Abstract
In this paper, the results of an application of global and local optimization methods to solve a problem of determination of strains in RC compressed structure members are presented. Solutions of appropriate sets of nonlinear equations in the presence of box constraints have to be found. The use of the least squares method leads to finding global solutions of optimization problems with box constraints. Numerical examples illustrate the effects of the loading value and the loading eccentricity on the strains in concrete and reinforcing steel in the a cross-section.Three different minimization methods were applied to compute them: trust region reflective, genetic algorithm tailored to problems with real double variables and particle swarm method. Numerical results on practical data are presented. In some cases, several solutions were found. Their existence has been detected by the local search with multistart, while the genetic and particle swarm methods failed to recognize their presence.
Highlights
Our problem is to determine the normal strains in the cross-sections of reinforced concrete structure members subjected to compression
Our numerical results have confirmed that the elaborated analytical deformation model may be used to determine the strains in rectangular cross-sections of RC compressed structure members
It can be applied to predict the behaviour of such structure members
Summary
Our problem is to determine the normal strains in the cross-sections of reinforced concrete structure members subjected to compression. It may be formulated as a task of solving sets of equations with box constraints. The presence of the box constraints makes a direct use of numerical methods for solving sets of nonlinear equations impractical. Our task is reformulated by means of the frequently used least squares method. It leads to a nonlinear, nonconvex optimization problem of finding a minimum of a nonlinear function with the restricted scope of variables
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