Finite Element Analysis of Axisymmetric Elastic Body Problems

Linear form functions are commonly used in a long time for a toroidal volume element swept bya triangle revolved about the symmetrical axis for general axisymmetrical stress problems.It is diffi-cult to obtain the rigidity matrix by exact integration,and instead,the method of approximate in-tegration is used.As the locations of element close to the symmetrical axis,the accuracy of this ap-proximation deteriorates very rapidly.The exact integration have been suggested by various authorsfor the calculation of rigidity matrix.However,it is shown in this paper that these exact integrationscan only be used for those axisymmetric bodies With central hole.For solid axisymmetric body,itcan be proved that the calculation fails due to the divergent property of rigidity matrix integration.In this paper a new form function is suggested.In this new form function,the radial displacementu vanishes as radial coordinates r approach to zero.The calculated rigidity matrix is convergenteverywhere,including these triangular