4,783 research outputs found
Weakly symmetric stress equilibration for hyperelastic materialmodels
A stress equilibration procedure for hyperelastic material models is proposed
andanalyzed in this paper. Based on the displacement-pressure approximation
computed with a stable finite element pair, it constructs, in a
vertex-patch-wise manner, an -conforming approximation to the first
Piola-Kirchhoff stress. This is done in such a way that its associated Cauchy
stress is weakly symmetric in the sense that its anti-symmetric part is zero
tested against continuous piecewise linear functions. Our main result is the
identification of the subspace of test functions perpendicular to the range of
the local equilibration system on each patch which turn out to be rigid body
modes associated with the current configuration. Momentum balance properties
are investigated analytically and numerically and the resulting stress
reconstruction is shown to provide improved results for surface traction forces
by computational experiments
Calculation of skin-stiffener interface stresses in stiffened composite panels
A method for computing the skin-stiffener interface stresses in stiffened composite panels is developed. Both geometrically linear and nonlinear analyses are considered. Particular attention is given to the flange termination region where stresses are expected to exhibit unbounded characteristics. The method is based on a finite-element analysis and an elasticity solution. The finite-element analysis is standard, while the elasticity solution is based on an eigenvalue expansion of the stress functions. The eigenvalue expansion is assumed to be valid in the local flange termination region and is coupled with the finite-element analysis using collocation of stresses on the local region boundaries. Accuracy and convergence of the local elasticity solution are assessed using a geometrically linear analysis. Using this analysis procedure, the influence of geometric nonlinearities and stiffener parameters on the skin-stiffener interface stresses is evaluated
Local Maximum Entropy Shape Functions Based FE-EFGM Coupling
In this paper, a new method for coupling the finite element method (FEM)and the element-free Galerkin method (EFGM) is proposed for linear elastic and geometrically nonlinear problems using local maximum entropy shape functions in theEFG zone of the problem domain. These shape functions possess a weak Kroneckerdelta property at the boundaries which provides a natural way to couple the EFGand the FE regions as compared to the use of moving least square basis functions.In this new approach, there is no need for interface/transition elements between theEFG and the FE regions or any other special treatment for shape function continuity across the FE-EFG interface. One- and two-dimensional linear elastic and two-dimensional geometrically nonlinear benchmark numerical examples are solved by the new approach to demonstrate the implementation and performance of the current approach
The Mullins effect in the wrinkling behavior of highly stretched thin films
Recent work demonstrates that finite-deformation nonlinear elasticity is
essential in the accurate modeling of wrinkling in highly stretched thin films.
Geometrically exact models predict an isola-center bifurcation, indicating that
for a bounded interval of aspect ratios only, stable wrinkles appear and then
disappear as the macroscopic strain is increased. This phenomenon has been
verified in experiments. In addition, recent experiments revealed the following
striking phenomenon: For certain aspect ratios for which no wrinkling occurred
upon the first loading, wrinkles appeared during the first unloading and again
during all subsequent cyclic loading. Our goal here is to present a simple
pseudo-elastic model, capturing the stress softening and residual strain
observed in the experiments, that accurately predicts wrinkling behavior on the
first loading that differs from that under subsequent cyclic loading. In
particular for specific aspect ratios, the model correctly predicts the
scenario of no wrinkling during first loading with wrinkling occurring during
unloading and for all subsequent cyclic loading.Comment: 15 pages, 9 figure
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