TY - JOUR
T1 - A class of strain-displacement elements in upper bound limit analysis
AU - Makrodimopoulos, Athanasios
N1 - Publisher Copyright:
© 2022 John Wiley & Sons Ltd.
PY - 2022/8/30
Y1 - 2022/8/30
N2 - The main restriction in applying the upper bound theorem in limit analysis by means of the finite element method is that once the displacement field has been discretized, the flow rule and the boundary conditions should be satisfied everywhere throughout the discretized structure. This is to secure mathematically that the result will be a rigorous upper bound of the exact limit load multiplier. So far, only the linear and the quadratic displacement elements with straight sides, which result in constant and linear strains, respectively, satisfy this requirement. In this article, it is proven both theoretically and practically that there is a general class of strain-displacement triangular elements with straight sides which provide rigorous upper bounds. The interpolation scheme is based on the Bernstein polynomials, and there is no upper restriction of the polynomial order. Both continuous and discontinuous displacements can be considered. The efficiency is examined through plane strain and Kirchhoff plate examples. The generalization to 3D (i.e., tetrahedral elements with plane faces) and other structural conditions is straightforward.
AB - The main restriction in applying the upper bound theorem in limit analysis by means of the finite element method is that once the displacement field has been discretized, the flow rule and the boundary conditions should be satisfied everywhere throughout the discretized structure. This is to secure mathematically that the result will be a rigorous upper bound of the exact limit load multiplier. So far, only the linear and the quadratic displacement elements with straight sides, which result in constant and linear strains, respectively, satisfy this requirement. In this article, it is proven both theoretically and practically that there is a general class of strain-displacement triangular elements with straight sides which provide rigorous upper bounds. The interpolation scheme is based on the Bernstein polynomials, and there is no upper restriction of the polynomial order. Both continuous and discontinuous displacements can be considered. The efficiency is examined through plane strain and Kirchhoff plate examples. The generalization to 3D (i.e., tetrahedral elements with plane faces) and other structural conditions is straightforward.
KW - Bernstein polynomials
KW - limit analysis
KW - upper bound
UR - http://www.scopus.com/inward/record.url?scp=85128411999&partnerID=8YFLogxK
U2 - 10.1002/nme.6985
DO - 10.1002/nme.6985
M3 - Article
AN - SCOPUS:85128411999
SN - 0029-5981
VL - 123
SP - 3681
EP - 3712
JO - International Journal for Numerical Methods in Engineering
JF - International Journal for Numerical Methods in Engineering
IS - 16
ER -