Finite Element Spectral Analysis for the Mixed Formulation of the Elasticity Equations
نویسندگان
چکیده
منابع مشابه
Mixed finite element formulation enriched by Adomian method for vibration analysis of horizontally curved beams
Abstract: The vibration analysis of horizontally curved beams is generally led to higher order shape functions using direct finite element method, resulting in more time-consuming computation process. In this paper, the weak-form mixed finite element method was used to reduce the order of shape functions. The shape functions were first considered linear which did not provide adequate accuracy....
متن کاملA Stabilized Mixed Finite Element Method for Finite Elasticity Formulation for Linear Displacement and Pressure Interpolation
A stabilized mixed finite element method for finite elasticity is presented. The method circumvents the fulfillment of the Ladyzenskaya-Babuska-Brezzi condition by adding mesh-dependent terms, which are functions of the residuals of the Euler-Lagrange equations, to the usual Galerkin method. The weak form and the linearized weak form are presented in terms of the reference and current configura...
متن کاملMixed finite elements for elasticity in the stress-displacement formulation
We present a family of pairs of finite element spaces for the unaltered Hellinger–Reissner variational principle using polynomial shape functions on a single triangular mesh for stress and displacement. There is a member of the family for each polynomial degree, beginning with degree two for the stress and degree one for the displacement, and each is stable and affords optimal order approximati...
متن کاملNonconforming Finite Element Methods for the Equations of Linear Elasticity
In the adaptation of nonconforming finite element methods to the equations of elasticity with traction boundary conditions, the main difficulty in the analysis is to prove that an appropriate discrete version of Korn's second inequality is valid. Such a result is shown to hold for nonconforming piecewise quadratic and cubic finite elements and to be false for nonconforming piecewise linears. Op...
متن کاملAn augmented mixed finite element method for the vorticity–velocity–pressure formulation of the Stokes equations
This paper deals with the numerical approximation of the stationary two-dimensional Stokes equations, formulated in terms of vorticity, velocity and pressure, with non-standard boundary conditions. Here, by introducing a Galerkin least-squares term, we end up with a stabilized variational formulation that can be recast as a twofold saddle point problem. We propose two families of mixed finite e...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 2013
ISSN: 0036-1429,1095-7170
DOI: 10.1137/120863010