Isoparametric quadrilaterals and hexahedrons for mesh‐grading algorithms

Abstract

SUMMARYTwo-dimensional (2-D) and three-dimensional (3-D) mesh-grading finite elements for problems with localized phenomena are presented. These quadrilaterals and hexahedrons permit mesh grading without element distortion and, if desired, can be used in a convenient recursive form. They are particularly well suited to adaptive finite element methods. Constraints associated with mesh grading are embedded in the basis functions, making the elements computationally efficient and easy to implement in standard finite element programs. Dramatic computational savings have been achieved. The computational complcxity for an implicit analysis of a point load on a 3-D uniform mesh is O(n7). For the equivalent graded mesh it is O(logzn). The corresponding 2-D analyses have computational complexities of O(n") and O(log,n).

3D modelling of multipass welding of a 316L stainless steel pipe

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Tet-to-Hex Conversion for Finite Element Analysis

“…The hexahedral element used is shown in Figure 3. The associated basis functions [8] are given in Equation 2. The first step in determining the quality of the hexahedra is to evaluate the Jacobian matrix at the centroid of the hexahedron.…”

An adaptive finite element procedure for the image segmentation problem

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