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Semi-analytical solution of path-independent nonlinear finite element models

机译:与路径无关的非线性有限元模型的半解析解

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Within the semi-analytical solution of the finite element model, the results of the analysis are expressed as a function of one or several parameters of the problem. Severe growth of the size of resulting expressions limits the direct use of symbolic systems to the small number of input parameters left in a symbolic form and to the linear finite element formulations. One of the solutions to the problem of expression growth, followed also in this paper, is to construct an approximated symbolic solution of the finite element model in a form of multivariate series expansion. In order to obtain the semi-analytical solution of middle-scale path-independent nonlinear problems, the presented approach combines dual symbolic-numeric finite element environment with the run-time power series expansion at individual finite element level and a recursive algorithm for the multivariate power series expansion of the solution to the system of linear equations.
机译:在有限元模型的半解析解中,分析结果表示为问题的一个或多个参数的函数。结果表达式大小的严重增长将符号系统的直接使用限制为以符号形式保留的少量输入参数以及线性有限元公式。本文还紧接着解决表达式增长问题的一种方法是以多元级数展开形式构造有限元模型的近似符号解。为了获得与路径无关的中尺度非线性问题的半解析解,本文提出的方法将双符号数字有限元环境与单个有限元级上的运行时幂级数展开以及多元算法相结合线性方程组解的幂级数展开。

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