On the use of Pade approximant in the Asymptotic Numerical Method ANM to compute the post-buckling of shells

被引:8
|
作者
Hamdaoui, Abdellah [1 ]
Braikat, Bouazza [1 ]
Tounsi, Noureddine [1 ]
Damil, Noureddine [1 ]
机构
[1] Univ Hassan II Casablanca, Fac Sci Ben MSik, Lab Ingn & Mat LIMAT, BP 7955, Casablanca, Morocco
关键词
Vectorial Pade approximant; Post-buckling; Shells; Continuation algorithm; Asymptotic Numerical Method (ANM);
D O I
10.1016/j.finel.2017.08.004
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we present a new ANM continuation algorithm with a predictor based on a new Pade approximant and without the use of a correction process. The ANM is a numerical method to obtain the solution of a nonlinear problem as a succession of branches [1-7]. Each branch is represented by a vectorial series which is obtained by inverting only one tangent stiffness matrix. The series representation can be replaced by a rational representation which reduces the number of branches necessary to obtain the entire branch of desired solution. In this work, we discuss the use of a new vectorial Pade approximants in the ANM algorithm. In previous works [1, 2, 4, 5], the Pade approximants have been introduced after an orthonormalization of the terms of the vectorial series. In a recent article [8], we have demonstrated that the coefficients b(i)(M) of the Pade approximants can be chosen in an arbitrary manner. For this purpose, we propose a new choice of vectorial Pade approximants {U-p(M)} at order which minimizes the relative error between two consecutive vectorial Pade approximants {U-p(M)} at order M and {U-p(M-1)} at order M - 1. This minimization has been made by a judicious choice of the coefficients bMi of the Pade {U(M)p(}) at order M as a function of coefficients b(i)(M-1) of the Pade approximants {U-p(M-1)} at order M - 1 obtained by the classical process of Gram-Schmidt orthonormalization. A comparison of the obtained results with those computed by the use of classical Pade approximants is presented.
引用
收藏
页码:1 / 10
页数:10
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