TY - JOUR
T1 - Numerical Solution of a Non-Smooth Variational Problem Arising in Stress Analysis: The Scalar Case
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 402
EP - 419
PY - 2009
DA - 2009/06
SN - 6
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/775.html
KW - Non-smooth optimization, stresses analysis, augmented Lagrangian method, finite elements approximation, elasticity theory.
AB - <p style="text-align: justify;">A non-smooth constrained minimization problem arising in the
stress analysis of a plastic body is considered. A numerical method for the
computation of the load capacity ratio is presented to determine if the elastic
body fractures under external traction. In the scalar case, the maximum principle
allows one to reduce the problem to a convex one under linear constraints.
An augmented Lagrangian method, together with an approximation by finite
elements is advocated for the computation of the load capacity ratio and the
corresponding elastic stress. The generalized eigenvalues and eigenvectors of
the corresponding operator are computed for various two-dimensional bodies
and fractures are discussed.</p>