APPLICATION OF TRIANGULAR SPACE-TIME FINITE-ELEMENTS TO PROBLEMS OF WAVE-PROPAGATION

The displacement hp space-time formulation derived from Hamilton’s weak principle (HWP) is studied for simultaneous space-time solutions. Without conventional “semi-discretizations”, a special type of discretization of space-time is presented in which both space and time dependency are removed. The theoretical basis for a displacement hp-version space-time finite element is developed; and a bilinear formulation of space-time dynamics is presented in which numerical studies can be performed for h- or p -version elements of any shape. The commitment to a weak formulation of force and momentum allows appropriate solution discontinuities to develop naturally at element boundaries. To predict the steep gradients of stress in wave-like motions, triangular elements are used to cut across space and time such that discontinuities in force or momentum can be located at the element boundary. A unified theory of shape functions for space-time finite elements is developed, and the shape functions for triangular and parallelogram elements are derived in terms of a set of orthogonal functions. The assembly procedure for hp-version space-time finite elements is also discussed. To speed the rate of convergence, an extraction technique is developed to obtain forces and momenta from integrals of generalized displacements, not from their derivatives. © 1994 Academic Press Limited.