Mixed fem for functionally graded and laminated HSDT composites resting on elastic foundation

Laminated composites are widely used in lightweight structural systems, and in many practical applications they operate while being supported by compliant media such as soil layers, polymeric cores, or elastic subgrades. In such cases, the plate response is strongly governed by the structure-foundation interaction; moreover, a one-parameter Winkler representation may be insufficient because it neglects shear coupling within the supporting medium, which can be captured by the two-parameter Winkler-Pasternak model. Motivated by this need, the present study develops a mixed finite element formulation for the flexural analysis of laminated composites resting on elastic foundations within the framework of Higher-Order Shear Deformation Theory (HSDT). The formulation is established using the Hellinger-Reissner variational principle, where displacement and stress components are treated as independent variables to improve accuracy and numerical robustness. Both Winkler and Pasternak foundation parameters are consistently incorporated to account for normal and shear interactions with the substrate. The model is validated through benchmark comparisons from the literature using different shear deformation functions, and a parametric study is then performed to quantify the effects of geometric ratios, foundation stiffness parameters, and laminate stacking sequence on displacement and stress responses. The numerical results demonstrate that the proposed mixed HSDT framework provides reliable predictions for laminated composites interacting with elastic foundations.