| Numerical manifold method is a numerical method with high precision, it absorbs the advantage of the finite element method and discontinuous deformation method. Numerical manifold method can express continuous and discontinuous properties, so it is able to calculate the problem with complex materials and geometric boundaries. It Have an advantage in the calculation of the static and dynamic problems, such as dislocation, sliding, rotation, crack and so on. Numerical manifold method is rarely used in three-dimensional problems, especially in 3D structural dynamics problems. What’s more, the element shape function of the finite element method is a power function of the static displacement field under the condition of the nodal displacement, which make the calculation accuracy of the stress is lower than that of the displacement. And it is more prominent in the calculation of dynamic stress of structure. In this condition, an attempt is made to the numerical manifold method for three dimensional dynamic problems. The three-dimensional numerical manifold method based on B spline function is proposed. The Important work includes the following aspects:(1)Established the 3D B-spline interpolation function based on one-dimensional B spline basis function.(2)Based on the principle of penalty function, the boundary conditions of simply supported beam and cantilever beam are derived.(3)Using the parameter coordinates, the stiffness matrix of the manifold element is established.(4)The Newmark method is introduced, and it is used as the time integral method of manifold method.(5)Complete the whole program with MATLAB.(6)In the static and dynamic problems, the three-dimensional manifold method is used to calculate and compare with the results of the finite element method. The feasibility and superiority of the method are proved.Following these works, this paper shows that numerical manifold method for dynamic calculation of three-dimensional structure have high precision in low frequency. |
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