Anisotropic Hybrid Displacement Singularity Element

by Michael C. Apostal, Sr. Research Engr.; MARC Analysis Research Corp., Providence, R.I.,
Stephen Jordan, MARC Analysis Research Corp., Providence, R.I.,
Frederick W. Braun, (M.ASCE), Sr. Engr.; Union Carbide Corp., Linde Div., Tonawanda, N.Y.,
George C. Lee, (M.ASCE), Prof. and Dir.; Dept. of Civ. Engrg., State Univ. of New York at Buffalo, Buffalo, N.Y.,

Serial Information: Journal of the Structural Division, 1977, Vol. 103, Issue 2, Pg. 335-354

Document Type: Journal Paper


The displacement-hybrid method of finite element formulation is extended to the development of a singularity super finite element which can be used to model the behavior of a sharp crack in a rectilinearly anisotropic plane. Functional representations of the displacement field surrounding a sharp crack in a rectilinearly anisotropic plane are developed from the planar form of the linear theory of anisotropic elasticity. The formulation of the displacement-hybrid singularity super element is based on a variational principle obtained from a generalization of the total potential energy. The displacement-hybrid model singularity element which results from the formulation possesses boundary and interior displacement fields which are distinctly different in nature. Certain available numerical results, which tend to confirm the validity of the formulation, are presented.

Subject Headings: Finite element method | Anisotropy | Hybrid methods | Displacement (mechanics) | Cracking | Linear functions | Elastic analysis | Domain boundary

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