Shengyu Duan

A High-Order Numerical Manifold Method Based on B-Spline Interpolation and its Application in Structural Dynamics

In this paper, a new numerical manifold method (NMM) is formulated on the basis of quintic polynomial interpolation. For linear elastodynamics analysis, the generalized instantaneous potential energy principle for the NMM is employed to obtain the formulation of its elastodynamic equilibrium equations. For the presented NMM, the penalty method is designed to deal with the boundary conditions. The initialization of the dynamic equilibrium equation coupled with its time integration method is exclusively designed. The proposed NMM is applied for static and dynamic analysis of an elastic beam to verify the validity of the proposed NMM. The calculation accuracy and computation efficiency analysis are conducted by comparing the NMM with the finite element method (FEM). Numerical result comparison shows that the proposed NMM possesses higher calculation accuracy than the FEM, especially for the gradient solutions. Time consumption analysis demonstrates that the proposed NMM provides far more accurate numerical results with lower time cost than the FEM.

An Explicit Time Integration Scheme Based on B-Spline Interpolation and Its Application in Wave Propagation Analysis

An explicit time integration scheme for hyperbolic equations is proposed using B-spline interpolation and weighted residual method. It has simple formulation and calculation procedure. With one adjustable algorithmic parameter, new scheme has higher accuracy when compared with other excellent explicit schemes. New scheme has controllable and also desirable period elongation which is verified by theoretical analysis and numerical simulations. Especially, a demonstrative dispersion analysis coupled with the corresponding wave propagation demonstrate the desirable numerical dissipation property and the effectiveness of the proposed scheme for wave propagation problems.