Efficient Solution of Load-Deflection Equations

by R. J. Melosh,
R. M. Bamford,

Serial Information: Journal of the Structural Division, 1969, Vol. 95, Issue 4, Pg. 661-676

Document Type: Journal Paper


Solution of a set of simultaneous equations is the central problem in static structural analysis. An integrated approach to equation solution is explained, the basis of which is the use of wavefront data processing and a modified Gauss solution algorithm. The wavefront processing involves the allocation of data in accordance with the structural connectivity rather than the bandwidth. Hence, larger sparse matrices of coefficients can be treated than with bandwidth processing. The paper describes the solution process from the point of view of the engineer; a detailed description of the steps of the process is also provided for the use of a program developer. Speed tests of the computer code show that while a negligible time penalty is incurred in some cases, there is a great improvement in others when the new approach is compared with a bandwidth Choleski process. Accuracy tests of the code show that the error in the modified Gauss is less than 0.006% for a problem in which the Choleski routine has 38% error.

Subject Headings: Displacement (mechanics) | Gaussian process | Standards and codes | Errors (statistics) | Statics (mechanics) | Static structural analysis | Algorithms | Matrix (mathematics)

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