Abstract This paper deals with the Saint-Venant torsion of elastic, cylindrically orthotropic bar whose cross section is a sector circular ring shaped bar. The homogeneous elastic wedge-shaped strengthened by on its curved boundary surfaces thin isotropic shells. An analytical method presented to obtain Prandtl’s stress function, torsional rigidity and shearing stresses. A numerical example ill...

Robots consisting of several concentric, preshaped, elastic tubes can work dexterously in narrow, constrained, and/or winding spaces, as are commonly found in minimally invasive surgery. Previous models of these "active cannulas" assume piecewise constant precurvature of component tubes and neglect torsion in curved sections of the device. In this paper we develop a new coordinate-free energy f...

The problem of the rigorous derivation of one-dimensional models for nonlinearly elastic curved beams is studied in a variational setting. Considering different scalings of the three-dimensional energy and passing to the limit as the diameter of the beam goes to zero, a nonlinear model for strings and a bending-torsion theory for rods are deduced.

In many cases, a torsional shaft may be a thick-walled radially inhomogeneous cylindrical object. The hollow shafts made of functionally graded materials (FGMs) are such kind of compositions which were studied in this paper. Cylindrical FG shafts are composed of ceramic and metallic parts with power function distribution across the radial direction. The ceramic phase is isotropic elastic and th...

In non-linear incompatible elasticity, the configurations are maps from a non-Euclidean body manifold into the ambient Euclidean space,Rk. We prove the Γ-convergence of elastic energies for configurations of a converging sequence, Mn → M, of body manifolds. This convergence result has several implications: (i) It can be viewed as a general structural stability property of the elastic model. (ii...

We minimize elastic energies on framed curves which penalize both curvature and torsion. also discuss critical points using the infinite dimensional version of Lagrange multipliers' method. Finally, some examples arising from applications are discussed numerical experiments presented.

Abstract-A solution to the equations of elastic equilibrium is developed in terms of two harmonic functions, such that on a certain plane, normal stresses are identically zero, whilst tangential stresses and displacements are expressible as simple derivatives. The solution is used to solve the problem of the penny-shaped crack subjected to an arbitrary tangential traction and the corresponding ...