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Numerical methods for static shallow shells lying over an obstacle.

Paolo Piersanti1, Xiaoqin Shen2

  • 1Institute of Mathematics and Scientific Computing, Karl-Franzens-Universität Graz, Heinrichstraße 36, A8010 Graz, Austria.

Numerical Algorithms
|September 24, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces a finite element analysis for static shallow shell obstacle problems in a half space. The numerical method is proven to converge, offering a reliable approximation for this complex engineering challenge.

Keywords:
Elliptic variational inequalitiesEnriching operatorNonconforming finite element methodObstacle problemsShallow shell

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Area of Science:

  • Computational Mechanics
  • Solid Mechanics
  • Numerical Analysis

Background:

  • Obstacle problems are crucial in engineering and physics.
  • Shallow shell structures confined in a half space present unique analytical challenges.
  • Existing numerical methods may require refinement for accuracy and convergence.

Purpose of the Study:

  • To develop and analyze a finite element method for solving static shallow shell obstacle problems.
  • To establish an error estimate for the approximate bilinear form.
  • To prove the convergence of the proposed numerical scheme.

Main Methods:

  • Finite element analysis (FEA).
  • Utilizing properties of enriching operators.
  • Conducting rigorous error analysis.

Main Results:

  • An estimate for the approximate bilinear form was established.
  • The convergence of the finite element scheme was mathematically proven.
  • The proposed method provides an accurate approximation for the problem.

Conclusions:

  • The presented finite element analysis is a viable and convergent numerical scheme.
  • This work contributes to the accurate computational modeling of static shallow shells with obstacles.
  • The findings are applicable to advanced engineering simulations.