USE OF INCOMPATIBLE DISPLACEMENT MODES IN A FINITE-ELEMENT MODEL TO ANALYZE THE DYNAMIC BEHAVIOR OF UNREINFORCED MASONRY PANELS

A finite element model, where a non-conforming quadrilateral element i s utilized, capable of analyzing the dynamic nonlinear behavior in a b iaxial stress field of unreinforced masonry panels is presented. For t he material, the linear elastic-plastic constitutive law is adopted. T he formulation for the linear element and the extension for the linear elastic-plastic element are proposed. The solution is carried out by a direct step by step integration procedure in time domain, based on t he Newmark method of the equilibrium equations, inclusive of inertial and damping actions, the latter evaluated using the Rayleigh hypothesi s. The procedure was implemented in a computer program and verified by the analysis of an unreinforced masonry shear panel, the dynamic beha vior of which was analyzed experimentally [1, 2]. The comparisons betw een the numeric results and laboratory test measurements show good agr eement, proving the good performance of the non-conforming quadrilater al element also for time-dependent and markedly nonlinear analyses. In addition, the case of Parma Cathedral Bell-Tower subjected to a dynam ic excitation available in literature, was analyzed using the proposed model. The same case was approached by a reliable finite element code [3], using quadratic serendipity elements and a more dense mesh than in the previous analysis. The results, in terms of kinematic parameter s, stress and strain fields, etc. obtained by the two models, agree, p roving that the use of a non-conforming quadrilateral element leads to analyses which are computationally economical and simple to use in in put.