Accession Number : ADA301132
Title : The Lagrangian Multiplier Method of Finding Upper and Lower Limits to Critical Stresses of Clamped Plates
Descriptive Note : Technical rept.
Corporate Author : NATIONAL AERONAUTICS AND SPACE ADMIN LANGLEY RESEARCH CENTER HAMPTON VA
Personal Author(s) : Budiansky, Bernard ; Hu, Pai C
Report Date : Jan 1946
Pagination or Media Count : 13
Abstract : The theory of Lagrangian multipliers is applied to the problem of finding both upper and lower limits to the true compressive buckling stress of a clamped rectangular plate. The upper and lower limits thus bracket the true stress, which cannot be exactly found by the differential-equation approach. The procedure for obtaining the upper limit, which is believed to be new, presents certain advantages over the classical Raleigh-Rite method of finding upper limits. The theory of the lower-limit procedure has been given by Trefftz but, in the present application, the method differs from that of Trefftz in a way that makes it inherently more quickly convergent. It is expected that in other buckling problems and in some vibration problems the Lagrangian multiplier method finding upper and lower limits may be advantageously applied to the calculation of buckling stresses and natural frequencies.
Descriptors : *BUCKLING , *STRESS ANALYSIS , LOADS(FORCES) , DEFORMATION , MODULUS OF ELASTICITY , APPROXIMATION(MATHEMATICS) , FOURIER SERIES , VIBRATION , NUMERICAL METHODS AND PROCEDURES , APPLIED MATHEMATICS , COMPRESSIVE STRENGTH , LAGRANGIAN FUNCTIONS , CONVERGENCE
Subject Categories : Mechanics
Distribution Statement : APPROVED FOR PUBLIC RELEASE