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Generalized hp-FEM for Lattice Structures

by A. W. Rüegg and A. Schneebeli and R. Lauper

(Report number 2002-23)

Abstract
Lattice block materials are mathematically modeled by periodic networks embedded in higher dimensional spaces. Elliptic two-scale problems on this dimensionally reduced structures are solved numerically by generalized Finite Elements. The choice of the problem adapted, conforming approximation spaces is motivated by an integral representation of the solution of the original problem extended to an infinite network with the same periodic pattern. The methods can be realized with algorithmic complexity independent of the micro scale, what is confirmed by numerical examples.

Keywords: generalized finite element method, lattice structures, networks, homogenization, two-scale problem

@Techreport{RSL02_309,
  author = {A. W. R\"uegg and A. Schneebeli and R. Lauper},
  title = {Generalized hp-FEM for Lattice Structures},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2002-23},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2002/2002-23.pdf },
  year = {2002}
}

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