AUTOMATIC ADAPTIVE 3-D FINITE-ELEMENT REFINEMENT USING DIFFERENT-ORDER TETRAHEDRAL ELEMENTS

Automatic refinement finite element analyses were carried out employin g three different-order tetrahedral solid elements for the solution of 3-D stress analysis problems. Numerical results indicated that the ad aptive refinement procedure could eliminate effectively the effect of singularities and the optimal convergence rate was achieved in all the examples tested. The preconditioned conjugate gradient technique was used for the solution of the large system of simultaneous equations. B y interpolating the initial guess of the iteration solver from the pre vious converged solution, the number of iterations needed for the solu tion is lower than expected. Furthermore, when the mesh density distri bution pattern has converged, it became even more efficient and indepe ndent of the number of degrees of freedom in the finite element mesh. The: relative efficiency of the three different-order tetrahedral elem ents has also been compared-in terms of storage and computational cost needed for achieving a certain accuracy. It is found that although th e cubic T20 element can achieve the highest convergence rate, the T10 element is the most competitive and effective element in terms of stor age and computational cost needed. (C) 1997 by John Wiley & Sons, Ltd.