Three-Dimensional Bar Cell for Elastic Stress Analysis

by Alexander Hrennikoff, (F.ASCE), Res. Prof. of Civ. Engrg.; Univ. of British Columbia, Vancouver, B.C., Canada,
A. Gantayat, Presently, Grad. Student; Dept. of Civ. Engrg., Univ. of British Columbia, Vancouver, B.C., Canada,

Serial Information: Journal of the Engineering Mechanics Division, 1970, Vol. 96, Issue 3, Pg. 313-326

Document Type: Journal Paper


A bar cell in the form of a rectangular parallelepiped, capable of imitating the action of homogeneous elastic bodies, is devised for three-dimensional stress analysis by the finite element method, and the stiffness matrix of the cell is derived. The cell is made up of triple bars located along the edges of the cell and two single diagonal bars in each of its six faces. The bars are endowed only with axial rigidity. The three-dimensional elastic body is idealized into an assemblage of cells interconnected by hinges at the nodes, and the model is solved for the displacements and stresses by the computer. The application of the method is demonstrated on the examples of infinite and semi-infinite spaces under the action of single concentrated loads, and the results are compared with similar solutions, utilizing cells advanced earlier by other authors, and the exact theory, with the use of several values of Poisson's ratio. The precision of the proposed method compares favorably with the other methods, especially at certain values of Poisson's constant.

Subject Headings: Three-dimensional analysis | Elastic analysis | Stress analysis | Finite element method | Bars (structure) | Three-dimensional models | Computer models | Homogeneity

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