In a half-plane problem with x 1 paralleling with the straight boundary and x 2 pointing into the medium, the stress components on the boundary whose acting plane is perpendicular to x 1 direction may be denoted by t 1 = [r 11 , r 12 , r 13 ] T . Stress components r 11 and r 13 are of more interests since r 12 is completely determined by the boundary conditions. For isotropic materials, it is known that under uniform normal loading r 11 is constant in the loaded region and vanishes in the unloaded part. Under uniform shear loading, r 11 will have a logarithmic singularity at the end points of shear loading. In this paper, the behavior of the stress components r 11 and r 13 induced by traction-discontinuity on general anisotropic elastic surfaces is studied. By analyzing the problem of uniform tractions applied on the half-plane boundary over a finite loaded region, exact expressions of the stress components r 11 and r 13 are obtained which reveal that these components consist of in general a constant term and a logarithmic term in the loaded region, while only a logarithmic term exists in unloaded region. Whether the constant term or the logarithmic term will appear or not completely depends on what values of the elements of matrices X and C will take for a material under consideration. Elements for both matrices are expressed explicitly in terms of elastic stiffness. Results for monoclinic and orthotropic materials are all deduced. The isotropic material is a special case of the present results.

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The three generalized Barnett-Lothe tensors L, S and H, appearing frequently in the investigations of the two-dimensional deformations of anisotropic piezoelectric materials, may be expressed in terms of the material constants. In this paper, the eigenvalues and eigenvectors for monoclinic piezoelectric materials of class m, with the symmetry plane at x 3 = 0 are constructed based on the extended Stroh formalism. Then the three generalized Barnett-Lothe tensors are calculated from these eigenvectors and are expressed explicitly in terms of the elastic stiffness instead of the reduced elastic compliance. The special case of transversely isotropic piezoelectric materials is also presented.

Finite field multiplier is a very important operation for realising elliptic curve cryptography. Dickson basis is a recently developed basis for representing finite elements in GF(2 m). This study will propose a unidirectional systolic multiplier for such Dickson basis. The unidirectional systolic structure offers low space and time complexities and can be easily modified to have error detection capability which can resist side-channel attacks.

In this paper, the problem of a crack embedded in a half-plane piezoelectric solid with traction-induction free boundary is analyzed. A system of singular integral equations is formulated for the materials with general anisotropic piezoelectric properties and for the crack with arbitrary orientation. The kernel functions developed are in complex form for general anisotropic piezoelectric materials and are then specialized to the case of transversely isotropic piezoelectric materials which are in real form. The obtained coupled mechanical and electric real kernel functions may be reduced to those kernel functions for purely elastic problems when the electric effects disappear. The system of singular integral equations is solved numerically and the coupling effects of the mechanical and electric phenomena are presented by the generalized stress intensity factors for transversely isotropic piezoelectric materials.