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Annular and Disk Finite Elements for Two-Dimensional Elastostatic Problems
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DOI：10.1142/s0219876226500350.png)
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Abstract
En 中文
Modeling materials and microstructures composed of circular particles using standard finite elements poses a dual challenge: the polynomial-based geometric mapping introduces discretization errors on curved boundaries, and the large number of internal degrees of freedom required for each particle creates a computational bottleneck. This paper presents a new annular finite element and a circular disk super element to address both issues for two-dimensional (2D) elastostatic problems. The annular element employs an exact analytical geometric mapping based on polar coordinates, while the displacement field is interpolated using standard 8-node quadrilateral shape functions to maintain compatibility with conventional finite element frameworks. A disk super element is further constructed by applying static condensation to eliminate internal degrees of freedom. Convergence studies confirm that the annular element achieves optimal convergence rates, consistent with those of the standard isoparametric counterpart, while providing exact geometric fidelity on circular boundaries. Additional benchmarks involving stress concentrations and concentrated loads validate the element's accuracy. The efficiency and physical consistency of the disk super element are demonstrated through disk packing simulations, where the effective Young's modulus converges with increasing number of disks, showing the method's potential for homogenization analysis of particulate composites.
Keywords:
Annular element
disk super element
2D elastostatic problems
Journal
I
IF:
1.6
Papers:
79
Citations:
1.6K