Displaying similar documents to “Microlocal Approach to Tensor Tomography and Boundary and Lens Rigidity”

Determination of the initial stress tensor from deformation of underground opening -- theoretical background and applications

Malík, Josef, Kolcun, Alexej

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In this paper a method for the detection of initial stress tensor is proposed. The method is based on measuring distances between some pairs of points located on the wall of underground opening in the excavation process. This methods is based on the solution of eighteen auxiliary problems in the theory of elasticity with force boundary conditions. The optimal location of the pairs of points on the wall of underground work is studied. The pairs must be located so that the condition number...

Determination of the initial stress tensor from deformation of underground opening in excavation process

Josef Malík, Alexej Kolcun (2022)

Applications of Mathematics

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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...

A paradox in the theory of linear elasticity

Jindřich Nečas, Miloš Štípl (1976)

Aplikace matematiky

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Let us have the system of partial differential equations of the linear elasticity. We show that the solution of this system with a bounded boundary condition is not generally bounded (i.e., the displacement vector is not bounded). This example is a modification of that given by E. De Giorgi [1].