Reduced integration for improved accuracy of finite element approximations

For completeness the finite element bases which are used for approximate solutions of elliptic problems of order 2p by the Ritz method must include the functions corresponding to the constant value of the pth derivative. In actual usage, to ensure a positive definite system of algebraic equations, additional interpolating functions are introduced. This leads to “multiple covering” of some of the system modes and results in overestimation of stiffness. Reduced integration techniques eliminate some of this multiple covering and thereby give improved accuracy. Selective reduced integration has been found useful in the analysis of flexural problems. In this paper we suggest the use of only the minimal covering that is sufficient for convergence. A technique for solution of the discretized system is given. Numerical performance data show remarkable improvement over conventional procedures. The proposed scheme yields good approximation even for very coarse meshes. This indicates the possibility of considerable economy in the cost of obtaining finite element solutions to complex problems, e.g. coupled field problems, three-dimensional problems, stress concentration etc.