IMPROVED NUMERICAL SIMULATION OF 2D FRAME STRUCTURES USING A GENERALIZED MODAL ANALYSIS

Resumo

The hybrid finite element method, proposed by Pian on the basis of the Hellinger-Reissner
potential, has proved itself a conceptual breakthrough among the discretization formulations. A
proposition made by Przemieniecki – for the generalized free vibration analysis of truss and beam
elements – was incorporated into the hybrid finite/boundary element method developed by the third
author and extended to the analysis of time-dependent problems by making use of an advanced mode
superposition procedure that adequately takes into account general initial conditions as well as general
body actions. It is shown that such a consistent approach leads to frequency-dependent stiffness and
mass matrices that enter a generalized modal analysis based on a nonlinear eigenvalue problem for
complex-symmetric systems. This paper presents the basic features of the formulation as applied to
plane frame structures and assesses some examples available in the technical literature to show that
remarkable improvements may be achieved with the proposed formulation when compared to the
classical structural dynamics. Although the formulation is generally valid for three-dimensional
analysis, owing to space restrictions only two-dimensional plane frames and trusses are dealt with. The
analytical frequency-domain expressions of beams with and without hinges on the extremities is
displayed to make evident how axial and transversal modes interact and should be properly taken into
account.