Response prediction of geometrically nonlinear structures

The response prediction of geometrically nonlinear elastic structures (GNS) is an important area of research in structural engineering and mechanics. Also, in professional practice it has become mandatory to carry out such an evaluation for long-span and slender structures such as suspension bridges. However, this is often a very difficult task, especially when randomness in loads and material properties have to be taken into account. In this study, the responses of GNS are obtained using the total Lagrangian formulation for finite-element discretization. In the presence of uncertainties, the mean and variance of the response of GNS are evaluated by first-order approximation and Monte Carlo simulation. Numerical examples are presented to illustrate the computational process and to study the effects of various parameters such as type of analysis (linear or nonlinear), magnitude of loads and load effects, and type of approximation (first order or simulation) on the main descriptors of the response of GNS. For the cases studied, the results show that first-order approximation and Monte Carlo simulation are in close agreement. This indicates that, at least for the numerical examples presented, first-order approximation can be used in place of Monte Carlo simulation. In this manner, computational time is drastically reduced without a significant loss in accuracy.