Papers by Keyword: Stroh Formalism

Abstract: In this paper, the bending singularity at the apex of V-notch in an anisotropic thick plate is investigated. The Stroh-like formalism is used to model the anisotropy of the material. Based on the Ressiner-Mindlin plate theory and the eigenfunction expansion method, the characteristic equation for bending singularity order is derived and the order can be determined numerically. The numerical results show that the singularity orders strongly depend on the plate angle a. In addition, the singularity orders also depend on the principal orientation of the anisotropic material. The singularity orders for the case of are stronger than for that of. In the case of, to reduce the anisotropy is helpful to release the singularity at the notch tip. For the other case of, it is preferable to increase the anisotropy to reduce the singularity. The disappearance conditions of the bending singularity can be found based on the numerical results.

Abstract: Analytical solutions are derived for multifunctional N-layered rectangular plates. The multilayered plate may consist of linear elastic or piezoelectric laminates of arbitrary thickness. The related equations and formulae are developed based on the Stroh like formalism. Solutions for multilayered plates are expressed in terms of the propagator matrix and satisfy the continuity conditions of material layers. Various types of electrical and mechanical loading may be considered. Numerical results of stresses, electric potential and displacement for some multifunctional multilayered plates are analyzed

Abstract: The analysis on a two-dimensional infinite anisotropic magnetoelectroelastic solid containing an elliptic hole subjected to a generalized force on the hole surface is performed in this paper. By employing the Stroh formalism, the method of analytical continuation, the technique of conformal mapping, the concept of superposition and the exact electromagnetic boundary conditions, the Green’s functions are obtained.

Abstract: The two-dimensional problem of an elliptic inclusion embedded into an anisotropic magneto-electro-elastic solid is studied. Based on the Stroh formalism combined with the technique of conformal mapping and the method of analytical continuation, general solutions for the stress and deformations in the entire domain are obtained when a generalized line force and a generalized line dislocation is located at a point outside, inside, or on the interface of an elliptical inclusion. Comparisons with some related solutions show that the present solutions are valid and general.

Abstract: The numerical solution for an edge crack problem in a two-dimensional (2-D) finite piezoelectric media has been discussed using extended finite element method. The four-fold standard enrichment functions are taken in conjugation with the interaction integral to evaluate the intensity factors (IFs). The intensity factors as well as the mechanical energy release rate and the total energy release rate has been analyzed for different electro-mechanical boundary conditions. It is observed that the IFs results are coupled and contrary to analytic solution which shows uncoupled behaviour.

Abstract: By employing the Stroh formalism for two-dimensional anisotropic thermoelasticity, fracture analyses of interface corners between two dissimilar anisotropic elastic materials under thermal loadings are considered in this paper. It was proved that the consideration of thermal effects will not influence the stress singularity but will induce heat flux singularity if the singularity of the temperature field is not permissible. To calculate the stress intensity factors via path independent H-integral, it was found that the one proposed previously for the mechanical loading conditions should be modified by adding an additional surface integral accounting for the thermal effects. Two examples considering cracks and corners in isotropic plates are presented to show the correctness and validity of the modified H-integral.

Abstract: Classical methods of two-dimensional elasticity can be extended to give an exact solution of the three-dimensional problem for the beam — i.e. a general solution for the pris- matic bar loaded on its lateral surfaces, subject only to the restriction that the tractions can be expanded as power series in the axial coordinate z. A series of sub-problems Pj is defined by successive partial differentiations with respect to z. For isotropic materials, a recursive al- gorithm can be used for generating the solution to Pj+1 from that for Pj in the context of the Papkovich-Neuber solution. For the generally anisotropic material, a similar strategy is proposed, based on partial integrations of Stroh’s formulation of the two-dimensional problem.

Abstract: By employing the Stroh formalism for plane anisotropic thermoelasticity, closed-form solutions for the orders of stress and heat flux singularities of multi-material wedges have been obtained. Several different boundary conditions are considered in this paper such as insulated or isothermal as well as free-free or fixed-fixed or free-fixed or fixed-free wedge boundaries. The solutions show that the singular orders are influenced by the wedge configurations (n wedge angles), boundary conditions, elastic constants and heat conduction coefficients, but are independent of the thermal moduli.