面向理论解的有限元等价模型态生成策略研究

Research on Generation Strategy of Model States of Original Model Considering Equivalency on Theoretical Results

在有限元技术的广泛应用中,存在一个普遍问题,即分析复杂模型十分耗费计算资源。怎样改造模型,使得模型改造前后的分析解的差异在可接受范围内,并有效提高计算效率一直是研究热点。引入的多态模型理论可通过降低初始模型复杂度生成模型态,并用模型态代替初始模型进行计算以提高计算效率。由有限元误差估计理论推导可知,为了使初始模型与其模型态的分析解差异可控,必须首先保证两者的理论解差异可忽略。因此,以初始模型中的几何特征为研究对象,探索合适的特征改造策略,使得依据该策略生成的模型态与初始模型的理论解差异可忽略不计,即两者在理论解的角度上是等价的,为进一步量化估计初始模型与模型态的分析解差异打下工作基础。

In the wide application of finite element technology, models with complex geometric information would cost large amount of computing resources. Much research has been done in order to reduce computing cost without sacrificing too much precision by simplifying geometric features in model. In multi-state model theory, model states are generated from reducing the geometric complexity of original model, which may help to improve computing efficiency by replacing the original model with its model states in computation. Given finite element error estimation theory, the equivalency of theoretical results of original model and its model states should be assured to make value difference between computing results of them meet computing requirement. Appropriate displacement and remove strategy towards geometric features in original model is researched in order to generate model states whose theoretical results equal their original model＇s for the purpose of evaluating the value difference between computing results of the original model and its model states.