More than three decades ago, Przemieniecki [1] introduced a formulation for the free vibration analysis of bar and beam elements based on a power series of frequencies. Recently, this formulation was generalized for the analysis of the dynamic response of elastic systems submitted to arbitrary nodal loads as well as initial displacements [2]. Based on the mode-superposition method, a set of coupled, higher-order differential equations of motion is transformed into a set of uncoupled second order differential equations, which may be integrated by means of standard procedures. Motivation for this theoretical achievement is the hybrid boundary element method [3, 4], as developed in [2] for time-dependent problems on the basis of a frequency-domain formulation, which, as a generalization of Pian's previous achievements for finite elements [5], yields a stiffness matrix that requires only boundary integrals, for arbitrary domain shapes and any number of degrees of freedom. The use of higher-order frequency terms drastically improves numerical accuracy. The introduced modal assessment of the dynamic problem is applicable to any kind of finite element for which a generalized stiffness matrix is available [6, 7]. The present paper is an attempt of consolidating this boundary-only theoretical formulation, in which a series of particular cases are conceptually outlined and numerically assessed: Constrained and unconstrained structures; initial displacements and velocities as nodal values as well as prescribed domain fields (including rigid body movement); forced time-dependent displacements; self-weight and domain forces other than inertial forces; evaluation of results at internal points. Two academic examples for 2D problems of potential illustrate the formulation.
展开▼
