Trilateration Adjustment by Finite Elements

by Naguib F. Danial, (M.ASCE), Prof. of Civ. Engrg.; Univ. of Petroleum and Minerals, Dhahran, Saudi Arabia,
Theodor Krauthammer, Visiting Asst. Prof.; Univ. of Illinois at Urbana-Champaign, Urbana, Ill.,

Serial Information: Journal of the Surveying and Mapping Division, 1980, Vol. 106, Issue 1, Pg. 73-93

Document Type: Journal Paper


The finite element method is used in adjusting trilateration nets. The principle is to consider the trilateration net with distances and points as a structural framework with members and nodes. The framework must be supported for structural stability according to the nature of the problem. Redundant elements are removed and initial coordinates are calculated for the nodes. Misfits are obtained as differences between measured and calculated lengths from the initial coordinates. Stiffnesses of the members are the same as the weights of the corresponding distances. All this information is introduced as input in the computer program FINITE. The output yields the displacements of the nodes in the directions of the axes of the coordinate system. It also prints out the final forces in the members. The nodal displacements are the corrections in the northings and eastings of the net points. The forces in the members divided by the corresponding weights give the corrections in the lengths of the distances.

Subject Headings: Finite element method | Frames | Displacement (mechanics) | Structural stability | Stiffening | Professional societies | Computer software

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