A refined quasi-3D higher-order shear deformation theory for static, free vibration, and buckling of laminated composite plates on kerr-type foundation

Composite laminate plates are widely used in different engineering fields, yet existing higher-order shear theories (HSDTs) often fail to capture shear deformation and the coupled effects of elastic supports, leading to design inaccuracies. This study aims to develop and validate a unified 2D/quasi-3D higher-order shear deformation theory (HSDT) that explicitly incorporates Kerr-type shear interactions alongside Winkler-Pasternak foundations and to assess its performance across a spectrum of geometries and orthotropy ratios, and ply orientations. By introducing a seven-unknown displacement field, the model naturally accounts for transverse shear, thickness stretching, and foundation coupling without shear correction factors. Static analyses reveal that Kerr foundations can reduce transverse deflections and stresses by up to 95 %, while 90° outer plies lower in-plane normal stresses by 80 %. In free-vibration and buckling studies, laminates with elastic modulus ratios E 1 /E 2 > 20 enter a fibre-dominated regime, with natural frequencies and critical loads increasing by as much as 68 % and 87 %, respectively, under strong foundation support. Compared with existing HSDTs and full 3D elasticity solutions, the proposed formulation delivers superior accuracy for slender, highly orthotropic laminates. The new Kerr-augmented HSDT offers engineers a robust, efficient framework for optimising composite plate designs on advanced elastic supports. • Refined quasi-3D HSDT enhances the accuracy of static, vibration, and buckling. • Kerr-type foundation enhances stiffness and stability predictions. • Thinner plates show lower stress errors and more uniform deformation. • Higher fibre angles increase deflections and stress variation. • Kerr model performs better than Winkler and Pasternak types for laminated.