Pergamon PII: s0045-7!449(%)00286-6 Compurers & Srrucrurc~ Vol. 62. No. I, pp. 81-92, 1997 Copyright 0 1996 Ekvier Science Ltd Fkntcd in Great Britain. All rights reserved 004s7949/97 $17.00 + 0.00 MODELLING PRESTRESS RESTORATION OF BUILDINGS BY GENERAL PURPOSE STRUCTURAL ANALYSIS AND OPTIMIZATION SOFTWARE, THE OPTIMIZATION MODULE OF MSC/NASTRAN M. E. Stavroulaki, G. E. Stavroulakis and B. Leftheris Institute of Applied Mechanics, Department of Engineering Sciences, Technical University of Crete, GR-73 100 Chania, Greece (Received 31 August 1995) Abstract-General purpose structural analysis and optimization techniques within the MSC/NASTRAN software are used in this paper for the analysis of optimal prestress restoration of buildings. To alleviate admissible stress violations a minimum prestress reinforcement is sought along with the position of the prestressed elements. Prestressing is modelled by fictitious thermal loading on the linear (rod) elements which model the prestressing cables (tendons). A quadratic cost function for the prestressing cost with a penalty term that counts for stress violations is assumed for the optimal prestressing problem. Certain aspects of the computer implementation, including the use of mathematical programming and structural optimization tools for large-scale structures, are included. The theory is illustrated by numerical examples concerning the prestress restoration of a masonry wall subjected to static loading. Copyright $2 1996 Elsevier Science Ltd. 1. INTRODtJfflON Practical computational aspects concerning the use of prestressed cables to reinforce an existing structure and to produce a beneficial stress distribution within it, are discussed in this paper. It is based on structural analysis techniques, the finite element method and general purpose structural optimization software. The aim is to find the optimum application of the prestressed cables, including the forces of prestressing and location of the cables. The optimization module of MSC/NASTRAN is used throughout this paper. The initial stress and strain induced by prestressing is modelled by equivalent “thermal” strain on the prestressed elements [l]. The cross-sectional areas of these rod elements are the design variables which are linked to the prestress quantities by simple relations. The optimization prestress problem for static loads consists of selecting optimal values for the design variables, related to the prestressing, such that the specified objective function, which in turn is related to the cost of prestressing, is minimized and a set of specified constraints that define the limits for the developed stresses are satisfied. The technological feasibility of using prestressed cables of both traditional (steel) and advanced (carbon fibre) materials has been investigated in recent publications and has been proposed for the strengthening of historical buildings [2, 31. Numerical methods based on mathematical programming are used for the solution of the optimization problem. In the numerical implementation, a near optimum design is automatically generated in an iterative manner. For the solution of general optimization problems several algorithms have been developed within the theory of nonlinear programming. There are some peculiarities of civil engineering applications. These relate to the large number of unknowns arising in the modelling of real world structures. For this reason there is need to reduce the design variables with appropriate linking techniques and to reduce the check-points which may increase the dimension of the problem unreasonably. In addition there is a need to use appropriate structural analysis models. Moreover stress inequality constraints must be taken into account by a penalty function technique since, otherwise, local stress violations lead to nonfeasible optimization problems which cannot be solved by standard mathematical programming methods. All these aspects require an engineering feeling and a good command of available computational mech- anics techniques. The latter techniques are discussed in this paper by using a model problem and a well-known software system. Linear elastic mechanical behaviour of both the structure and the reinforcing elements is considered throughout in this paper. This choice is justified from the simplicity in the collection of the material data and is adopted in most structural analysis appli- cations. Nevertheless some results are of general validity and can be used in connection with nonlinear structural analysis applications as well. Optimal prestress problems with nonlinear structural response 81