An elementary theory of defective beams

Abstract

Material conservation and balance laws of elementary beam theory have been derived. The application to beams with discontinuities in the stiffness results in a surprisingly simple formula to calculate stress intensity factors of cracked beams. (IWM

Structural analysis of gradient elastic components

“…Furthermore, a procedure introduced by Kienzler and Herrmann (1986) and based on the principle of virtual work, is employed in order to compute the strain energy release rate of the cracked bar under tension. The study concludes with the assessment of the gradient-elasticity effect on both the normalized stiffness and toughness of the structural components under discussion.…”

Eshelby stress tensor in large strain anisotropic damage mechanics

“…Golebiewska-Herrmann [10] presented a unified variational formulation leading to field equations and conservation laws in physical and material space. Kienzler [13] and Kienzler and Herrmann [11,12] discussed the elementary beam theory within this context. Furthermore, Stumpf and Le [14] developed variational settings with application to brittle fracture problems, and Maugin and Trimarco [15] critically examined various formulations of the balance of linear momentum in nonlinear inhomogeneous elasticity.…”

Mixed-mode fracture & non-planar fatigue analyses of cracked I-beams, using a 3D SGBEM–FEM Alternating Method

“…Since the I-beam has the characteristics of both three-dimensional finite bodies as well as slender bars, it is quite difficult to find the exact solution for stress intensity factors for cracked I-beams by the existing classical analytical methods. By applying the conservation laws and elementary beam theory, Kienzler and Hermann [2] obtained the approximate stress intensity factors for cracked beams with different crack geometries and a rectangular cross section. Hermann and Sosa [3] applied the method in [2] to find the stress intensity factors of cracked pipes under different loading conditions.…”