Boundary element transient analysis of problems with random boundary conditions

Abstract

Fhundary ele~rle~ll forr~~nla t ions for the t,reatrnent of bounditry vitlue problerl~s i t ] 2-D elast,icit,y with random boundary cm~~ditions are presented. It is assumed that ritr~doin boundary conditions may be described as second order rar~dorn fields that possess finite moments up to the second order. Spatially ~orre la t~ed ti111eilldependent and time-dependent houndary condit,ions are c:o~~sidrred. For tinre-independent boundary corltlitions, a stochastic equivalei~t of Somigliana's idew tity is utilized to obtain detern~inistic integral equa~ i o r ~ s for matl~ernatical expectations and covariances of t11e response variables. T l ~ e r a ~ ~ d o r r ~ field used tjo drscrihe the boundary conditions is discretized into a bite set of randoni variables defined a t the element nodes. Quadratic, conforming boundary elements itre used L O arrive at discretized equations for the response statistics of u r ~ k t ~ o w ~ l houndary variables. These values lllay t1le11 he used to calculate the response statistics of internal variables itntf b o u ~ ~ d a r y stresses. The ;tl)ove procedure is next extended for the t,reatrr~e~iL of tin~e-dependent, spatially correlated boundary conditions. A stochast,ic equivalelir of St,okes' time-domitin integral represent at ion is utilized to obtain deterministic i ~ ~ t e g r a l equalioris for the response stmatistics of unktlowrl b o u ~ ~ d x r y vitriahles. Arl approximate procedure for the ca lcu la t io~~ of t,lw covariitl~c:e matrix, tha t reducrs the r~urrlber of matrix operations and comput,er storage reqriiren~ents, is developed. The derivations for the treat melit o f hour~ditry ~ond i t ions tha t are random in tilne and nlay be described as it11 evolutionary wltit,e 'Associate: Professor ' Rrscarch lZssistar~t Copyright @ 1993 American Institute of Aeronautics and Astronautics, Inc. All rights reserved. noise are also presented.