Algorithm for Aging Viscoelastic Structures Under Periodic Load

Abstract

A numerical step-by-step algorithm for the analysis of concrete strud';1res exposed to a periodic history of environmental humidity or temperatun; IS p~sented. The ~~ law of concrete is assumed to be linear, and the relationship between hwrudity and shrinkage is also linear. Cracking is assumed to be absent. The effect of concrete age on creep properties is taken into account. Th~ creep law is considered in a rate-type form corresponding to the Maxwell ~ model. The well-known exponential algorithm is genera1ized to complex Variables to describe the periodic part of the response. Since this part cannot ~ separat~d in .advance from the drifting mean response, the standard exponentia! algonthm m !eal va~bles and the new one in complex variables are u.sed slIDultaneously m each time step to provide the total response. The algonthm allo,,:s an arbitrary increase of the time step, and time steps that are ~rders of magrutude larger than the fluctuation period, as well as the relaxation times: are possible without causing inaccuracies and numerical instability. The alg~nthm le~ds to a s~rie~ of increme?tal elastic problems in which the stresses, str~s, elastic moduli, stiffness matrices, etc., are all complex variables. These spatial problems are solved by finite elements. The proposed algorithm is useful for spectral analysis of the response of concrete structures exposed to random en~o~ental humi~ity or temperature, and tremendously reduces the co~putation time when high frequencies are present in the spectral density of enVironment. IProf. o~ Civ. Engrg. and Dir., Center for Concrete and Geomaterials, The Tet~?!ogJcal Inst., Northwestern Univ., Evanston, lli. 60201.. VlSlting Scholar, Northwestern UniV.i on leave from the Huai River CommisSion , Bangbu, Anhui, China. Note.-Discus~ion open until November 1, 1984. To extend the closing date one month,.a wntten ~eq1;1est must be filed with the ASCE Manager of Technical an~

Spectral Finite Element Analysis of Random Shrinkage in Concrete

“…This could be quite demanding for computer time, since in the present approach it is not possible to choose time intervals, At = ts+1 -t s , increasing with time in a geometric progression, as is usual in creep structural analysis for steady loads. However, it is possible to develop a different algorithm which permits the time step to be increased and reach values much larger than the fluctuation period (10).…”

Response of Aging Linear Systems to Ergodic Random Input

“…input to be ergodic. Although certain practical applications of the pres ent new method have already been published (6,7,8,22), a simple illus trative example will be presented. Finally, similarities to and differences from previous studies of nonstationary response (5,(9)(10)(11)15,16,21,23,25) will be pointed out.…”