Optimal Topology Of Eigenstrains In The
Assessment Of Tunnel Structures
Author(s)
P. Procházka, V. Doležel & S. Pešková
Abstract
Eigenstresses and eigenstrains act out a very important role in many branches of
applied mechanics. The eigenparameters may represent plastic strains, or
relaxation stresses (or also prestresses, changes of temperature, etc.), and may
also serve as free parameters for improving numerical models to get the
computed quantities that should be as close as possible to the real state. A special
variational formulation can be formulated, dealing with the minimum variance of
differences between measured and computed values. When using a very useful
treatment, the generalized transformation field analysis (GTFA), having recently
been proposed by Dvorak and Procházka, and the Disturbed State Concept
proposed by Desai, the primary problem leads to a linear system of algebraic
equations. First, we briefly introduce an estimation of physically nonlinear
behavior of the body by Desai. The eigenparameters will then be introduced in
such a manner that the optimal variance of errors from measurement and
numerical results are sought. It appears that the number of components of
eigenparameters should not exceed the number of data points from
measurements either on site or on a scale model, and hence, the number of free
eigenparameters is restricted. The main problem remains: how to select the zones
with, say, uniformly distributed eigenparameters in order to achieve the
minimum deviation of computed and measured results in dependence of the
minimum variation of errors from computation and of the topology of the
eigenparameters zone. They basically influence the final results from the
procedure to be described. The main goal of this paper consists in finding out
both the phenomena. While the minimum of the error functional leads to linear
algebraic equations, searching for optimal topology of eigenparameters zones
brings about a nonlinear problem, which should be solved in some reasonable
way. We first concentrate on the optimization of the error functional under the
condition that the zones are known and then the zones will be sought.
Keywords
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