USE OF SPECTRAL SUPERELEMENTS IN DYNAMIC ANALYSIS OF “SOIL BASE - FOUNDATION - BUILDING” SYSTEMS

Summary. Problem statement . Modern analysis of the dynamic conduct of constructions and structures relies on numerical modeling. The difficulty and complexity of dynamic problem solving encourages model simplification and the use of more advanced numerical modeling algorithms. Many buildings are characterized by the presence of repetitive structural elements (e.g. typical floors). This feature can be used to improve the efficiency of numerical methods by reducing the size of the equation system while meeting the requirements of direct integration methods. Purpose. The paper presents the theory and practical implementation of an improved technique for solving high-order dynamic problems using explicit methods and the help of spectral super-elements for selected substructures. This approach can reduce the order of the algebraic system and conduct dynamic (and thus - seismic) analysis of buildings and structures while taking into account nonlinear deformations of the soil foundation. Analysis of recent research. Modern methods and computer tools allow analysis of dynamic problems while taking into account nonlinear deformations. Such problems have systems of equations with millions of variables and require significant computational resources and time. To reduce the order of the system, commonly used approaches include dynamic reduction methods (e.g. Guyan reduction) or methods relying on reduced-order substructural models. In particular, a paper by Ray W. Clough suggests that the dynamic properties of FE have a higher level of approximation than mechanical properties. For buildings and structures, it is usually most convenient to use substructural models relying on eigenform-based motion representation, as proposed by Craig Jr. R.R., Bampton M. and other authors. However, the proposed options lead to a non-diagonal mass matrix and limit the effective use of explicit integration schemes. Results. The paper describes a method of use of superelement technology of solving tasks of dynamic for investigation of the interaction of buildings with the soil base. On the base Craig-Bempton approach, variant of getting reduction matrix for developed superelement of spectral is offered for taken subconstruction which is providing preservation diagonal mass matrix and allows the use of efficient explicit integration methods. The results of the study of a building interaction with a non-linear soil base under active seismic load are shown. Use an actual construction as an example, it is shown that the use of spectral superelements reduced of the order of the equation system by a factor of more than 2.8 while maintaining the required accuracy of the calculation. Conclusion. The described method of solving dynamic problems, using the proposed spectral superelements, significantly reduces the order of the equation system while still allowing the use of explicit numerical integration schemes. This allows the more efficient dynamic analysis of the behavior of the “soil base - foundation - building” system.