基于矩形独立覆盖初步实现结构静力分析的自动计算

采用前期研究的基于矩形独立覆盖的新型数值流形法,提出结构线弹性静力分析的自动计算方法,包括自动的前处理、自适应分析等。根据独立覆盖的特点提出几个后验误差指标:独立覆盖之间条形连接区域的应变连续性指标;边界应力指标和独立覆盖的高阶误差指标。利用新方法的h型网格加密及p型升阶的方便性,选择一种路径尝试h-p型的混合自适应,其中,对于矩形独立覆盖采用简单的二分法实现覆盖加密。通过几个二维算例验证了新方法实现自动计算的可行性,只需人工输入结构外形、材料参数和边界条件,其它工作完全交由计算机完成,最终得到满足一定精度的计算结果。

Preliminary Implementation of Automatic Computation for Static Analysis of Structures Using NMM Based on Independent Rectangular Covers

By means of numerical manifold method (NMM) based on independent rectangular covers proposed in previous study, we present an automatic computation method for static analysis of linear-elastic structures, including automatic pre-processing, self-adaptive analyses and so on. According to the characteristics of independent covers, we give 3 indexes for posterior error such as index of strain continuity in strip area between two covers, stress index on boundary surfaces and high-order error in an independent cover. By using convenient h-version mesh refinement and p-version order increasing in the new method, we implement h-p version self-adaptivity in a selected way to realize h-version refinement of rectangular covers by using simple bisection method. Some 2D numerical examples are given to illustrate the feasibility of automatic computation, in which all the procedures are automatically accomplished by the computer, except for necessary manual input of structural outlines, material parameters, and boundary conditions. Finally, we obtain calculated data with certain precision.