A boundary element strategy for elastostatic inverse problems involving uncertain boundary conditions

In this paper, a convenient strategy is developed to "nd solutions for a class of uncertain-boundary-value problems by the Boundary Element Method (BEM). Such problems are ill-posed, but ill-conditioning of the associated algebraic systems of equations can be controlled to a large extent, and useful boundary data can be obtained despite ill-conditioning. Interior data of not only su$cient quantity, but also of good quality at good locations contribute to good solutions. Our strategy permits the condition number of the algebraic systems, as a function of interior-data locations, to be monitored, such that measured data from displacement sensors and/or strain sensors, at locations found to be good ones for the problem at hand, can be used. The present strategy is based upon the concept of a Greenʹs-function library through partitioning of the BEM algebraic system. Algebraic systems are solved using least squares via Singular Value Decomposition (SVD). The library idea takes advantage of modern data storage and retrieval technology and permits the process of repeated trials, in order to determine good data sensor locations, to be done quickly and e$ciently. Several numerical examples are given to demonstrate the strategy. Some examples examine the consequences of errors in measured data.