Development-process-of-nonlinearity-based reliability evaluation of structures

A reliability evaluation approach based on the development process of the structural nonlinearity is presented. The traditional structural system reliability theory for structural safety regarding combination of failure modes is first revisited. It is seen that it stemmed from, and was heavily affected by, the assumption of perfect elasto-plasticity of materials. This will make the number of the failure modes increase in a non-polynomial form against the number of the potential plastic hinges. Moreover, the above methodology does not work appropriately in the case of nonlinearity in general form other than perfect elasto-plasticity, as commonly encountered in engineering practice. Discussions show that total information of the structure is involved in the development process of its nonlinearity, be it a deterministic case or stochastic counterpart. The information needed for reliability evaluation of structures could be extracted, for example, by capturing the probabilistic information of the extreme value of the corresponding response, which could be obtained by using the probability density evolution method. Therefore, the reliability evaluation for structural safety could then be directly evaluated without searching the failure modes. Taking a 10-bar truss as an example, the proposed method is theoretically elaborated and numerically exemplified.