A semi-analytical discretization method for the near-field analysis of unsymmetrically laminated multimaterial junctions

In the present contribution, the theoretical basics of a novel semi-analytical discretization procedure are described. The method relies on the discretization of the structural situation into an arbitrary number of sectorial elements in which adequate displacement formulations are postulated. Speaking in terms of a cylindrical coordinate system, the sectorial elements are supposed to be of infinite dimensions in the radial direction, hence the actual discretization takes place in the circumferential direction only. While linear shape functions are employed in each of the infinite sectorial elements in the circumferential direction, a set of unknown displacement functions is postulated in each of the resultant interfaces between the individual elements with respect to the radial coordinate. The principle of minimum elastic potential yields the governing Euler–Lagrange equations straightforwardly which allow for closed-form solutions for the unknown interface displacement functions. Since the method yields closed-form solutions for all state variables with respect to the radial coordinate and employs a discretization in the circumferential direction exclusively, we may actually speak of a semi-analytical methodology. Examples are presented for the near-field analysis of unsymmetrically laminated multimaterial notches. The presented semi-analytical method proves to be of high accuracy. Furthermore, while this novel discretization procedure clearly outperforms purely numerical analysis methods like FEM in terms of computational time and effort, it works with comparable accuracy which makes it very attractive for any practical application purpose with involved localization effects where reliable results need to be computed with low computational effort.