32,906 research outputs found
An isogeometric analysis for elliptic homogenization problems
A novel and efficient approach which is based on the framework of
isogeometric analysis for elliptic homogenization problems is proposed. These
problems possess highly oscillating coefficients leading to extremely high
computational expenses while using traditional finite element methods. The
isogeometric analysis heterogeneous multiscale method (IGA-HMM) investigated in
this paper is regarded as an alternative approach to the standard Finite
Element Heterogeneous Multiscale Method (FE-HMM) which is currently an
effective framework to solve these problems. The method utilizes non-uniform
rational B-splines (NURBS) in both macro and micro levels instead of standard
Lagrange basis. Beside the ability to describe exactly the geometry, it
tremendously facilitates high-order macroscopic/microscopic discretizations
thanks to the flexibility of refinement and degree elevation with an arbitrary
continuity level provided by NURBS basis functions. A priori error estimates of
the discretization error coming from macro and micro meshes and optimal micro
refinement strategies for macro/micro NURBS basis functions of arbitrary orders
are derived. Numerical results show the excellent performance of the proposed
method
The A-decomposability of the Singer construction
Let denote the Singer construction on an unstable module over the
Steenrod algebra at the prime two; is canonically a subobject of
, where is the polynomial algebra on s generators of degree
one. Passage to -indecomposables gives the natural transformation , which identifies with the dual of the
composition of the Singer transfer and the Lannes-Zarati homomorphism.
The main result of the paper proves the weak generalized algebraic spherical
class conjecture, which was proposed by the first named author. Namely, this
morphism is trivial on elements of positive degree when s>2. The condition s>2
is necessary, as exhibited by the spherical classes of Hopf invariant one and
those of Kervaire invariant one.Comment: v2 15 pages. Minor revision. v3 17 pages, revision following
referee's recommendations. Accepted for publication J. Al
Geometrically nonlinear isogeometric analysis of laminated composite plates based on higher-order shear deformation theory
In this paper, we present an effectively numerical approach based on
isogeometric analysis (IGA) and higher-order shear deformation theory (HSDT)
for geometrically nonlinear analysis of laminated composite plates. The HSDT
allows us to approximate displacement field that ensures by itself the
realistic shear strain energy part without shear correction factors. IGA
utilizing basis functions namely B-splines or non-uniform rational B-splines
(NURBS) enables to satisfy easily the stringent continuity requirement of the
HSDT model without any additional variables. The nonlinearity of the plates is
formed in the total Lagrange approach based on the von-Karman strain
assumptions. Numerous numerical validations for the isotropic, orthotropic,
cross-ply and angle-ply laminated plates are provided to demonstrate the
effectiveness of the proposed method
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