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This paper presents an analytical approach to determine the singular stress fields near sharp corners in anisotropic notched plate subjected to bending. The first-order shear deformation plate theory (FSDPT) is used and the material anisotropy is modeled by the Stroh formalism. Based on the Mellin transform method, the stress singularity orders as well as the stress intensities are determined analytically. The results presented in this paper give us the singular behaviors for various plate angle α, material orientation angles ϕ and the anisotropic parameters e. These new findings are helpful in reducing or even eliminating the singularities near the sharp corner.

This paper aims at the stress singularities in a sectorial plate based on Reissner–Mindlin plate theory. The Mellin transform is applied to solve the governing equations of the plate. Both the bending stress singularities due to concentrated moments at boundaries and transverse shear stress singularities due to concentrated transverse shear forces at boundaries are investigated. The application of inverse Mellin transform gives the exact forms of singular stress fields near the corner, including the stress singularity orders and the generalized stress intensity factors. For various plate angles and loading conditions, the singular stress parameters are computed by finite element models and the results are compared to the analytical solutions. The comparisons reveal that the stresses obtained by the analytical procedure proposed in this paper are correct.

In this paper, the mode II strain energy release rates (SERR) of a cracked sandwich beam (CSB) subjected to a three-point loading are investigated. Due to the stiff face sheets and soft core, the displacements in the sandwich beam have the zigzag distribution through the thickness. A literature survey reveals that SERR of the CSB can be determined by the first-order shear deformation theory (FSDT). However, the accuracy of the results in FSDT is limited due to the lack of zigzag phenomenon. In this paper, we re-solve the CSB based on the refined zigzag theory (RZT), in which the kinematics of the displacements are assumed to have zigzag characteristic. The kinematic variables of the displacements can be determined from solving the governing equations of RZT in conjunction with the boundary conditions and continuity conditions of the CSB, and then SERR can be calculated by the compliance method. We show that for sandwich beams with slender aspect ratio (large L/h) or with thin face sheet (large rh), the FSDT can provide a satisfactory results due to the insignificant zigzag displacements. Otherwise for small L/h or small rh, the RZT should be used to take the significant zigzag displacements into consideration. For a given crack length, the FSDT give a result that the SERR is independent of the beam length. By using the RZT, it is found that the SERR depends on the beam length for a given crack length, especially for long crack length that a/L is ranged from 0.4 to 0.5. The material properties of the core materials on SERR are also investigated. By comparing with the finite element method (FEM), the deflections, compliances and SERRs in the CSB obtained by RZT are more accurate than those by FSDT. It is found that, for the cases of the core with very small shear modulus, the RZT gives correct results that are validated by FEM. For such cases, the FSDT gives incorrect calculations for SERR due to the lack of the zigzag model. The results arose in this study show the superior advantages of the use of the RZT in the SERR calculation of CSB specimen.

In this paper, the electro-elastic fields in a functionally gradient piezoelectric strip with an internal semi-infinite electrode are analyzed by using Fourier transform and Wiener-Hopf technique. The exact forms of asymptotic solutions and intensity factor and energy are obtained. The energy density criterion is proposed to study the fracture behavior near the electrode tip. The fracture initiation angle depends on the fracture resistance of the piezoelectric ceramic, bonding strength between piezoelectric and electrode, and the direction of least energy density factor S inside the piezoceramic.

IA piezoelectric strip with semi-infinite electrode is investigated. Two combinations of mechanical–electrical loadings are considered. They consist of the anti-plane deformation with in-plane electrical field and the in-plane electroelastic field. Based on the Fourier transform and the Wiener–Hopf technique, the electroelastic local stress fields are found to exhibit the square root singularity near the electrode tip. The energy density factor criterion is applied to examine the fracture behavior near the electrode tip.

This paper presents the formulation of piezoelectric elasticity under generalized plane deformation derived from the three-dimensional theory. There are four decoupled classes in the generalized plane deformation formulation, i.e. when l 3 ( μ )= l 2 * ( μ )=0, l 3 ( μ )= l 3 * ( μ )=0, l 3 * ( μ )= l 2 * ( μ )=0 or l 3 ( μ )= l 3 * ( μ )= l 2 * ( μ )=0. Only the inplane fields of the first class and the antiplane field of the second class include the piezoelectric effect. Several examples of wedge problem often encountered in smart structures, such as sensors or actuators are studied to examine the stress singularity near the apex of the structure. The bonded materials to the PZT-4 wedge are PZT-5, graphite/epoxy or aluminum (conductor). The influencing factors on the singular behavior of the electro-elastic fields include the wedge angle, material type, poling direction, and the boundary and interface conditions. The numerical results of the first case are compared with Xu's graphs and some comments are made in detail. In addition, some new results regarding the antiplane stress singularity of the second class are obtained via the case study. The coupled singularity solutions under generalized plane deformation are also investigated to seek the conditions of the weakest or vanishing singular stress fields.

A prototype of a stylus probe with an interferometric transducer for surface profiling and roughness measurement was recently developed for surface texture, form error, radius, inclination and dimension measurement. A reflective cylindrical holographic diffraction grating fabricated into cylindrical shape, referred to as the `length master', acts as the moving part governing the path length of light. The surface profile information was transformed into electrical signals using a laser diode grating interferometer to measure the rotational motion of the measuring lever. To precisely define the performance capability of the system, error analysis was performed in order to assess the potential measuring error due to imperfections in manufacturing and assembly of the system's mechanical components. The uncertainty relating to the construction of the device, geometrical features, operating environment and optical characteristics is also presented.

Based on the generalized Lekhnitskii formulation and Mellin transform, the thermo-electro-elastic fields of a piezoelectric bonded wedge are investigated in this paper. From the potential theory in a wedge-shaped region, a general form of the temperature change is proposed as a particular solution in the generalized Lekhnitskii formulation. The emphasis is on the singular behavior near the apex of the piezoelectric bonded wedge, including singularity orders and angular functions, which can be computed numerically. The interface between two materials can be either perfectly bonded, namely type A, so that the continuity of electric displacements holds, or a thin electrode, namely type B, so that the electric potential is grounded. Case studies of PZT-5H/PZT-4 and graphite-epoxy/PZT-4 bonded wedges reveal that, in most cases, the type B continuity condition has more severe singularities than type A due to the mixed boundary point of the electrostatics at the apex of the wedge. The results of this study show that the reduction or disappearance of singularity orders is possible through the appropriate selection of poling/fiber orientations and wedge angles.