Spectral Finite Element Analysis of Random Shrinkage in Concrete

Abstract

The spectral method, previously generalized for aging linear systems, is applied in conjunction with the finite element method to an~lyze shrinkage stresses in aging viscoelastic structures exposed to random enVIronmental humidity. The age-dependence of both drying diffusivity and creep properties are taken into account. The solution of pore humidity is obtained from a matrix differential equation in time, with complex-valued matrices. Elastic shrinkage stresses are then obtained from the matrix equations of the finite element method, in which the matrices are also complex-valued. The stresses in presence of aging creep are detennined by a sllperposition integral in time based on the relaxation function. Numerical examples concerning a long cylindrical vessel exposed at the outer surface are given. The standard deviations of pore humidity and of stresses significantly vary with time, and their standard deviation exhibits fluctuations about a drifting mean. The solution is practically meaningful only if concrete does not crack, e.g., when a prestress sufficient to prevent cracking is introduced. For environmental fluctuations of long periods, such as one year, the computation is quite efficient; however, if shorttime fluctuations are considered, the computing time becomes very large.

Concrete creep at variable humidity: constitutive law and mechanism

“…The total strain including the averaged contribution from microcracking is c = e +! ; in which e is the strain used in equation (18), representing the elastic deformation plus shrinkage plus creep (and plus thermal expansion), and ! ; is the additional strain associated with strainsoftening (smeared-out cracking) as expressed in the previous work (equations (1), (7), (12) in reference [10]).…”

“…Due to the relatively large size of the aggregate, it does not make sense to use very small finite elements; typically, only six finite elements along the radius have been used in analyzing the test data. The matrix equations for the axisymmetric analysis in one dimension are listed in references [7] and [18].…”

“…G=LGf" 11 (18) in which x and IX represent the column matrices of the components of the shrinkage coefficient tensor and the thermal expansion coefficient tensor. Given that the dependence on the stress tensor a ij is linear and that the isotropy conditions must be satisfied, the most general form of these tensors is: (20) in which oij=Kronecker delta.…”

Algorithm for Aging Viscoelastic Structures Under Periodic Load

“…For some problems, such as the shrinkage stresses in an aging viscoelastic half-space, the frequency response function can be obtained by numerical evaluation of certain integrals (9). For arbitrary structures, a solution of the frequency response function by the finite element method, in which the stresses, strains, and displacements are treated as complex variables, was recently developed (10). In this formulation, the frequency response function is obtained by step-by-step numerical integration in time.…”

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.…”