EFG-SBM Based Partitioning Algorithms For Cyclically Symmetrical Structures

The Scaled Boundary Method(SBM)is a semi-analytical method developed in the 1990s.It is more efficient than the traditional finite element method for problems involving unbounded domain or stress singularities,and is discretized only at the boundary of a subdomain but need not a fundamental solution as the tradional boundary element method.By now,SBM has been greatly developed and applied in various fields.However there seems no any direct report relevant to its exploration on the viscoelastic problem that relates to many engineering issues.Higher computing expense,mainly caused by an eigenproblem,is one of the barriers for the further application of SBM.Viscoelastic problem or inversion calculation needs solving algebraic equations many times,which also will spend much computing expense.For the two-dimensional elastic/viscoelastic or steady-state heat transfer analysis of cyclically symmetrical structures,with the use of cyclic symmetry,the thesis is to present EFG-SBM based partitioning algorithms which can decouple the original problems,so that the solution scale is reduced and the computational efficiency is improved.The thesis also presents a temporally-piecewise adaptive algorithm based EFG-SBM to solve viscoelastic problems.Main works include:1.In the two-dimensional elastic analysis,it is proved that the coefficient matrices of eigenvalue equation and system equation of EFG-SBM for cyclically symmetrical structure are block-circulant after introducing the coordinate transformation matrix.Furthermore,a corresponding partitioning algorithm is proposed and then both the eigenvalue and system equations can be decoupled into a number of smaller independent problems.The proposed algorithm can improve the computational efficiency.2.For the two-dimensional steady-state heat transfer analysis of cyclically symmetrical structures,the coefficient matrices of eigenvalue equation and system equation of EFG-SBM are proved to be block-circulant.An EFG-SBM based partitioning algorithm is proposed.Therefore both the eigenvalue and system equations can be partitioned into a number of smaller problems which can be solved independently and the computational efficiency can be improved.3.A temporally-piecewise adaptive algorithm based EFG-SBM is proposed to solve viscoelastic problems.A space-time domain coupled problem can be converted into a series of recurrent boundary value problems which are solved by EFG-SBM.The proposed algorithm can make the most of advantages of SBM that is semi-analytical and can also ensure computational accuracy via an adaptive computing process in time domain.Both creep and relaxation analyses can easily be carried out using the proposed algorithm.4.Based on the proposed algorithm in sections 3,a recursive partitioning algorithm is developed for the two-dimensional viscoelastic analysis of cyclically symmetrical structures.The eigenvalue equation,system equation and a series of equations of expanding coefficients can be partitioned into a number of smaller problems which can be solved independently.Therefore the computational efficiency can be improved.Numerical examples are given to illustrate the advantages of the proposed algorithms.Solutions by the proposed algorithms are compared with the analytical solutions or other reference solutions and discussions are given in detail.