American Society of Civil Engineers

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.), and George C. Lee, M.ASCE, (Prof. and Dir., Dept. of Civ. Engrg., State Univ. of New York at Buffalo, Buffalo, N.Y.)

Journal of the Structural Division
, Vol. 103, No. 2, February 1977, pp. 335-354

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Document type: Journal Paper
Abstract: 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.

ASCE Subject Headings:
Engineering mechanics
Finite element method