Characteristic equation solution strategy for deriving fundamental analytical solutions of 3D isotropic elasticity  

作　　者：傅向荣 袁明武 岑松 田歌 

机构地区：[1]College of Water Conservancy&Civil Engineering,China Agricultural University [2]School of Engineering,Peking University [3]Department of Engineering Mechanics School of Aerospace,Tsinghua University [4]Key Laboratory of Applied Mechanics&High Performance Computing Center,School of Aerospace,Tsinghua University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2012年第10期1253-1264,共12页应用数学和力学（英文版）

基　　金：supported by the National Natural Science Foundation of China (Nos. 10872108 and10876100);the Program for New Century Excellent Talents in University (No. NCET-07-0477);the National Basic Research Programs of China (Nos. 2010CB731503 and 2010CB832701)

摘　　要：A simple characteristic equation solution strategy for deriving the fun- damental analytical solutions of 3D isotropic elasticity is 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 is established. Then, by substitution of the characteristic general solution vectors, which satisfy various reduced characteristic equations, into various reduced ad- joint matrices of the differential operator matrix, the corresponding fundamental analyt- ical solutions for isotropic 3D elasticity, including Boussinesq-Galerkin （B-G） solutions, modified Papkovich-Neuber solutions proposed by Min-zhong WANG （P-N-W）, and quasi HU Hai-chang solutions, can be obtained. Furthermore, the independence characters of various fundamental solutions in polynomial form are also discussed in detail. These works provide a basis for constructing complete and independent analytical trial func- tions used in numerical methods.A simple characteristic equation solution strategy for deriving the fun- damental analytical solutions of 3D isotropic elasticity is 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 is established. Then, by substitution of the characteristic general solution vectors, which satisfy various reduced characteristic equations, into various reduced ad- joint matrices of the differential operator matrix, the corresponding fundamental analyt- ical solutions for isotropic 3D elasticity, including Boussinesq-Galerkin （B-G） solutions, modified Papkovich-Neuber solutions proposed by Min-zhong WANG （P-N-W）, and quasi HU Hai-chang solutions, can be obtained. Furthermore, the independence characters of various fundamental solutions in polynomial form are also discussed in detail. These works provide a basis for constructing complete and independent analytical trial func- tions used in numerical methods.

关 键 词：characteristic equation solution strategy fundamental analytical solution modified Papkovich-Neuber solution HU Hai-chang solution analytical trial function 

分 类 号：O343.2[理学—固体力学]