Tensionless contact of a finite beam resting on Reissner foundation

Abstract

A more generalized model of a beam resting on a tensionless Reissner foundation is presented. Compared with the Winkler foundation model, the Reissner foundation model is a much improved one. In the Winkler foundation model, there is no shear stress inside the foundation layer and the foundation is assumed to consist of closely spaced, independent springs. The presence of shear stress inside Reissner foundation makes the springs no longer independent and the foundation to deform as a whole. Mathematically, the governing equation of a beam on Reissner foundation is sixth order differential equation compared with fourth order of Winkler one. Because of this order change of the governing equation, new boundary conditions are needed and related discussion is presented. The presence of the shear stress inside the tensionless Reissner foundation together with the unknown feature of contact area/length makes the problem much more difficult than that of Winkler foundation. In the model presented here, the effects of beam dimension, gap distance, loading asymmetry and foundation shear stress on the contact length are all incorporated and studied. As the beam length increases, the results of a finite beam with zero gap distance converge asymptotically to those obtained by the previous model for an infinitely long beam.

The Mexican hat effect on the delamination buckling of a compressed thin film

“…(2) The nonlinear stress-strain relation of the substrate, which is characterized by the neo-Hookean constitutive law [23] or the bilinear [24] and exponential [25] elastic foundation models. (3) The fact that the substrate responds differently to tension and compression [20,26,27]. With an increase of compression in the post-buckling region, the nonlinear reaction of the substrate can stand out and even become dominant on the formation of buckling patterns [28,29].…”

“…(21) to capture either of the shapes in the post-buckling region. Thirdly, because the elastic foundation model is introduced to study the response of the foundation surface to loads, it has the problem of accurately describing stresses [26,30,31]. The post-buckling stresses around the delamination edge are complex and have abrupt changes [1,2].…”

Extracting nanobelt mechanical properties from nanoindentation

“…Before we start the derivation of flexural NB contact with substrate, it is helpful for us to have a brief review and comment on the previous contact models which have obfuscating names. The contact problem of flexural structure is called differently as the receding contact, 42 unbonded contact, [43][44][45] tensionless contact, [46][47][48][49] and unilateral contact. 50 Despite their different names they all emphasize one essential thing: bending and lift-off of flexural structure.…”

Dynamic stability of Timoshenko beams on Pasternak viscoelastic foundation

“…The effects of the foundation stiffness parameters and the frequency parameter are illustrated by several numerical calculations. As an improved Winkler model, twoparameter Reissner foundation is used for studying contact lengths and deflection of a finite beam subjected to symmetric or asymmetric loading is studied in [5]. Zhang and Murphy [6] developed a general analytical model for the static response of a beam resting on a tensionless elastic foundation subjected to a lateral point load.…”