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Volume 6, Issue 3
Numerical Solution of a Non-Smooth Variational Problem Arising in Stress Analysis: The Scalar Case

A. Caboussat & R. Glowinski

Int. J. Numer. Anal. Mod., 6 (2009), pp. 402-419.

Published online: 2009-06

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  • Abstract

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.

  • Keywords

Non-smooth optimization, stresses analysis, augmented Lagrangian method, finite elements approximation, elasticity theory.

  • AMS Subject Headings

65K10, 65N30, 49S05, 74G70

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-6-402, author = {A. Caboussat and R. Glowinski}, title = {Numerical Solution of a Non-Smooth Variational Problem Arising in Stress Analysis: The Scalar Case}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2009}, volume = {6}, number = {3}, pages = {402--419}, abstract = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/775.html} }
TY - JOUR T1 - Numerical Solution of a Non-Smooth Variational Problem Arising in Stress Analysis: The Scalar Case AU - A. Caboussat & R. Glowinski 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 -

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.

A. Caboussat and R. Glowinski. (2009). Numerical Solution of a Non-Smooth Variational Problem Arising in Stress Analysis: The Scalar Case. International Journal of Numerical Analysis and Modeling. 6 (3). 402-419. doi:
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