Damage quantification, damage limit state criteria and vulnerability analysis for single-layer reticulated shell

In this paper, a ductile damage constitutive model was used to describe the damage evolution of material while a structure is subjected to earthquake loading. And embedding this constitutive model into UMAT subroutine using software ABAQUS to introduce damage constitutive equations. A damage index which includes both maximum and cumulative deformations was then used to estimate the different degrees of damage of structural members caused by cyclic loading. The collapse mechanism of single-layer reticulated shell was investigated through incremental dynamic analysis (IDA). Two types of collapse, dynamic instability and dynamic strength failure, were obtained. It was found that material damage accumulation had little effect on plastic development and collapse pattern when the structure was in dynamic instability; but the effect of material damage accumulation was obvious and could not be ignored when the structure was in dynamic strength failure due to large plastic development. Last, two different structural damage models-one including multiple structural responses and the other including deformation and energy-are defined based on limit state criteria. It was found through comparison of results that these two structural damage models can be used to accurately define and quantify different damage degrees of single-layer reticulated shells during earthquake. The vulnerability at different damage degrees of structure using the structural damage model was conducted through IDA analysis, which could be used for seismic performance evaluation and risk assessment.