Dynamic Interactions of Inelastic Structures and Fluids
A semi-analytic algorithm for the analysis of dynamie intera.ction between an elastoviscoplastic beam and the linear compressible fluid in a rectangular containment is presented. The inelastic parts of the strain in the beam are treated as unknown eigenstrains acting upon the linear elastic background structure. By means of this consistent eigenstrain analogy, the dynamic interaction problem is represented in a linear form. Using a substructure technique, dynamic influence functions for the eigenstrains are developed in the frequency domain and transformed back to the time domain, partly by analytic transformation, and partly by FFT. The eigenstrains are subsequently evaluated from the inelastic constitutive equations in a time stepping procedure, the influence functions being used, in connection with appropriate non-linear algorithms.
H.M. WESTERGAARD, Water pressure on dams during earthquakes, Proc. ASCE, 57, 1303-1318 and Trans. ASCE, 98, 418-433, 1933.
A.K. CHOPRA, Earthquake behaviour of reservoir – dam systems, J. Eng. Mech. Div. ASCE, 94, Nr EM6,1475-1500, 1968.
P. CHAKRABARTI AND A.K. CHOPRA, Earthquake analysis of gravity dams including hydrodynamic interaction, Earthquake Engng. and Struc. Dynamics, 2, 143-160, 1973.
B. NATH, Hydrodynamic pressure on arch dams – by mapping finite element method, Engng. and Struc. Dynamics, 9, 17-1231, 1981.
C.S. PORTER and A.K. CHOPRA, Dynamic analysis of simple arch dams including hydrodynamic interaction, Earthquake, Engng. and Struc. Dynamics, 9, 573-597, 1981.
CH.Y. YANG and V. CHIARITO, Random hydrodynamic force in dams from earthquake motion, Engng. Mech. Division, ASCE, EMI, 117-129, 1981.
F. HOLLINGER, Zur Interaktion einer schwingenden elastischen Platte mit der Flüssigkeit in einem Rechteckbecken, ZAMM, 61, T43-T45, 1981.
F. HÖLLINGER, Ein Randintegralverfahren für Flüssigkeitsschwingungen in beliebig geformten Staubecken mit elastischen Sperrenkonstruktionen, ZAMM, 62, T46-T48, 1982.
F. HÖLLINGER, Time-harmonic and nonstationary stochastic vibrations of arch dam-reservoir systems, Acta Mech., 49, 1153-1167, 1983.
F. HÖLLINGER and F. ZIEGLER, lnstationäre Zufallsschwigungen einer elastischen Gewichtsmauer bei beliebig geformten Becken, ZAMM, 63, T49-T54, 1983.
F. ZIEGLER, F. HÖLLINGR and B. ZHANG, Random vibrations of dams and offshore structures: A nonstationary spectral approach, Stochastic Structural Mech., 31, 487-507, 1987.
F.D. FISCHER, F.G. RAMMERSTORFER and K. SCHARF, Earthquake resistent design of anchored and unanchored liquid storage tanks under three-dimensional earthquake excitation, Structural Dynamics-Recent Advances, 317-371, 1991.
H. REISSNER, Eigenspannungen und Eigenspannungsquellen, ZAMM, 11, 1-31, 1931.
H. IRSCHIK and F. ZIEGLER, Dynamics of linear structures with selfstress: A unified treatment for linear and nonlinear problems, ZAMM, 68, 199-205, 1988.
P. FOTIU, H. lRSCHIK and F. ZIEGLER, Dynamic plasticity: Structural drift and modal projections, Proc. IUTAM-Symp. on Nonlinear Dynamics in Engineering Systems, 75-82, 1990.
P. FOTIU, H. IRSCHIK and F. ZIEGLER, Material science and numerical aspects in dynamics of damaging structures, Structural Dynamics-Recent Advances, 235-255, 1991.
P. FOTIU, H. IRSCHIK and F. ZIEGLER, Forced vibrations of an elastoplastic and deteriorating beam, AM, 69, 193-203, 1987.
W. BRUNNER and H. IRSCHIK, An efficient algorithm for elaasto-viscoplastic vibrations of multi-layered composites using second-order theory, Nonlinear Dynamics, 1, 1-12, 1994.
P. PERZYNA, The constitutive equations for rate-sensitive plastic materials, Quarterly Applied Mech., 20, 321-332, 1963.
W. BRUNNER and H. IRSCHIK, Inelastic beams excited by earthquakes: Dynamic fluid-solid interaction, Structural Dynamics-Eurodyn’93, 33-39, 1993.
F. ZIEGLER, Mechanics of solids and fluids, Springer-Verlag, New York 1991.
R. HEUER, H. IRSCHIK, P. FOTIU and F. ZIEGLER, Nonlinear flexural vibrations of layered plates, Intern. J. Solids Structures, 20, 1813-1818, 1992.
N.M. NEWMARK and E. ROSENBLUETH, Fundamentals of earthquake engineering, Prentice Hall, Englewood Cliffgs, N.Y., 177-214, 1971.
M.A. CHRISFIELD, A faster modidfied Newton-Rhapson iteration, Computational Methods for Applied Engineering, 20, 267-278, 1979.
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