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This paper aims to present the integrated teaching activity carried out in the Studios of the Master of Science “Architecture-Building Architecture” held at the School of Architecture Urban Planning Construction Engineering of the “Politecnico di Milano,” Milan, Italy. The integrated teaching activity related to the structural disciplines was in Sgambi et al., 2019; here the structure of the MSc training and its disciplinary synergies will be presented. Indeed, this type of activity characterizes all the Studios of this Master of Science and involves all the disciplines that contribute to the development of an architectural and cultural heritage preservation project.

In the Studios of the aforementioned Master of Science, teachers of different subjects are involved, working together to guide the student in the development of an architectural project sustainable in all aspects. The fundamentals of each discipline are taught using the best suited teaching methodology and the application phase of each discipline is carried out directly on the students' projects in the form of “learning by making.” The students are thus stimulated to deepen their basic knowledge of each single discipline, making their design choices sustainable.

This experience, born in 2003 and still active, has also achieved good results in employment. Students train using the “learning by making” method to acquire proficiencies in various disciplines of design, giving them the ability to communicate competently with experts belonging to different construction sectors.

The approach illustrated in this paper does not represent the didactic experimentation of a single discipline, but it is typical of the study program of an entire Master of Science. Although this approach is entirely built on a “learning by making” and “active learning” philosophy, it maintains the teaching of the theoretical contents of disciplines at a significantly high level when compared with the contents of a frontal-taught theoretical course. The development of this structure required a strong commitment on the part of the teaching staff in their search for effective teaching methods in each individual discipline and aimed at the architectural project. The results obtained give an added value to the training of future architects.

The purpose of this paper is to establish and implement a direct topological reanalysis algorithm for general successive structural modifications, based on the updating matrix triangular factorization (UMTF) method for non-topological modification proposed by Song et al. [Computers and Structures, 143(2014):60-72].

In this method, topological modifications are viewed as a union of symbolic and numerical change of structural matrices. The numerical part is dealt with UMTF by directly updating the matrix triangular factors. For symbolic change, an integral structure which consists of all potential nodes/elements is introduced to avoid side effects on the efficiency during successive modifications. Necessary pre- and post processing are also developed for memory-economic matrix manipulation.

The new reanalysis algorithm is applicable to successive general structural modifications for arbitrary modification amplitudes and locations. It explicitly updates the factor matrices of the modified structure and thus guarantees the accuracy as full direct analysis while greatly enhancing the efficiency.

Examples including evolutionary structural optimization and sequential construction analysis show the capability and efficiency of the algorithm.

This innovative paper makes direct topological reanalysis be applicable for successive structural modifications in many different areas.