Kronecker delta property and considers the field quantity normal derivatives of boundary nodes, which avoids the problem of imposing the essential boundary conditions and improves the accuracy of meshless approximation. The effects of the scaling factor, node density, and node arrangement on the accuracy of the proposed method are investigated. Numerical examples are given for assessing the proposed method and the results uniformly demonstrate the proposed method has excellent performance in analyzing piezoelectric materials.

A Brief Introduction on the Development of Ti-Based Metallic Glasses

Ti-based metallic glasses (MGs) possess high specific strength, low elastic modulus, high elasticity, high wear and corrosion resistance, and excellent biocompatibility, which make them highly attractive as lightweight high-strength materials as well as biomaterials. However, the glass forming ability (GFA) of Ti-based MGs, particularly those bearing no toxic, noble, or heavy metals, that is, Be, Pd, or Cu alike, largely sets back their wide applications for the restricted critical glass forming size of these Ti-based MGs. In this review, the outlines in developing Ti-based MGs are delineated in order to provide an overall view on the efforts ever made to fabricate bulk size Ti-based MGs. The state of the art in the knowledge on the GFA of Ti-based MGs is briefly introduced, and possible directions for fabricating bulk size toxic and noble element free Ti-based MGs are discussed.