The stability of stars of simplicial hybrid equilibrium finite elements for solid mechanics

2015 ◽  
Vol 107 (8) ◽  
pp. 633-668 ◽  
Author(s):  
E. A. W. Maunder ◽  
J. P. Moitinho de Almeida ◽  
O. J. B. Almeida Pereira
Keyword(s):  
Finite Elements ◽  
Solid Mechanics ◽  
Stability Of Stars ◽  
The Stability ◽  
Equilibrium Finite Elements

Impact of f(R,T) gravity in evolution of charged viscous fluids

2021 ◽  
Vol 30 (04) ◽  
pp. 2150027
Author(s):  
I. Noureen ◽  
Usman-ul-Haq ◽  
S. A. Mardan
Keyword(s):  
Stability Analysis ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Viscous Fluids ◽  
Fluid Distribution ◽  
Perturbation Scheme ◽  
Field Equations ◽  
Dynamical Equations ◽  
Stability Of Stars ◽  
The Stability

In this work, the evolution of spherically symmetric charged anisotropic viscous fluids is discussed in framework of [Formula: see text] gravity. In order to conduct the analysis, modified Einstein Maxwell field equations are constructed. Nonzero divergence of modified energy momentum tensor is taken that implicates dynamical equations. The perturbation scheme is applied to dynamical equations for stability analysis. The stability analysis is carried out in Newtonian and post-Newtonian limits. It is observed that charge, fluid distribution, electromagnetic field, viscosity and mass of the celestial objects greatly affect the collapsing process as well as stability of stars.

Modeling Beam–Solid Finite Element Interfaces: A Stabilized Formulation for Contact and Coupled Systems

2018 ◽  
Vol 10 (09) ◽  
pp. 1850094 ◽  
Author(s):  
Jorge A. Montero ◽  
Ghadir Haikal
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Computational Models ◽  
Solid Mechanics ◽  
Pressure Field ◽  
Coupled Systems ◽  
Weak Continuity ◽  
Finite Element Discretizations ◽  
Geometric Compatibility ◽  
Element Discretizations

A number of engineering applications involve contact with bodies modeled using specialized theories of solid mechanics like beams or shells. While computational models for contact in 2D and 3D solid mechanics have been extensively developed in the literature, problems involving contact with beams or shells have received less attention. When modeling contact between a solid body represented with beam or shell theory and a domain discretized with solid finite elements, the contact model faces the typical challenges of enforcing geometric compatibility and the transfer of a complete pressure field along the contact interface, with the added complications stemming from the different underlying mathematical formulations and finite element discretizations in the connecting domains. Resultant-based beam and shell theories do not provide direct estimates of surface tractions, therefore rendering the issue of pressure transfer on beam–solid and shell–solid interfaces more problematic. In the absence of specialized contact formulations for solid–beam and solid–shell interfaces, contact models have relied almost exclusively on the Node-To-Surface (NTS) geometric compatibility approach. This formulation suffers from well-known drawbacks, including instability, surface locking and incomplete pressure fields on the interface. The NTS approach, however, remains the method most readily applicable to contact with beam or shell elements among the vast variety of available methods for computational contact modeling using finite elements. The goal of this paper is to bridge the gap in the literature on coupling domains with beam and solid finite element discretizations. We propose an interface formulation for beam–solid interfaces that ensures the transfer of a complete pressure field while enforcing geometric compatibility using standard NTS constraints. The formulation uses a stabilization approach, based on a special form of the Discontinuous Galerkin method, to enforce weak continuity between the stress fields on the solid side of the interface, and the moment and shear resultants in the contacting beam. We show that the proposed formulation is a robust approach for satisfying compatibility constraints while ensuring the transfer of a complete pressure field on beam–solid finite element interfaces that can be used with bilinear and quadratic interpolations in the solid, and Euler or Timoshenko formulations for the beam.

scholarly journals Equilibrium Finite Elements of Spherical Shells in Analysis Problems

2013 ◽  
Vol 57 ◽  
pp. 515-523 ◽  
Author(s):  
Stanislovas Kalanta ◽  
Juozas Atkočiūnas ◽  
Tomas Ulitinas
Keyword(s):  
Finite Elements ◽  
Spherical Shells ◽  
Equilibrium Finite Elements
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