摘要
在重根特征向量导数计算方法的发展中 ,为了从无限个特解中确定出唯一的通解 ,提出过不同定解条件 ,但正确定解条件是唯一的。最后公认的定解条件为ZTMZ′+Z′TMZ =-ZTM′Z ,这里认为Z′TMZ≠ZTMZ′。由此便引出物理矩阵 (刚度阵和质量阵 )的二阶导数。为了避免物理阵二阶导数的计算 ,本文在满足前述定解条件的前提下 ,利用一种特殊的迭代格式回避了物理阵二阶导数的引入。同时该迭代过程可直接获得通解 ,不同于目前流行的做法 :先由一个不定支配方程求其特解 ,然后才由定解条件确定通解。另外 ,数值表明 ,动柔度迭代式的精度可与直接迭代式相匹敌 ,可是动柔度迭代式用于许多特征向量导数计算时 。
In the field of eigenvector derivative computation to find an unique general solution from infinite particular solutions,the distinct Conditions of Determining Solution(CDS)were proposed,so that different general solutions were obtained.Finally,the CDS:Z TMZ+Z TMZ ′=-Z TM ′Z for repeted eigenvalue case is universally accepted,that is,Z ′T MZ≠Z TMZ ′is generally acknowledged .This CDS leads to occurrence of the second order derivatives of the physical matrices(i.e. stiffness and mass matrices).Under prerequisite of satisfying the previous CDS the calculation of the second order derivatives of the physical matrices is avoided by using an iterative format in this paper.In addition,this iterative process can directly find the general solution,but the existing methods give first particular solution,then determine general solution.Dynamic flexibility iterative method can economically be utilized in the calculation of many eigenvector derivatives in comparison with direct iterative method.
出处
《强度与环境》
2003年第2期17-30,共14页
Structure & Environment Engineering
