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中文摘要：
提出了一种简单的推导各向同性材料,三维弹性力学问题基本解析解的特征方程解法.应用三维问题控制微分方程的算子矩阵,通过计算其行列式可得到问题特征通解所需满足的特征方程.将满足各种不同简化特征方程的特征通解,代入到微分方程算子矩阵所对应的不同的缩减伴随矩阵,可推导得出相应的三维弹性力学问题的基本解析解,包括B-G解、修正的P-N（P-N-W）解和类胡海昌解.进一步对各类多项式形式的基本解析解的独立性进行了讨论.这些工作为构造数值方法中所需的完备独立的解析试函数奠定了基础.
英文摘要：
A simple characteristic equation solution strategy for deriving the fundamental analytical solutions of 3D isotropic elasticity was proposed.By calculating the determinant of the differential operator matrix obtained from the governing equations of 3D elasticity,the characteristic equation which the characteristic general solution vectors must satisfy was established.Then,by substitution of the characteristic general solution vectors,which satisfied various reduced characteristic equations,into various reduced adjoint matrices of the differential operator matrix,the corresponding fundamental analytical solutions for isotropic 3D elasticity,including B-G solutions,modified P-N（P-N-W） solutions,and quasi HU Haichang solutions,could be obtained.Furthermore,the independence characters of various fundamental solutions in polynomial form were also discussed in details.These works provide a basis for constructing complete and independent analytical trial functions used in numerical methods.
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