A new scaled boundary finite element formulation for the computation of singularity orders at cracks and notches in arbitrarily laminated composites

A new formulation of the scaled boundary finite element method (SBFEM) is presented for the static analysis of composites in the framework of classical laminated plate theory. In the SBFEM, the domain is described by the mapping of its boundary with respect to a scaling centre. Therefore, only the boundary needs to be discretised. A local coordinate system is introduced, where a scaling coordinate measures the distance from the scaling centre to the boundary and the other coordinate describes the circumferential direction along the boundary. The displacements are approximated as products of displacement shape functions and unknown functions of the scaling coordinate. Via the virtual work principle, a system of ordinary differential equations for the determination of the unknown displacement functions is obtained, which can be solved in a closed-form analytical manner. Element stiffness matrices for bounded and unbounded domains can be computed, using appropriate subsets of the solution. In the case of cracked composites, the SBFEM enables the effective and precise calculation of singularity orders of stresses, if the scaling centre is selected at the crack tip. Numerical examples show the accuracy and efficiency of the scaled boundary finite element method applied to laminated plate bending problems.