Fractional-Order models for the static and dynamic analysis of nonlocal plates

This study presents the analytical formulation and finite element solution of a fractional-order nonlocal plate under both Mindlin Kirchhoff formulations. By employing consistent definitions for kinematic relations, governing equations associated boundary conditions are derived based on variational principles. Remarkably, model gives rise to self-adjoint positive-definite system that accepts unique solution. Further, owing difficulty in obtaining solutions this differ-integral problem, 2D is presented. Following thorough validation against benchmark problems, fractional used static as well free dynamic response plates subject various loading conditions. It established nonlocality leads reduction stiffness structure thereby increasing displacements reducing natural frequency vibration plates. it seen effect stronger higher modes when compared fundamental mode. These effects observed irrespective nature More specifically, from lead mathematical ill-posedness inaccurate (paradoxical) predictions such hardening absence effects, typical classical strain-driven integral approaches elasticity. consistency result well-posed accept