A piezoelectric screw dislocation interacting with an imperfect piezoelectric bimaterial interface

AbstractA general method is presented for the analytical solution of a piezoelectric screw dislocation located within one of two joined piezoelectric half-planes. The bonding along the half-plane is considered to be imperfect with the assumption that the imperfect interface is mechanically compliant and dielectrically weakly (or highly) conducting. For a mechanically compliant interface tractions are continuous but displacements are discontinuous across the imperfect interface. In this context, jumps in the displacement components are assumed to be proportional to their respective interface traction components. Similarly, for a dielectrically weakly conducting interface the normal electric displacement is continuous but the electric potential is discontinuous across the interface. The jump in electric potential is proportional to the normal electric displacement. In contrast, for a dielectrically highly conducting interface the electric potential is continuous across the interface whereas the normal electric displacement has a discontinuity across the interface which is proportional to a certain differential expression of the electric potential. Explicit expressions are derived for the complex field potentials. The results show that there are two dimensionless parameters measuring the interface “rigidity” as compared to one for the purely elastic case. When the imperfect interface is compliant and weakly conducting, the two dimensionless parameters can be positive real values or complex conjugates with positive real parts. When the imperfect interface is compliant and highly conducting the two dimensionless parameters can only be positive real values. An expression for the image force acting on the screw dislocation due to its interaction with a compliant and weakly conducting interface is also given. It is found that the image force is only dependent on two dimensionless generalized Dundurs constants as well as two dimensionless parameters measuring the interface “rigidity”

Shape optimization against buckling of micro- and nano- rods

In this paper, we analyze elastic buckling of micro- and nano-rods based on Eringen's nonlocal elasticity theory. By using the Pontryagin's maximum principle, we determine optimality condition for a rod simply supported at both ends and loaded with axial compressive force only. Thus, the problem that we treat represents a generalization of the classical Clausen problem formulated for Bernoulli–Euler rod theory. Several concrete examples are treated in details, and the increase in buckling load capacity is determined. In solving the problem numerically, we used a first integral of the resulting system of equations, which helped us to monitor error of the numerical procedure. Our results show that nonlocal effects decrease the buckling load of optimally shaped rod. However, nonlocal theory leads to the optimal rod with the cross-sectional area at the rod ends different from zero. This is important property since zero value of the cross-section at the ends, which optimally shaped rod according to Bernoulli–Euler rod theory has, is unacceptable in applications