Mathematics

Compact finite elements based on modified equations of the plate theory

B. D. Annin^ab, Yu. M. Volchkov<sup>ab

a</sup> Lavrentiev Institute of Hydrodynamics SB RAS, 15 Lavrentiev Avenue, Novosibirsk 630090, Russia
^b Novosibirsk State University, 1 Pirogov Street, Novosibirsk 630090, Russia

Abstract: The modified equations of the elastic layer are used to construct compact finite elements, the conjugation conditions between which are formulated as conditions for the continuity of efforts and moments on their faces. The proposed finite elements can be effectively used in the numerical solution of problems of the stress-strain state of layered structures and deformed bodies containing cuts and cracks, since compact elements are natural regularizers in problems containing singularities in a stressed state.
The paper compares the results of a numerical and analytical solutions to the problem of determining the stress-strain state in the vicinity of the crack tip located in the elastic plane. The numerical solution to the problem is obtained using the iterative procedure of self-balanced residuals.

Keywords: modified equations of the elastic layer, compact finite elements, crack.

UDC: 539.3

Received: 08.10.2019
Revised: 04.02.2020
Accepted: 17.02.2020

DOI: 10.25587/SVFU.2020.29.95.001

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