ADAPTIVE APPROXIMATIONS IN FINITE-ELEMENT STRUCTURAL-ANALYSIS

Adaptive computer programs are expected to gain control of the discretization error by increasing the number of degrees of freedom in regions where the initial finite element model is not adequate. This automated convergence process is monitored by convenient local error criteria. There are three advantages. First the number of finite elements is determined by the geometry rather than requirements of precision. In many cases a dramatic reduction of the data preparation effort is possible. Secondly the procedure itself validates the finite element model. The analyst's task is considerably simplified. Thirdly the minimum number of degrees of freedom may be used to get the desired level of precision. A computational scheme which allows for efficient reanalysis has been recently implemented. New degrees of freedom are defined by introducing higher order displacement modes on the same grid. The improved stiffness matrix contains the previous stiffness matrix as a submatrix and the numerical effort expended in triangularizing the previous stiffness matrix can be saved. The new approach is demonstrated by applications to two- and three-dimensional elasticity, including singularity problems. © 1979.