Application of asymptotic expansion homogenization in vibration analysis of masonry structures using finite elements

Abstract

The asymptotic expansion homogenization (AEH) method, which is a rigorous mathematical homogenization theory, is applied here to the modeling of the mechanical behavior of masonry structures for practical dynamic analysis applications. A homogenization process reduces the modeling complexity associated with a detailed component representation of masonry structures and permits the use of a continuous macro-scale model. The method is validated and demonstrated through several applications to masonry structures with the aid of the commercial finite element software ABAQUS in conjunction with a simple self-made program to automate the procedure. The obtained equivalent elastic coefficients for the continuous macro-scale model are used to evaluate the performance of AEH method in determining natural frequencies and modal shapes of various masonry panels and structures. Comparison of results between analyses based on the AEH model and the discrete element model demonstrates the high potential of the AEH model in the seismic analysis of masonry structures.