Modal analysis of soil structure interaction

Foundation analysis and coupling of three dimensional solid structures with one dimensional ones require the use of different mechanical models that, generally cannot be solved provided some junction is introduced. This is due mainly to pure mathematical properties of equations solving the mechanical models that become actual difference on the number of degree of freedom at contact points of different dimensional structures. Engineering practice is nowadays asking for the possibility of effective coupling of structures to foundations especially when earthquake response of structures has to be evaluated in order to prevent some local amplification of the seismic effects due to resonance. The use of BEM for three dimensional structure modeling allows to simplify the structure analysis and results in FEM-like stiffness matrix of the structure. The stiffness matrix is able to link displacements at a finite number of points on the body surface to the generalized forces acting on them. Moreover, by means of traction free solution it is possible to consider solely contact points within the formulation. The so obtained stiffness matrix is introduced into FEM model of the one dimensional, say frame, structure provided that ‘non local’ coupling is adopted. Non locality of the joints can be seen as a consequence of the derivation of one dimensional, i.e. beam, model by integration over the cross sectional area. The integration produces that not only displacement but also its derivative play the role of primal displacement unknown. For these reasons the beam body interface has to be considered recalling some characteristic area on which the displacement and the traction of the body have to be integrated in order to get actual frame nodal displacement and forces. In the present work, the application of BEM FEM coupling is proposed in order to perform modal analysis of frame structures on elastic foundation. The influence of the elasticity of the foundation on the modal response of the structure is highlighted and the feasibility of the method, which can be easily introduced into routinely structural codes used in practice, is presented. In the work, the use of the Boussinesque solution for elastic half-space loaded on its limit plane produces that simplified integral equation can be written. Some modal analysis of frame structures on elastic foundation are presented and discussed. References [1] Tullini N, Tralli A, Static analysis of Timoshenko beam resting on elastic half-plane based on the coupling of locking-free finite elements and boundary integral, Computational Mechanics, 45, 2-3, 211-225, 2010. [2] Gonzalez JA, Park KC, Felippa CA, FEM and BEM coupling in elastostatics using localized Lagrange multipliers, International Journal for Numerical Methods in Engineering, 69, 10, 20582074, 2007. [3] Mandolini A, Minutolo V, Ruocco E, Coupling of underground pipelines and slowly moving landslides by BEM analysis, CMES-Computer Modeling in Engineering & Sciences, 2, 1, 39-47,2001. [4] Guarracino F, Minutolo V, Nunziante L, A simple analysis of soil structure inetraction by BEMFEM coupling,Engineering Analysis With Boundary Elements, 10, 283-289, 1992.