G. De Roeck

Application of the substructuring technique to non-linear dynamic structural analysis

Abstract The use of the substructuring technique for the solution of two-dimensional non-linear problems of dynamic response with the direct time integration method is examined. The object is to develop schemes that can considerably reduce the computational expense in analyses of locally and fully non-linear dynamic problems as compared with a traditional analysis. After a review of the principle of the incremental equilibrium equations of motion, some practical illustrations of the technique are dealt with in detail. A specific flow chart is proposed and a number of numerical examples are presented.

Multi-level substructuring in the elasto-plastic domain

Abstract The application of the multi-level substructuring technique to the analysis of elasto-plastic and local nonlinear problems is studied. After a review of principles and formulations a practical implementation and a typical flow chart of the procedure for the technique are presented. Two numerical examples are provided to demonstrate the efficiency that can be reached by using a multi-level substructuring algorithm.

ZONED FINITE STRIP METHOD AND ITS APPLICATIONS IN GEOMECHANICS

Abstract The technique of Finite Strip method has been extended for zoned strips. One strip can have several different materials in horizontal direction including dummy materials. The new developed zoned Finite Strip (Z.F.S.) method has many engineering applications, particularly in geomechanical problems. The formulation is presented and three different geotechnical problems have been solved using the new Z.F.S. method, which could not be solved by the original Finite Strip method. The results are compared with the solution for the same problems obtained by analytical and/or numerical (Finite Element) methods. The reduced input and output for the Z.F.S. method compared to the Finite Element method makes this method attractive particularly for practising engineers. However the results can be as good as the well known Finite Element method.

Multi-level substructuring and an experimental self-adaptive newton-raphson method for two-dimensional nonlinear analysis

Abstract The substructuring technique has been employed in structural analysis for 25 years. Until now, the use of this technique in nonlinear analysis has been limited to localized situations. Moreover, the benefit in calculation time one can obtain is restricted to the amount of 50%. However, as will be described in this paper, a new scheme of multi-level substructuring technique in nonlinear analysis has been developed. With this scheme an efficiency of 75–85% has been reached and a connection level higher than three can easily be expanded. The Newton-Raphson method and its modified version are the most well known algorithms in nonlinear numerical analysis. The former has, nevertheless, the severe disadvantage of reforming the stiffness matrix at every iteration and, in fact, some of the stages are not necessary. The latter has also the disadvantage of a slow convergence, as the recalculation of the stiffness matrix is executed in certain fixed iterations. Thus, to overcome the difficulties mentioned above, an experimental self-adaptive Newton-Raphson algorithm, which offers an automatic decision as to whether the stiffness matrix is reformed or not, is introduced. In applying this algorithm a saving of 30–50% in execution time can be achieved. Combining these two new schemes in 2-D nonlinear analysis, a dramatic effort of 85–90% is yielded. A typical flow chart and two numerical examples are also presented.

The zoned finite strip method in geodynamics

Abstract The Zoned Finite Strip method, where one strip can have several different materials in the horizontal direction, has been extended for dynamic problems. Eigenfrequencies and eigenmodes are calculated e.g. in order to perform a response spectra analysis in the case of an earthquake loading. Besides the new dynamic capabilities, some improvements are proposed for the static case. Also some very efficient solution methods, specially for finite strip problems, are included and commented upon. The extensions have been applied to three different problems and the results are compared with analytical and numerical (finite element) methods. The examples show good agreement between the different methods.