Abstract:

A new numerical manifold (NMM) method is derived on the basis of quartic uniform B-spline interpolation. The analysis shows that the new interpolation function possesses higher-order continuity and polynomial consistency compared with the conventional NMM. The stiffness matrix of the new element is well-conditioned. The proposed method is applied for the numerical example of thin plate bending. Based on the principle
of minimum potential energy, the manifold matrices and equilibrium equation are deduced. Numerical results reveal that the NMM has high interpolation accuracy and rapid convergence for the global cover function and its higher-order partial derivatives.

Key words: basic system of equations of atmospheric motion, stability, stratification theory, transversal stratum, numerical manifold method (NMM), thin plate bending, manifold element, B-spline