The Singular Finite Elements And Elements With Generalized Coefficients For Fracture Analysis Of Structures

This dissertation presents the systematic research work on finite element analysis of fracture problem. The stress intensity factors(SIF) are calculated by means of three methods: singular element,singular element plus inter- element and the finite elements with generalized coefficients, which are programmed computed via Fortran90 code. Examples are presented to illustrate the accuracy and efficiency of methods proposed.The main contributions of the thesis are as follows:1.Based on isoparametric element and the linear elastic fracture mechanics theory, the finite elements program for plane problem was composed as the foundation of subsequent studies.2.In order to reflect the singular property of stress field around the tip of crack, singular isoparametric finite element was introduced. SIF was calculated and compared with theoretic result.3. In order to improve the accuracy of SIF's computation, inter-element was considered between singular element and regular isoparametric element along the interface of singular and regular domain, which would be well intergradated from the singular filed to regular fields. The shape functions of inter-element can be obtained by modifying those of singular elements. Thus the computing program was easily composed, and the results agree well with those by singular elements.4.The finite element with generalized coefficients for fracture problems was established. The global displacement field can be constructed using Williams series. The singular sectorial subdomain can be approximately regarded as the assemblage of finite numbers of similar trapezoidal element. The local displacement field of every trapezoidal element can be constructed via traditional FEM procedures. Based on the principle that the local field must be compatible with the global field, the finite element with generalized coefficients can be constructed. The conclusion could be achieved: the finite elements with generalized coefficients for fracture problem yield results of more accuracy and efficiency than singular elements, and can be used easily and abroadly.