Computational structural mechanics

The three topics selected for this paper are taken from structural engineering with special emphasis on civil engineering. The tool for numerical solutions of the respective engineering problems is the :nite element method. The :rst topic is structural stability. From a design-orientated viewpoint, it is frequently not necessary to perform a fully non-linear analysis to obtain stability limits on nonlinear load–displacement paths. Instead, linear eigenvalue problems may be used to compute estimates of such limits. Based on the consistent linearization of the criterion for stability limits on non-linear load–displacement paths, higher-order estimation functions can be calculated. The order of the errors resulting from such estimates is de:ned in an asymptotic sense. An ab initio criterionfor identi:cation of the type of loss of stability is presented. The second topic is adaptive :nite element analysis of reinforced concrete (RC) shells. It is based on an error estimator applicable to elasto-plastic problems accounting for hardening as well as softening material behaviour. Essential features of the developed strategy are multi-surface plasticity theory for constitutive modelling of concrete, consideration of the steel–concrete interaction and a time-e?ective calculation scheme allowing restart of the calculation at the increment at which the prespeci:ed error tolerance was found to be exceeded. Results from adaptive ultimate load analyses of a hyperbolic RC cooling tower subjected to dead load and quasistatic wind load are presented. The third topic is the assessment of safety degrees in shotcrete tunnel shells. A hybrid method combining 3D displacement measurements and thermochemomechanical modelling of shotcrete is presented. The material law for shotcrete is cast in the framework of thermodynamics of reactive porous media. In the course of the mentioned hybrid method, displacement :elds obtained from interpolation of values measured at measurement points are prescribed as boundary conditions on the outer surface of the investigated part of the tunnel shell