Stress singularity removal and size effect analysis of symmetrical laminated sandwich plates with gradient elasticity theory

Abstract This study presents a static analysis of symmetrical laminated sandwich plates using gradient elasticity theory, focusing on the removal of stress singularities in both the face sheets and core layers, and on the size-dependent response evaluated in the face sheets. The finite element implementation of the adopted gradient elasticity approach uses linear interpolation functions and a single internal length scale parameter (ILSP). The employed finite element has five degrees of freedom (DOF) per node and its formulation is based on the first-order shear deformation theory (FSDT). The sandwich plate model incorporates layerwise material properties, enabling distinct stress evaluations across different layers. Numerical examples are presented for sharp crack tips and concentrated loads, where the gradient elasticity formulation produces finite stress values and size-dependent responses. The effectiveness of the implementation is further verified through error analyses. Additionally, comparisons of through-thickness stress distributions between classical and gradient elasticity solutions reveal that, even with a single ILSP across all layers, the absolute stress reduction is more pronounced in the stiffer face sheets than in the softer core. The numerical results demonstrate finite crack tip and concentrated load stresses, reduced stress magnitudes with increasing ILSP, and improved convergence of the gradient elasticity solutions compared with classical elasticity. These findings indicate that material stiffness contrast influences the magnitude of the gradient-induced stress reduction, particularly in the stiffer face sheets, and should therefore be considered when assessing localized responses in layered structures.