UNCOUPLED DUAL FORMULATIONS OF THE VARIATIONAL BOUNDARY-ELEMENT METHOD IN PROBLEMS OF THE THEORY OF ELASTICITY

Uncoupled dual formulations (UDFs), different from those considered pr eviously [1-3], are proposed for the boundary functionals of the linea r theory of elasticity, in the sense that the displacements and stress es are varied independently, and the equations of state on the boundar y are treated as constraints involving Lagrange multipliers. The idea of this device-using Lagrange multipliers to get rid of restrictions i n the variational problem, represented by the equations of state-was u sed previously [4] to formulate dual variational problems of the linea r theory of elasticity based on the Lagrange-Castigliano principle. A finite element approximation of the solutions of these problems yields mixed formulations of the finite element method [5]. Thus, the bounda ry element approximations (BEAs) proposed below for the UDF may be reg arded as a special mixed finite element method. Simultaneous BEA of th e displacements and stresses extends the applicability of UDFs to case s in which allowance must be made for singularities of the solution, e .g. in contact problems of the theory of elasticity and in fracture me chanics (crack problems).