Explicit solution for linear systems with parametric stiffness and application to uncertain structures

The paper proposes a novel approximateexplicit solution for the static response of structuralsystems discretized by finite elements with parametricstiffness. The solution exploits the following properties:(a) if the system comprises one parameter only,i.e. a single finite element has parametric stiffness,then the exact explicit solution can always beobtained; (b) if all element stiffnesses are consideredas parameters and the exact solution is available at agiven point of the parameter space (i.e. for a givenrealization of the parameters), then it is also knownalong the line passing through that point and the originof the parameter space. The joint use of the twoproperties allows an accurate explicit relationship fornodal displacements which is suitable for treatingdifferent structural problems such as optimization, reanalysis,inverse analysis and reliability. The latterwill be investigated in the numerical applicationswhere Monte Carlo samples are produced by theexplicit relationship rather than by the re-analysis ofthe structural problem with an evident reduction ofcomputational burden.