FU Xiang-rong, YUAN Ming-wu, CEN Song, TIAN Ge. A Characteristic Equation Solution Strategy for Deriving the Fundamental Analytical Solutions of 3D Isotropic Elasticity[J]. Applied Mathematics and Mechanics, 2012, 33(10): 1170-1179. doi: 10.3879/j.issn.1000-0887.2012.10.003
Citation: FU Xiang-rong, YUAN Ming-wu, CEN Song, TIAN Ge. A Characteristic Equation Solution Strategy for Deriving the Fundamental Analytical Solutions of 3D Isotropic Elasticity[J]. Applied Mathematics and Mechanics, 2012, 33(10): 1170-1179. doi: 10.3879/j.issn.1000-0887.2012.10.003

A Characteristic Equation Solution Strategy for Deriving the Fundamental Analytical Solutions of 3D Isotropic Elasticity

doi: 10.3879/j.issn.1000-0887.2012.10.003
Funds:  国家自然科学基金资助项目(10872108;10876100);国家重点基础研究发展计划基金资助项目(2010CB731503;2010CB832701);教育部新世纪优秀人才支持计划基金资助项目(NCET-07-0477);中国航天科学基金资助项目(ASFC)
  • Received Date: 2011-08-19
  • Rev Recd Date: 2012-04-27
  • Publish Date: 2012-10-15
  • 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 Hai-chang 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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