Dynamic stiffness formulation for isotropic and orthotropic plates with point nodes. (1st October 2022) - Papkov, S.O.
Highlights: The dynamic stiffness theory for point noded plates is developed for the first time. Discrete Fourier transform is applied in a unique way to develop the theory. Usefulness and accuracy of the theory in free vibration of plates are demonstrated. The new theory permitted the application of non-classical boundary conditions. Computational method for free vibration analysis of plate is significantly advanced. Abstract: In this paper, the dynamic stiffness method for isotropic and orthotropic rectangular plates with point nodes is developed, making it possible to integrate the dynamic stiffness properties for plates with the dynamic stiffness properties of other elements such as bars and beams, but importantly, the advanced theory allows amalgamation of the dynamic stiffness method with the conventional finite element method for the first time. The derivation of the dynamic stiffness matrices for isotropic and orthotropic plates with point nodes has been accomplished by implementing the Fourier coefficients of the boundary values of the amplitudes of forces and displacements of the plate to form the force–displacement relationship at nodal points, including the corners. This innovative objective has been achieved by developing a new form of discrete Fourier transform technique for modified trigonometric functions. Using some carefully chosen illustrative examples, the convergence of results is ascertained by using different number of node points and their locations on the plate edges. The proposed theory has substantial advantages over conventional dynamic stiffness theories for plates, particularly when applying non-classical different boundary conditions on plate edges. The computed numerical results are discussed with significant conclusions drawn.