Researches Of Singular Fields In Anisotropic Materials And Piezoelectric Materials

Anisotropic materials and piezoelectric materials are often used by oneself or bonded with other materials. Unfortunately, strong singularities in the tips of the cracks, interface edges and inclusions may lead to function invalidation or even earlier destroy of components. To ensure the safety and reliability of the devices and structures, it is meaningful to understand completely and exactly the local singular fields. Commonly, the singular fields surrounding the singular points can be expressed as ∑ = k r~λ F(θ), in which (r,θ) is the polar coordinate system whose origin is set at the singular point, eigenvalue X and angular variation function F(θ) are eigensolutions, k is the magnified coefficient depending on the given loading, the geometry of the structure and material constants. To determine the singular fields and the fracture parameters, both the eigensolutions and the magnified coefficients should be solved. The main objective of this dissertation is to establish several kinds of super singular elements, and combine them with the standard hybrid element to solve the singular fields of anisotropic and piezoelectric materials. To establish the super singular elements, two steps are needed: Firstly, the eigensolutions of singular fields in the crack-tips of anisotropic materials are solved by a kind of ad hoc finite element eigenanalysis method; Secondly, based on generalized Hellinger-Reissner variational functional, a kind of super crack-tip singular element is established. In terms of materials and geometries in the researches, the main contents are described as following:1) A kind of super crack-tip singular element is developed to investigate the singular fields around the crack-tips of bonded anisotropic materials, and the numerical solutions of stress intensity factors (SIFs) are obtained by the solved singular stresses. The new model is verified with avaible solutions. Other new numerical results are also given to investigate the influences of fibre orientation, cracks length, crack distances, material mismatches and material geometry.2) A kind of super crack-tip element model is developed to investigate the singular electro-elastic fields around the crack-tips of inplane polarized piezoelectric materials, in which three kind of boundary conditions, i.e., impermeable condition, limited permeable and...