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


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/a301132.pdf


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
      Numerical Mathematics


Distribution Statement : APPROVED FOR PUBLIC RELEASE