论文部分内容阅读
针对工程结构中的共性问题,即算子,提出了工程结构的算子自定义小波有限元构造方法及自适应解耦计算方法。在建立了多分辨有限元空间的基础上,根据工程结构问题中的算子,即小波函数与尺度函数之间的内积关系式,提出了基于稳定完备法的算子自定义小波单元构造方法;提出自适应算子自定义小波有限元法,该方法的优点是在保持初始尺度分析结果的基础上,向局域添加所有大于局部误差阈值的算子自定义小波基,实现工程结构问题的高效分析。数值算例表明:算子自定义小波有限元法所推导的多尺度刚阵解耦比率为89.65%,自适应算子自定义小波有限元法的计算量最大降低比率为49.23%,适合工程结构问题的高效多尺度计算。
Aiming at the common problem in engineering structure, namely operator, a construction method of operator-defined wavelet finite element for engineering structure and a method of adaptive decoupling are proposed. Based on the establishment of multi-resolution finite element space and based on the inner product relation between the wavelet function and the scale function, the operator-defined wavelet unit construction method based on the stability-complete method The self-adaptive wavelet operator finite element method is proposed. The method has the advantage of adding operator-defined wavelet bases larger than the local error threshold to the local area based on the initial scale analysis results, and realizing the structural problems Efficient analysis. The numerical example shows that the decoupling ratio of multi-scale rigid-matrix deduced by operator-defined wavelet finite element method is 89.65%, and the maximum reduction rate of self-adaptive wavelet finite element method is 49.23%, which is suitable for engineering structure Efficient multiscale computation of the problem.