Asymptotic behavior of straight rods with different order of thickness
نویسندگان
چکیده
Once we have established the appropriate estimates, we introduce a rescaling operator which allows to work in a fixed domain. Then, we give the limit of the displacements and we show a few relations between some of them. Since some of the a priori estimates established depend on the variable thickness we introduce some weighted Sobolev spaces which allow to obtain the limit fields in a natural way.
منابع مشابه
Asymptotic behavior of structures made of straight rods
This paper is devoted to describe the deformations and the elastic energy for structures made of straight rods of thickness 2δ when δ tends to 0. This analysis relies on the decomposition of the large deformation of a single rod introduced in [7] and on the extension of this technique to a multi-structure. We characterize the asymptotic behavior of the infimum of the total elastic energy as the...
متن کاملStraight rod with different order of thickness
In this paper, we consider rods whose thickness vary linearly between and . Our aim is to study the asymptotic behavior of these rods in the framework of the linear elasticity. We use a decomposition method of the displacement fields of the form u = Ue + ū, where Ue stands for the translation-rotations of the cross-sections and ū is related to their deformations. We establish a priori estimates...
متن کاملNumerical modeling and comparison study of elliptical cracks effect on the pipes straight and with thickness transition exposed to internal pressure, using XFEM in elastic behavior.
The present work deals with the effect of an external circumferential elliptical crack located at thickness transition on a varied stepped diameter pipe . The purpose is the application of the extended finite element method (XFEM) for the calculation of SIF at the thickness transition region of pipe considering internal pressure and compare the effect of the crack between pipes straight and wi...
متن کاملStraight Configurations of Shearable Nonlinearly Elastic Rods
Investigating obstacle problems for elastic rods we are sometimes confronted with the question to look for a solution which has a prescribed shape along some part of it. In the simplest case the rod is enforced to be straight along some contact area (cf., e.g., Gastaldi & Kinderlehrer [3]). Motivated by such applications we study straight configurations of elastic rods in this paper. More preci...
متن کاملNumerical Analysis of the Effect of External Circumferential Cracks in Transition Thickness Zone of Pressurized Pipes Using XFEM – Elastic-Plastic Behavior
The elastic-plastic behavior of the material is considered to analyze the effect of an external circumferential crack on a pipe with thickness transition and double slopes. Using the extended finite element method (XFEM), the J-integral of 3D cracks were investigated and compared between straight pipes and pipes with thickness transition and different slopes. Considering internal press...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2017