A von Karman plate analogue for solving anti-plane problems in couple stress and dipolar gradient elasticity

The proposed analogy is achieved through the von Karman plate theory where the plate is pre-stressed by a constant biaxial tension. The plate theory involves properties such as the plate thickness h, the Poisson's ratio ν and the bending stiffness D. This information, together with the pre-stress N transforms into properties required by the anti-plane couple stress and dipolar gradient elasticity problems: the shear modulus G, the internal length ℓ and the coefficient η. In both problems the two dimensional space remains the same, including the presence of cracks and other defects. The analogy permits numerical and analytical solutions of demanding anti-plane problems of gradient elasticity (couple stress and dipolar) utilizing the von Karman plate corresponding, and vice versa.