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SUMMARYThis paper illustrates the use of the theorems of geometric variation for the reanalysis of finite element structures. The formulations presented here form the basis for an efficient computer implementation.

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SUMMARYThis paper describes how the theorems of structural variation mag be used in finitc clement analysis. The efficiency of the theorems is examined and their application to structural and geotechnical problems illustrated. 1NTRODUCTIONEfficient reanalysis tcchniques must be used during a non-linear analysis or optimizition design procedure if numerical methods are to be used effectively. This is particularly true when the structure to be analysed is large and repeated application of the matrix displacement method would require a large number of simultaneous equations to be reformed and solved. In an attempt to avoid repeated analysis a number of reanalysis algorithms4 have been developed 'to find the response of a modified structure using the original analysis of the structure such that the computational effort is less than that required for a fresh analysis'. These reanalysis algorithms are obviously applicable to any numerical procedure in which the stiffness of the structure changes, such as in non-linear analysis and optimization design. One such technique, based on the theorems of structural variation, was presented for trusses by Majid and Elliott *-I0 and dekeloped for frames by Majid, Saka and Celik.'1,'2 The usc of the theorems for finite elemcnt analysis was proposed in References 14 and 15.In this paper a general formulation of the theorems of structural variation for finite element problems is presented. These theorems of structural variation were previously presented for variations in structural properties of one element.'4,15 In this paper they are extended for the simultaneous modification of more than one element. This is important if the theorems are to be used as an efficient rcanalysis technique. The theorems are then presented in matrix form.5 The approach enables an efficient computer implementation of the technique to be identificd.In addition, the efficiency of the theorems of structural variation as a reanalysis technique is investigated. The efficiency tests have been undertaken on some simple finite element structures where the number of modified elements is progressively increased. In each case, the reanalysis time was compared with the time taken for a complete or fresh analysis. The measure of efficiency was