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Accurate Prediction of Strains and Stresses in 2-D Elasticity Using Adini’s Finite Element

[+] Author Affiliations
Donovan A. Aguirre-Rivas, Karim H. Muci-Küchler

South Dakota School of Mines and Technology, Rapid City, SD

Paper No. IMECE2015-51647, pp. V009T12A012; 10 pages
doi:10.1115/IMECE2015-51647
From:
  • ASME 2015 International Mechanical Engineering Congress and Exposition
  • Volume 9: Mechanics of Solids, Structures and Fluids
  • Houston, Texas, USA, November 13–19, 2015
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-5752-6
  • Copyright © 2015 by ASME

abstract

In the interest of obtaining accurate stress predictions in linear elastic problems while keeping the computational cost low, a finite element solution approach using cubic elements that include not only the displacement but also the spatial derivatives of the displacement as nodal degrees of freedom (DOFs) is explored in this paper.

The proposed approach has the advantage that the nodal values of the strains, and hence the stresses, can be directly computed from the finite element solution and, as shown in this paper, it is capable of converging faster to the analytical solution than the commonly used reduced integration Serendipity quadratic element.

Because the proposed approach is capable of achieving high accuracy using less DOFs, it is possible to use coarser meshes than with conventional elements. This is of particular importance in dynamic problems in which explicit techniques are used and the size of the time step is tied to the element size. Moreover, the proposed approach can be beneficial in non-linear problems in which stepping techniques are used to solve a linearized problem and the strains or stresses of the current step are used as input for the following step.

Copyright © 2015 by ASME

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