正交各向异性薄板弯曲问题分裂模量有限元法

Splitting Modulus Finite Element Method for Orthogonal Anisotropic Plate Bending

讨论了建立分裂模量有限元法的必要性 ,推导了正交各向异性薄板弯曲问题分裂模量变分原理的泛函 ,以此为基础建立了该问题的分裂模量有限元法· 该模型的特点是其中含有一个被称为分裂因子的参数 ,通过算例说明 :适当调整分裂因子的值 ,可以达到调整有限元模型的刚度、降低有限元刚度矩阵的谱条件数、克服常规有限元病态问题的目的 。

Splitting modulus variational principle in linear theory of solid mechanics was introduced, the principle for thin plate was derived, and splitting modulus finite element method of thin plate was established too. The distinctive feature of the splitting model is that its functional contains one or more arbitrary additional parameters, called splitting factors, so stiffness of the model can be adjusted by properly selecting the splitting factors. Examples show that splitting modulus method has high precision and the ability to conquer some ill_conditioned problems in usual finite elements. The cause why the new method could transform the ill_conditioned problems into well_conditioned problem, is analyzed finally.