George Gerard

Secant Modulus Method for Determining Plate Instability Above the Proportional Limit

The classical plate instability equation is considered in terms of strain rather than stress. Upon the assumption that the critical stress and critical strain are implicitly related by the stress-strain curve of the material, it is found tha t the secant modulus can be used in the plate buckling equation to predict critical stress above the proportional limit. The assumption is confirmed by tests on aluminum alloy Z and channel sections.

A Creep Buckling Hypothesis

Published work on creep buckling has implied that failure of columns after a critical time is caused by initial imperfections. Such analyses are relatively complex and ultimately leave the choice of selecting the proper value of the initial imperfection to the designer. Furthermore, recent test results on creep buckling of columns have indicated that there is a random and relatively unimportant effect of small initial imperfections on the critical time. To avoid the difficulties associated with initial imperfections, a formulation of the creep buckling phenomenon in terms of classical stability theory is presented. The theorj^ permits the extension of known solutions for plastic buckling of certain thin plates and shells to creep buckling problems.

Plastic Stability Theory of Thin Shells

Ai = plasticity coefficients B = axial rigidity, B = Est/(1 v ) D = bending rigidity, D = Est /12(1 v), also diameter ei = strain intensity E = modulus of elasticity E„ = secant modulus Et = tangent modulus k = buckling coefficient, k = <rtL/irD L — length of cylinder m — number of longitudinal half wave lengths M = bending moment per unit width n = number of circumferential wave lengths N = loading per unit width p = external pressure R = radius t — thickness u, v, w = displacements x, y, z = coordinates Z = cylinder curvature parameter, Z = (L/Rt) (1 -vY = (3/o-t) (1 Et/Es) (3 = wave-length parameter 7 = shear strain e = axial strain 7] = plasticity reduction factor v = Poissons ratio ve = elastic value of Poissons ratio, ve — 0.3 a = axial stress ai = stress intensity r = shear stress curvature differential operator V4 = (d/dx + b/dy)

Optimum Number of Webs Required for a Multicell Box Under Bending

In multicell construction that may be used on the wing and tail surfaces of high-speed aircraft, the relatiyely thick compression surface is stabilized by a series of webs. I t is necessary to determine the correct combination of number of webs and compression cover thickness which will result in the design of minimum weight. Theoretical results are obtained in which the optimum number of webs is determined to be a function of only the structural thickness ratio. Nondimensional design charts are presented from which optimum conditions can be obtained. In addition to optimum conditions, an investigation was made to determine the weight penalty involved in using a number of webs other than optimum. I t was found that for a slight weight penalty it is possible to reduce the number of webs required and still maintain an efficient design.

Life Expectancy of Aircraft Under Thermal Flight Conditions

This paper is concerned with certain new structural problems which result from flight of aircraft under variable stress and elevated temperature conditions arising from aerodynamic heating. Since creep is a governing factor in determining life expectancy under elevated temperatures, a review was made of test data under cyclic stress conditions at elevated temperatures. These data indicate that gust loadings under elevated temperature conditions may not materially affect the life expectancy of the aircraft. Furthermore, the total creep under cyclic loading conditions appears to result from the net time spent at a particular stress level. Based on these data, a cumulative creep hypothesis is suggested for use in analysis of life expectancy under variable stress and temperature conditions.

Bending Tests of Thin-Walled Sandwich Cylinders

A series of tests was conducted on thin-walled circular sandwich cylinders under bending loads using aluminum-alloy faces and either cellular cellulose acetate or end grain balsa cores. I t was found that for cylinders with cellular cellulose acetate cores, the buckling strength averaged 32 per cent higher than the theoretical value. From previous tests under compressive loads, excellent agreement was obtained between the corresponding theoretical value and tests. Thus, it was concluded that, under bending loads, the buckling stress depends upon the average stress on the cross section rather than on the maximum stress. This behavior has been noted previously from tests on homogeneous cylinders.

Buckling Efficiencies of Plate Materials at Elevated Temperatures

The structural efficiencies of plates that fail as a result of elastic or plastic buckling are considered. Several materials are evaluated on the basis of short-time elevated temperature properties using structural efficiency criteria that depend upon whether failure is due to elastic or plastic buckling. Efficient temperature ranges of application for the materials considered are determined. Relative weight penalties resulting from decreased physical properties at elevated temperatures are indicated.

Note on Bending of Thick Sandwich Plates

BENDING THEORIES for homogeneous plates are of three types, which essentially depend upon the thickness of the plate, h, relative to either the deflection, 8, or a characteristic length, I: (a) Linear bending theory for thin plates is used when the deflections and thickness are small—i.e., 8/h <t:ismdh/K.l. (b) Nonlinear or large deflection theory for bending of thin plates is required when the thickness is small, h/l <C 1, and the deflections are of the order of magnitude of the thickness. (c) Bending theory for moderately thick plates is based on the assumption t ha t the deflections are small, 8/h <C 1, bu t t ha t the thickness relative to the characteristic length is not small; hence, this theory includes the deflections due to shear. A theory for sandwich plates corresponding to the conditions specified for Case (a) for homogeneous plates has been given by Libove and Batdorf, among others, and also by an order of magnitude analysis t ha t depends upon the conditions 8/h <C 1 and h/l <C 1 for the sandwich plate. Since core materials are usually weak in shear, these theories necessarily account for the deflections due to shear and consequently embrace the theory of Case (c) also. Corresponding to Case (b) for the homogeneous plate, a large deflection theory for sandwich plates has been given by Reissner.