Based On The Combined Hybrid Variational Principle Of Axisymmetric Finite Element Method

Combined hybrid functional is a special saddle point variational principle, which is based on a weighed average of two systems of saddle point conditions corresponding to domain-decomposed Hellinger-Reissner variational principle and its dual. In this thesis, the application of combined hybrid method to axisymmetric elasticity problem and the optimization of combined hybrid axisymmetric finite elements are discussed in a manner of combination of mathematical analysis with numerical investigation.A new four-node axisymmetric element ACH8 is derived based on the combinedhybrid variational principle, which uses Wilson's displacements and linear stress suffering from energy compatibility. The resulting element exhibits excellent results in displacements and stresses and is suitable for nearly incompressible materials without any locking phenomena, insensitive to mesh distortion.Zero energy-error is used to optimize combined hybrid axisymmetric finiteelements ACH8 and RACH8 through adjusting the combined factor. Numericalresults all indicate that the two axisymmetric finite elements exhibit better numerical precision, excellent performance at the nearly incompressible limit and distortions of the element geometry, and element performances are improved after optimization.The layout of this thesis is follows. Firstly, some basic concepts and background knowledge are introduced. Three schemes of axisymmetric problems are given. Secondly, axisymmetric element with energy compatibility is constructed in detail.The performance of this axisymmetric element is discussed by numerical examples. Thirdly, Zero energy-error is introduced and used to optimize combined hybrid axisymmetric finite elements through adjusting the combined factor. The influence of combined factor on axisymmetric elements is discussed. Finally, the main points ofthe whole paper are summed up and some further thoughts are put forward.