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Calculation Method of Non-Linear Stiffness Matrix in Spline Finite Element Method
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Author: Jian Qin, Liang Qiao, Jun Chen, Jianhua Feng, Lili Wang, Yimin Ma
Abstract: According to the analytical characteristics of cubic B spline function, such as compactness and discontinuous smoothness, two methods, Global integral method and Assembling method are proposed to calculate the non-linear stiffness matrix in the spline finite element method. The Global integral method transforms the integral of the product of spline functions into the sum of boundary data of the product by integral by parts. The Assembling method used the compactness characteristics of the spline function, reduces the n+3 order stiffness matrix in unit interval to the 4 order matrix, and then obtains the global matrix by assembling the small ones. The two proposed methods are clear in theory and easy to be realized by computer program, which can effectively improve the efficiency of the algorithm for nonlinear spline element method.
Keywords: non-linear stiffness matrix; spline function; integral by parts; matrix assembly
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