Alberto Franchi

A modified gradient method for finite element elastoplastic analysis by quadratic programming

Abstract The finite analysis problem with piecewise linear constitutive laws is formulated as a linear complementarity and a quadratic programming problem. The solution techniques using the well-known optimization methods of mathematical programming are discussed and a procedure, belonging to the class of gradient methods, is proposed which overcomes the computational difficulties that arise when there is a large number of variables. Through a physical interpretation of the gradient of the objective function, each mathematical step of the proposed optimization technique is translated into a corresponding physical operation on the structure and a mechanical solution procedure with a finite number of steps is derived. Finally, for the incremental analysis problem under non-holonomic constitutive laws the same procedure is adopted combined with the multistage loading technique. Illustrative examples for each of the preceding problems are given.

Mathematical programming and nonlinear finite element analysis

Abstract The paper is concerned with the application of mathematical programming techniques to a variety of structural plasticity problems. The incremental and finite elastoplastic analysis problems, as well as the plastic limit analysis problem, are formulated as a variety of linear complementarity, quadratic, linear and nonlinear programming problems. A unified computational scheme is presented, and comparisons are made between the mathematical programming techniques and the so-called “direct” methods for nonlinear finite element analysis.

From BIM to FEM: the analysis of an historical masonry building

The construction design process is starting to change with the advent of Building Information Modelling technology. Thanks to the high level of BIM interoperability, it has been possible to transform a BIM model of an historical building, obtained from a laser scanner survey, into an accurate 3D Finite Element Model. The model is able to exploit all the geometrical information collected and organized during the survey phase. The object of the analysis is Castel Masegra, a XI century masonry historical building on the alpine mountains overlooking to Sondrio (Italy). The implementation of the BIM model has been carried out by keeping in mind that the final goal was the construction of a reliable finite element model with a compatible and regular mesh, reproducing the irregularities and complexities that could influence the mechanical behaviour of the structure. Once it has been obtained the 3D finite element model, the historical and diagnostic information have been integrated into the BIM model and a construction stage analysis has been studied and then carried out. The huge amount of information and the large number of finite elements employed introduced some difficulties in data management and results interpretation. However, thanks to the always increasing computational capacity of personal computers, it has been possible to deal with a model composed by more than 700,000 elements, obtaining the results in terms of stresses and displacements of the whole building.

Multimodal Pushover Analysis for R.C. Bridges

In recent years, Italian technical-scientific community has increased its interest on the evaluation of the seismic response of existing structures. Among this wide range of structures, reinforced concrete bridges stand out for their strategic relevance and technical complexity. Most of these structures were built between 60ies and 70ies, according to design procedures which ignored nowadays knowledge in seismic engineering. Thus, the necessity to evaluate the real strength capacity of these structures with modern analysis techniques has become essential, leading to the determination of their safety level in case of an earthquake. In particular, for the assessment of several bridges of a motorway network, a multi-modal pushover analysis approach has been considered. This analysis technique allows considering the nonlinear behaviour and the complex dynamic response of such structures without exceeding in high computational costs. Some basic rules were defined (constitutive laws of materials, finite element type, plastic hinge models, etc.) for the modelling of bridges, in order to guarantee homogeneous comparable results among different structures of a network. At the end, some of the results are compared to see the variation of the verification level with respect to both the number of modes considered and the analysis’s accuracy in terms of number of loading steps.

Stainless Steel Rebar for Seismic Applications

This paper is meant to present themechanical characteristics of austenitic stainless steel rebars under monotonic and cyclic loadings. Furthermore, some results concerning the experimental tests on column prototypes subjected to cyclic loadings are presented, with the intent of comparing with results obtained on analogous columns reinforced with standard high ductile carbon steel rebars.