Open AccessFINITE ELEMENTS OF THE PLANE PROBLEM OF THE THEORY OF ELASTICITY WITH DRILLING DEGREES OF FREEDOM
Author(s) -
V. S. Karpilovskii
Publication year - 2020
Publication title -
international journal for computational civil and structural engineering
Language(s) - English
Resource type - Journals
eISSN - 2588-0195
pISSN - 2587-9618
DOI - 10.22337/2587-9618-2020-16-1-48-72
Subject(s) - mathematics , finite element method , degrees of freedom (physics and chemistry) , elasticity (physics) , mathematical analysis , convergence (economics) , drilling , rotation (mathematics) , symmetry (geometry) , geometry , instability , mechanics , structural engineering , physics , engineering , mechanical engineering , quantum mechanics , economics , thermodynamics , economic growth
Twelve new finite elements with drilling degrees of freedom have been developed: triangular and quadrangular elements based on a modified hypothesis about the value of approximating functions on the sides of the element, which made it possible to avoid dimensional instability when all rotation angles are zero; incompatible and compatible triangular and quadrangular elements which can have additional nodes on the sides. Approximating functions satisfy the following condition: the value of the rotational degree of freedom of a node is nonzero and equal to one only for one of them. Numerical examples illustrate estimated minimum orders of convergence for displacements and stresses. All created elements retain the existing symmetry of the design models.