g Hua Qin

Extraordinary Photoluminescence and Strong Temperature/Angle-Dependent Raman Responses in Few Layer Phosphorene

Phosphorene is a new family member of two-dimensional materials. We observed strong and highly layer-dependent photoluminescence in few-layer phosphorene (two to five layers). The results confirmed the theoretical prediction that few-layer phosphorene has a direct and layer-sensitive band gap. We also demonstrated that few-layer phosphorene is more sensitive to temperature modulation than graphene and MoS2 in Raman scattering. The anisotropic Raman response in few-layer phosphorene has enabled us to use an optical method to quickly determine the crystalline orientation without tunneling electron microscopy or scanning tunneling microscopy. Our results provide much needed experimental information about the band structures and exciton nature in few-layer phosphorene.

Trefftz Finite Element Method and Its Applications

This paper presents an overview of the Trefftz finite element and its application in various engineering problems. Basic concepts of the Trefftz method are discussed, such as T-complete functions, special purpose elements, modified variational functionals, rank conditions, intraelement fields, and frame fields. The hybrid-Trefftz finite element formulation and numerical solutions of potential flow problems, plane elasticity, linear thin and thick plate bending, transient heat conduction, and geometrically nonlinear plate bending are described. Formulations for all cases are derived by means of a modified variational functional and T-complete solutions. In the case of geometrically nonlinear plate bending, exact solutions of the Lame-Navier equations are used for the in-plane intraelement displacement field, and an incremental form of the basic equations is adopted. Generation of elemental stiffness equations from the modified variational principle is also discussed. Some typical numerical results are presented to show the application of the finite element approach. Finally, a brief summary of the approach is provided and future trends in this field are identified. There are 151 references cited in this revised article. DOI: 10.1115/1.1995716

A closed crack tip model for interface cracks inthermopiezoelectric materials

Abstract The interface crack problem of a bimaterial thermopiezoelectric solid was treated byapplying the extended version of Strohs formalism and singular integral equation approach. Theinterface crack considered is subjected to combined thermal, mechanical and electric loads.Under the applied loading, the interface crack is assumed to be partially opened. Formulation ofthe problem results in a set of singular integral equations which are solved numerically. Thestudy shows that the contact zone is extremely small in comparison with the crack length. Basedon the formulation, some physically meaningful quantities of interest such as stress intensityfactors and size of contact zone for a particular material group are analyzed.

An arbitrarily-oriented plane crack terminating at the interface between dissimilar piezoelectric materials

Abstract The plane problem of a crack terminating at the interface of a bimaterial piezoelectric, and loaded on its faces, is treated. Emphasis is placed on how to transform this problem into a non-homogeneous Hilbert problem. To make the derivation tractable, the concept of the axial conjugate is introduced and related to the complex conjugate. The angle between the crack line and the interface may be arbitrary.

Damage analysis of thermopiezoelectric properties: Part I — crack tip singularities

Abstract This is Part I of the work on a two-dimensional analysis of thermal and electric fields of a thermopiezoelectric solid damaged by cracks. It deals with finding the singular crack tip behavior for the temperature, heat flow, displacements, electric potential, stresses and electric displacements. By application of Fourier transformations and the extended Stroh formalism, the problem is reduced to a pair of dual integral equations for the temperature field with the aid of an auxiliary function. The electroelastic field is governed by another pair of dual integral equations. The inverse square root singularity is found for the heat flow field while the logarithmic singularity prevailed for the electroelastic field regardless of whether the crack lies in a homogeneous piezoelectric solid or at an interface of two dissimilar piezoelectric materials. Results are given for the energy release rate and a finite length crack oriented at an arbitrarily angle with reference to the external disturbances. Part II of this paper considers the modelling of a piezoelectric material containing microcracks. A representative cracked area element is used to obtain the effective conductivity and electroelastic modulus. Numerical results are given for a peizoelectric Bati O3 ceramic with cracks.

Variational formulations for TFEM of piezoelectricity

Abstract The paper presents a family of variational formulations of Trefftz finite elements wherein the assumed internal displacement and electric potential fields a priori fulfil the governing differential equations of the problem over the element sub-domain, while the inter-element continuity and the boundary conditions are enforced using a modified variational principle together with an independent frame field defined on each element boundary. It is based on four free energy densities, each with two kinds of independent variables as basic independent variables, i.e. ( σ , D ) , ( e , E ) , ( e , D ) , and ( σ , E ) . Based on the assumed intra-element and frame fields, an element stiffness matrix equation is obtained which is implemented into computer programs for numerical analysis. Some numerical examples are considered to show the application of the proposed formulation.

Application of hybrid-Trefftz element approach to transient heat conduction analysis

The paper presents a hybrid-Trefftz element approach for the numerical solution of transient linear heat conduction problems. In the proposed method, the transient heat conduction equation is first discretized with respect to time and then the resulting set of elliptic equations is solved by the corresponding time independent hybrid Trefftz element approach. At the end of the paper, the proposed method is assessed through numerical examples.

BEM for crack-hole problems in thermopiezoelectric materials

Abstract The boundary element formulation for analysing interaction between a hole and multiple cracks in piezoelectric materials is presented. Using Greens function for hole problems and variational principle, a boundary element model (BEM) for a 2-D thermopiezoelectric solid with cracks and holes has been developed and used to calculate stress intensity factors of the crack-hole problem. In BEM, the boundary condition on the hole circumference is satisfied a priori by Greens function, and is not involved in the boundary element equations. The method is applicable to multiple-crack problems in both finite and infinite solids. Numerical results for stress and electric displacement intensity factors at a particular crack tip in a crack-hole system of piezoelectric materials are presented to illustrate the application of the proposed formulation.

A family of quadrilateral hybrid-Trefftz p-elements for thick plate analysis

Reference EPFL-ARTICLE-102742View record in Web of Science Record created on 2007-04-23, modified on 2016-08-08

Hybrid-Trefftz finite element method for Reissner plates on an elastic foundation

Abstract A modified variational principle for analysis of Reissner plates on an elastic foundation prevented. The foundation may be of Winkler type or Pasternak type. A hybrid Trefftz (HT) finite element (FE) model has been developed based on the principle and a new set of T-complete functions. Several numerical examples are considered to assess the effectiveness of the proposed method.