On the computation of seismic energy in inelastic structures

Abstract The explicit computation of energy balance for structures subjected to seismic excitation is useful to assess the accuracy with which dynamic equilibrium is achieved in each time-step. Examples on the use of the energy balance concept are presented in the first part of this paper for simple inelastic structures excited by various ground motions. It is shown how the energy approach can guide the designer in appreciating the nonlinear behaviour of the structure, the hierarchy of mechanisms that occur in time, and the ductility requirements of the various components. This was achieved using an unconditionally stable time marching algorithm with no algorithmic damping. A parametric study is then presented on the influence of algorithmic damping on seismic energy response of multi-degree-of-freedom structures. Finally, the Newmark-Beta method, with and without algorithmic damping, and the Alpha method are used in comparative analyses to evaluate the response of bilinear hysteresis models of multi-degree-of-freedom structures.

[1]  前田 潤滋.  Low Speed Aerodynamics Laboratory National Research Council of Canada Ottawa, Ontario, Canda K1A 0R6 , 1990 .

[2]  I. C. Medland,et al.  ESTIMATION OF BASE ISOLATED STRUCTURE RESPONSES , 1978 .

[3]  C. Uang,et al.  Evaluation of seismic energy in structures , 1990 .

[4]  Douglas A. Foutch,et al.  Seismic Performance of Low-Rise Steel Perimeter Frames , 1991 .

[5]  William Robinson,et al.  Lead‐rubber hysteretic bearings suitable for protecting structures during earthquakes , 1982 .

[6]  Ted Belytschko,et al.  On the Unconditional Stability of an Implicit Algorithm for Nonlinear Structural Dynamics , 1975 .

[7]  Andre Filiatrault,et al.  Comparative performance of friction damped systems and base isolation systems for earthquake retrofit and aseismic design , 1988 .

[8]  Andre Filiatrault,et al.  Seismic Design Spectra for Friction‐Damped Structures , 1990 .

[9]  Thomas J. R. Hughes,et al.  Stability, convergence and growth and decay of energy of the average acceleration method in nonlinear structural dynamics , 1976 .

[10]  Pierre Léger,et al.  Seismic cracking and energy dissipation in concrete gravity dams , 1993 .

[11]  T. Belytschko,et al.  Efficient large scale non‐linear transient analysis by finite elements , 1976 .

[12]  W. K. Tso,et al.  Seismic energy demands on reinforced concrete moment‐resisting frames , 1993 .

[13]  W. J. Hall,et al.  Assessment of Seismic Structural Damage , 1989 .

[14]  Pierre Léger,et al.  Seismic-Energy Dissipation in MDOF Structures , 1992 .

[15]  Jörg-Martin Hohberg,et al.  A joint element for the nonlinear dynamic analysis of arch dams , 1992 .

[16]  James M. Nau,et al.  Inelastic Modeling and Seismic Energy Dissipation , 1987 .

[17]  Pierre Léger,et al.  Non‐linear seismic response analysis using vector superposition methods , 1992 .

[18]  R. Clough,et al.  Dynamics Of Structures , 1975 .

[19]  Theodore V. Galambos,et al.  Earthquake Load for Structural Reliability , 1989 .

[20]  Thomas J. R. Hughes,et al.  Improved numerical dissipation for time integration algorithms in structural dynamics , 1977 .

[21]  W. J. Hall,et al.  Earthquake Energy Absorption in SDOF Structures , 1984 .

[22]  David P. Billington,et al.  Analysis of Seismic Failure in Skew RC Bridge , 1991 .

[23]  Kuldeep Virdi,et al.  Non-linear finite element dynamic analysis of two-dimensional concrete structures , 1991 .

[24]  Thomas J. R. Hughes,et al.  A note on the stability of Newmark's algorithm in nonlinear structural dynamics , 1977 .

[25]  Avigdor Rutenberg,et al.  Seismic base isolation of asymmetric shear buildings , 1986 .

[26]  Peter Fajfar,et al.  A measure of earthquake motion capacity to damage medium-period structures , 1990 .

[27]  L. Vu-Quoc,et al.  NEW PREDICTOR/CORRECTOR ALGORITHMS WITH IMPROVED ENERGY BALANCE FOR A RECENT FORMULATION OF DYNAMIC VEHICLE/STRUCTURE INTERACTION , 1991 .