Asymptotic near-field analysis of wedges in anisotropic composite plates using first-order shear deformation theory

摘要

In the present work, a complex potential approach is proposed in order to study the singular solution behaviour at wedges or sharp notches in fibre-reinforced composite plates using first-order shear deformation plate theory. The singularity exponent λ as a measure of the strength of the singularity is calculated for different notch opening angles and boundary conditions along the notch faces. Furthermore, the influence of the fibre orientation on the singularity exponent is discussed in detail. Asymptotic solutions of the governing system of partial differential equations are derived employing a Lekhnitskii-like formalism using three holomorphic potentials. Choosing the complex potentials according to prescribed boundary conditions finally leads to an eigenvalue problem where the singularity exponents appear as roots of the corresponding characteristic equation. In contrast to the classical Kirchhoff-Love plate theory, it is shown that the present approach allows for a distinction between singularities associated to transverse shear forces and to bending moments and that the fibre orientation significantly affects the singularity exponent. The obtained asymptotic near fields are compared to finite element data. The findings are in very good agreement with numerical results and results from literature available for the limit case of isotropic material behaviour.