4,483 research outputs found
Analysis of and workarounds for element reversal for a finite element-based algorithm for warping triangular and tetrahedral meshes
We consider an algorithm called FEMWARP for warping triangular and
tetrahedral finite element meshes that computes the warping using the finite
element method itself. The algorithm takes as input a two- or three-dimensional
domain defined by a boundary mesh (segments in one dimension or triangles in
two dimensions) that has a volume mesh (triangles in two dimensions or
tetrahedra in three dimensions) in its interior. It also takes as input a
prescribed movement of the boundary mesh. It computes as output updated
positions of the vertices of the volume mesh. The first step of the algorithm
is to determine from the initial mesh a set of local weights for each interior
vertex that describes each interior vertex in terms of the positions of its
neighbors. These weights are computed using a finite element stiffness matrix.
After a boundary transformation is applied, a linear system of equations based
upon the weights is solved to determine the final positions of the interior
vertices. The FEMWARP algorithm has been considered in the previous literature
(e.g., in a 2001 paper by Baker). FEMWARP has been succesful in computing
deformed meshes for certain applications. However, sometimes FEMWARP reverses
elements; this is our main concern in this paper. We analyze the causes for
this undesirable behavior and propose several techniques to make the method
more robust against reversals. The most successful of the proposed methods
includes combining FEMWARP with an optimization-based untangler.Comment: Revision of earlier version of paper. Submitted for publication in
BIT Numerical Mathematics on 27 April 2010. Accepted for publication on 7
September 2010. Published online on 9 October 2010. The final publication is
available at http://www.springerlink.co
A family of higher-order single layer plate models meeting -- requirements for arbitrary laminates
In the framework of displacement-based equivalent single layer (ESL) plate
theories for laminates, this paper presents a generic and automatic method to
extend a basis higher-order shear deformation theory (polynomial,
trigonometric, hyperbolic, ...) to a multilayer higher-order shear
deformation theory. The key idea is to enhance the description of the
cross-sectional warping: the odd high-order function of the basis model
is replaced by one odd and one even high-order function and including the
characteristic zig-zag behaviour by means of piecewise linear functions. In
order to account for arbitrary lamination schemes, four such piecewise
continuous functions are considered. The coefficients of these four warping
functions are determined in such a manner that the interlaminar continuity as
well as the homogeneity conditions at the plate's top and bottom surfaces are
{\em a priori} exactly verified by the transverse shear stress field. These
ESL models all have the same number of DOF as the original basis HSDT.
Numerical assessments are presented by referring to a strong-form Navier-type
solution for laminates with arbitrary stacking sequences as well for a sandwich
plate. In all practically relevant configurations for which laminated plate
models are usually applied, the results obtained in terms of deflection,
fundamental frequency and local stress response show that the proposed zig-zag
models give better results than the basis models they are issued from
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