累积线性法在细长柔性悬臂梁结构分析中的应用

为了研究几何大位移悬臂梁的结构响应,在充分利用线性有限元原理与流程的基础上,本文提出"累积线性法" 来对这一问题进行结构建模与求解策略的探讨,数值计算过程表明：该方法在常规有限元软件平台上十分容易实现,并与常规的"一次线性法" 和"非线性求解" 进行了数值对比. 针对本文问题,不仅从理论上指出"累积线性法" 的合理与可行和"一次线性法" 存在的结果不可信等问题;同时,数值仿真也表明前两种方法得到的结果也是不同的, 前者更接近非线性求解的结果. 最后,给出4 点结论.

APPLICATION OF THE ACCUMULATED LINEARIZATION TO THE STRUCTURAL ANALYSIS OF SLENDER AND FLEXIBLE CANTILEVER BEAM

In order to study the structural response of geometrically large displacement in a cantilever beam, based fully on utilizing the linear finite element method (FEM) principle and procedure, the "accumulated linearization" is proposed to construct the structural model and to search the solving strategy for this kind of problem. The process of the numerical calculation shows that the proposed method is easy to realize in the widely available FEM software. Meanwhile, the "one time linearization" and the "non-linearization solving" in the numerical calculation are compared with this method. For the above problem, the proposed method is not only rational and feasible, but also can check the results of "one time linearization" to some extent. And the numerical simulation results of the two approaches are distinctly different, in which the former's results approach those of the "non-linearization solving".