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Malík, Josef; Kolcun, Alexej

Determination of the initial stress tensor from deformation of underground opening in excavation process. (English) Zbl 1538.65539

Appl. Math., Praha 67, No. 3, 297-318 (2022).
Summary: A method for the detection of the initial stress tensor is proposed. The method is based on measuring distances between pairs of points located on the wall of underground opening in the excavation process. This methods is based on solving twelve auxiliary problems in the theory of elasticity with force boundary conditions, which is done using the least squares method. The optimal location of the pairs of points on the wall of underground openings is studied. The pairs must be located so that the condition number of the least square matrix has the minimal value, which guarantees a reliable estimation of initial stress tensor.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74A10 Stress
93E24 Least squares and related methods for stochastic control systems
65K10 Numerical optimization and variational techniques
74B99 Elastic materials

Keywords:

initial stress tensor; first boundary value problem of the theory of elasticity; least square method; condition number of matrix; continuous dependence of eigenvalues on matrix elements
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References:

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