Methods for solving systems of linear equations of structure mechanics with interval parameters
Abstract
Interval analysis permits to calculate guaranteed a posteriori bounds for the solutions of problems with uncertain (interval) input data. Most of the methods of interval analysis assume that all input data vary independently within the given lower and upper bounds. In many practical applications it need not be a case, and the assumption of independence may lead to large overestimation of the set of solutions. The subject of this work is the problem of solving systems of linear interval equations with coefficients linearly dependent on a set of interval parameters called coefficient dependence problem. The purpose of this work is to present methods producing sharp bounds for the set of solutions of systems with dependent input data. The paper starts with an introduction to systems of linear interval equations and the problem of data dependencies in such systems. A parametric formulation of the coefficient dependence problem follows next. Finally, three algorithms to calculate tighter bounds for problems with linearly dependent coefficients, namely the Rump's method, its improved version developed by the author, and the IPM method based on the results from Neumaier [8] are presented and discussed. The algorithms are evaluated and compared using some examples of truss structure analysis.
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References
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