A NUMERICAL METHOD FOR NON LINEAR ANALYSIS OF MASONRY ARCHES

The paper deals with a numerical procedure available for the analysis of voussoir arches, or any other masonry structure, modelled on a discrete system of rigid blocks connected by unilateral elastic contact constraints. In order to simplify, as much as possible, structural problems involving non-isoresistant materials, the assumption of no tensile strength for the masonry has been adopted. A convenient way to define the contact device which links the blocks, through which a mortar joint could be simulated, is to consider a curtain of elastic bars, orthogonal to the contact surface between two adjacent blocks, and an additional bar tangent to the same contact surface. In accordance with the assumptions of no tensile strength in the mortar joint, only compressive forces can be transmitted from one element to another. Generally the analysis of structural problems involving unilateral constraints, expressed through systems of equations and inequalities, requires the use of Q.P. techniques. The numerical method presented here permits to obtain the solution by using a step by step procedure according to which the solution relative to the standard material ( linear elastic and bilateral) is assumed as a starting point and is subsequently corrected according to the actual material skills. Such a method has already been practised by Castigliano in 1879. The procedure is based on the opportune use of Moore-Penrose generalized inverse.