TY - JOUR
T1 - A displacement potential function using complex variables for numerical computations of three-dimensional elasticity problems
AU - Mares Carreño, Jesús
AU - Ortega Herrera, José Ángel Lodegario
AU - Abarca Jiménez, Griselda Stephany
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature.
PY - 2021/5
Y1 - 2021/5
N2 - This paper shows the development of a displacement potential function based on the Galerkin potential using complex variables. The displacement potential function results in a more suitable method for numerical calculations since it avoids the strenuous integration process associated with stress potential methods. Completeness of the displacement potential function is demonstrated. The displacement potential function was applied to the solution of the first fundamental problem of elasticity over a three-dimensional domain with known boundary conditions. It’s application for numerical calculations is demonstrated by solving the pure shear problem over a three-dimensional unit hexahedral cell. Finally, the obtained numerical results are compared against finite element results, proving the validity of the displacement potential function in solving three-dimensional linear elasticity problems.
AB - This paper shows the development of a displacement potential function based on the Galerkin potential using complex variables. The displacement potential function results in a more suitable method for numerical calculations since it avoids the strenuous integration process associated with stress potential methods. Completeness of the displacement potential function is demonstrated. The displacement potential function was applied to the solution of the first fundamental problem of elasticity over a three-dimensional domain with known boundary conditions. It’s application for numerical calculations is demonstrated by solving the pure shear problem over a three-dimensional unit hexahedral cell. Finally, the obtained numerical results are compared against finite element results, proving the validity of the displacement potential function in solving three-dimensional linear elasticity problems.
KW - Displacement potential function
KW - Functions of complex variable
KW - Numerical computations
KW - Three-dimensional elasticity
UR - http://www.scopus.com/inward/record.url?scp=85099765279&partnerID=8YFLogxK
U2 - 10.1007/s00419-021-01885-6
DO - 10.1007/s00419-021-01885-6
M3 - Artículo
AN - SCOPUS:85099765279
SN - 0939-1533
VL - 91
SP - 2331
EP - 2344
JO - Archive of Applied Mechanics
JF - Archive of Applied Mechanics
IS - 5
ER -