ON NONREFLECTING BOUNDARY-CONDITIONS IN UNBOUNDED ELASTIC SOLIDS

Problems in unbounded domains can be solved using domain-based computa tion by introducing an artificial boundary, and then selecting appropr iate boundary conditions. The DtN method, which specifies such boundar y conditions, is investigated in this work for wave problems in elasti c solids. The DtN method defines an exact relation between the displac ement field and its normal and tangential tractions on an artificial b oundary. This relation is expressed in terms of an infinite series. Th e DtN boundary conditions are shown to be non-reflective, thus uniquen ess of the solution is guaranteed. For practical purposes the full DtN operator is truncated. The truncated DtN operator fails to completely inhibit reflections of higher modes, resulting in loss of uniqueness at characteristic wave numbers of higher harmonics. Guidelines for det ermining a sufficient number of terms in the truncated operator to ret ain uniqueness of the solution at any given wave number are derived. T he validity of these guidelines is examined and verified by numerical examples. Local DtN boundary conditions are also investigated, and it is shown that local boundary conditions guarantee uniqueness of the so lution for all wave numbers, regardless of the number of terms in the operator. This property is used here to modify the truncated DtN opera tor and to enhance its capability to retain uniqueness of solutions. A modified DtN operator, combining the truncated operator with the loca l one, is introduced. The modified DtN operator is shown to retain uni queness of solutions regardless of the number of terms and regardless of the wave number. (C) 1998 Elsevier Science S.A. All rights reserved .