About the Cover:The figures on the cover illustrate three aspects of the validation of a computational model developed to predict the vibration response of historic masonry monuments. Top right: The National Cathedral, Washington, DC, where vibration response of vaults is experimentally measured to assess the effect of structural damage. The measurements provide acceleration time series used to verify and validate predictions of the numerical simulation. Top left: The computational finite element model is shown to illustrate the mesh discretization of a vault. The model is analyzed to simulate the vibration response. Colors represent different material properties whose uncertainties are propagated through the calculation. Bottom: The measurement of a vibration mode shape of the structure (solid line) is compared to the prediction of the finite element model (dashed line). Crosses illustrate the uncertainty of predictions due to variability of the boundary conditions and material properties. Statistical tests are implemented to quantify the accuracy of the finite element model, given measurement variability and prediction uncertainty. Tables Table 3-
Calibration Under Uncertainty for Finite
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ABSTRACTHistorical unreinforced masonry buildings often include features such as load bearing unreinforced masonry vaults and their supporting framework of piers, fill, buttresses, and walls. The masonry vaults of such buildings are among the most vulnerable structural components and certainly among the most challenging to analyze. The versatility of finite element (FE) analyses in incorporating various constitutive laws, as well as practically all geometric configurations, has resulted in the widespread use of the FE method for the analysis of complex unreinforced masonry structures over the last three decades. However, an FE model is only as accurate as its input parameters, and there are two fundamental challenges while defining FE model input parameters: (1) material properties and (2) support conditions. The difficulties in defining these two aspects of the FE model arise from the lack of knowledge in the common engineering understanding of masonry behavior. As a result, engineers are unable to define these FE model input parameters with certainty, and, inevitably, uncertainties are introduced to the FE model.As the complexity of the building increases, as is the case for historical unreinforced masonry buildings, the errors and uncertainties in the analysis also increase. In the presence of high and numerous uncertainties originating from multiple sources, deterministic approaches in which parameters are defined as constant values assumed to be known with certainty cannot be implemented reliably. Probabilistic methods, however, provide a rigorous and rational means in treating the uncertainty present in the FE analysis of historical unreinforced masonry buildings. The way in which uncertainty in historical unreinforced masonry construction is treated is one of the novel and main contributions...