Structural Analyses With Multiple Cracks Based On The Scaled Boundary Finite Element Method

Safety, economy and applicability of engineering structures are basic requirements, and security is particularly important for some large structures.Structural fatigue crack is an important factor affecting the structural safety. The scaled boundary finite element method possesses a significant advantage on analyzing crack problem, and it is an efficient and accurate numerical method,and especially fits in solving problems with big varying structural characteristic gradients with respect to boundary variables, such as stress concentration problems and crack problems with boundary singularity. It is an effective and accurate numerical method, being integrated with a semi-analyzing solution.In this thesis,the scaled boundary finite element method was improved, being integrated with the Clenshaw-Curtis quadrature rule, the first class Chebyshev polynomial function, which were selected as a mapping function and shape functions.By use of an eigenvalue method with Jordan decomposition or a function matrix technique, the numerical solutions of structural displacements and stresses were derived, being integrated with a transferring method dealing with the complex eigenvalues and eigenvectors with zero eigenvalues. A set of software dealing with the scaled boundary finite element method was programmed, based its method formula and the development platform of ABAQUS. And its method and this software were verified by use of several typical structure examples. Structures with multiple cracks were successfully analyzed by this method and the programmedsoftware. Numerical results show that this method possesses the advantages of good accuracy and high computational efficiency, and its correctness and effectiveness simultaneously were verified.