摘要
首先,利用共轭算子的性质,将张鸿庆等提出的求伴随算子对的方法推广到了求一类非线性(即部分非线性的)算子矩阵的伴随算子向量.其次,利用机械化的构造方法给出了求解一类非线性(即,部分非线性的,且以所有线性的为其特例)非齐次微分方程组的统一理论,即通过齐次化和三角化求得恰当的变换,从而将原方程组化为较简单的形式,一般为对角化的.最后利用该方法求得了一些弹性力学方程组的解析解.
Flrstly, an approach is presented for computing the aOjoint operator vector of a class of nonlinear （i. e. partial-nonlinear） operator matrix by generalizing the method presented by Zhang et al. and the conjugate operators. Secondly, a united theory is given for solving a class of nonlinear （i. e. partial-nonlinear and including all linear ） and non-homogeneous differential equations by the mathematics-mechanization method. In other words, a transformation is constructed by homogenization and triangulation which can reduce the original system to the simpler one which is diagonal, Finally, some practical applications are given in elasticity equations.
出处
《应用数学和力学》
EI
CSCD
北大核心
2008年第11期1268-1278,共11页
Applied Mathematics and Mechanics
基金
国家重点基础研究专项基金资助项目(2004CB318000)
关键词
AC=BD模
部分非线性
伴随
共轭
板壳
AC = BD model
partial-nonlinear
adjoint
conjugate
plate and shell
