A time domain FEM approach based on implicit Green's functions for non‐linear dynamic analysis

Abstract

SUMMARYThe present paper describes an unconditionally stable algorithm to integrate the equations of motion in time. The standard FEM displacement model is employed to perform space discretization, and the time-marching process is carried out through an algorithm based on the Green's function of the mechanical system in nodal co-ordinates. In the present 'implicit Green's function approach' (ImGA), mechanical system Green's functions are not explicitly computed; rather they are implicitly considered through an iterative pseudo-forces process. Under certain simplifying hypothesis, iterations are not necessary and the ImGA becomes cheaper than standard Newmark/Newton-Raphson algorithm. At the end of the paper numerical examples are presented in order to illustrate the accuracy of the present approach.

Wind-Induced Response Analysis of the Cylindrical Reticulated Mega-Structures

“…The Newmark- step-by-step integration method (Soares and Mansur [16]) is then adopted to solve the dynamic equation in time domain, and the structural geometrical nonlinearity is considered by Newton-Raphson iterative technique (Kim et al [17]) to obtain the structural wind-induced response.…”

High-Speed Train Passage Effects in Buildings: Vibration Assessment and Isolation

“…Computational effort has been reduced with truncation techniques and interpolation procedures. Two different FEM formulations have been used: the nonlinear Newmark GN22 scheme proposed by Chang [18], and the implicit Green's function approach presented by Soares and Mansur [19].…”

Acoustic modelling by BEM–FEM coupling procedures taking into account explicit and implicit multi‐domain decomposition techniques

“…In the present work, an expression for an optimal relaxation parameter is presented, improving the efficiency of the methodology. Direct BEM-FEM coupling procedures are also reported in the literature: Rizos and Wang [12], for instance, developed a direct time-domain coupling algorithm based on the 3D BEM techniques previously presented by Rizos and Rizos and Karabalis [13,14]; Soares et al [15][16][17] proposed coupling procedures based on time-marching algorithms formulated with implicit Green's functions [18], etc. Considering frequency-domain BEM-FEM coupling analyses taking into account domain decomposition methods, the works of Boubendir et al [19,20] and Bielak et al [21] are referred.…”