Dimensional reduction for energies with linear growth involving the bending moment
نویسندگان
چکیده
A Γ-convergence analysis is used to perform a 3D-2D dimension reduction of variational problems with linear growth. The adopted scaling gives rise to a nonlinear membrane model which, because of the presence of higher order external loadings inducing a bending moment, may depend on the average in the transverse direction of a Cosserat vector field, as well as on the deformation of the mid-plane. The assumption of linear growth on the energy leads to an asymptotic analysis in the spaces of measures and of functions with bounded variation.
منابع مشابه
Analysis of Thermal-Bending Stresses in a Simply Supported Annular Sector Plate
The present article deals with the analysis of thermal-bending stresses in a heated thin annular sector plate with simply supported boundary condition under transient temperature distribution using Berger’s approximate methods. The sectional heat supply is on the top face of the plate whereas the bottom face is kept at zero temperature. In this study, the solution of heat conduction is obtained...
متن کاملThe Nonlinear Bending Analysis for Circular Nano Plates Based on Modified Coupled Stress and Three- Dimensional Elasticity Theories
In this paper, the nonlinear bending analysis for annular circular nano plates is conducted based on the modified coupled stress and three-dimensional elasticity theories. For this purpose, the equilibrium equations, considering nonlinear strain terms, are calculated using the least energy potential method and solved by the numerical semi-analytical polynomial method. According to the previous ...
متن کاملNon-linear inplane deformation and buckling of rings and high arches
A non-linear theory is presented for stretching and inplane-bending of isotropic beams which have constant initial curvature and lie in their plane of symmetry. For the kinematics, the geometrically exact one-dimensional (1-D) measures of deformation are specialized for small strain. The 1-D constitutive law is developed in terms of these measures via an asymptotically correct dimensional reduc...
متن کاملInvestigating the Effectiveness of a Composite Patch on Repairing Pipes Subjected to Circumferential Cracks under Combined Loadings
The purpose of this study is to investigate bending moment and the axial load capacity of a pressurized pipe suffering from a through-wall circumferential crack repaired by a composite sleeve. The three-dimensional finite element method (FEM) was adopted to compute the results, and the failure assessment diagram (FAD) was employed to investigate the failure behavior of the repaired pipe. The fi...
متن کاملStrain Hardening Analysis for M-P Interaction in Metallic Beam of T-Section
This paper derives kinematic admissible bending moment – axial force (M-P) interaction relations for mild steel by considering strain hardening idealisations. Two models for strain hardening – Linear and parabolic have been considered, the parabolic model being closer to the experiments. The interaction relations can predict strains, which is not possible in a rigid, perfectly plastic idealizat...
متن کامل