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NASA NTRS1978

Theoretical-experimental correlation for buckling of composite cylinders under combined compression and torsion

Comparison between theory and experiment for buckling of laminated graphite-epoxy and boron-epoxy cylinders under combined compression and torsion are presented. The experimental results are compared to a theory by Wu. It is shown that there is excellent agreement between theory and experiment for pure torsional loading (positive and negative), experimental buckling loads for pure compression are well below the predicted values, and good correlation is exhibited between theory and experiment for buckling under combined loading when compared in the form of normalized buckling interaction diagrams in axial-torsional load space.

Herakovich, C. T.↗

NASA NTRS1978

On a numerical solution of the plastic buckling problem of structures

An automated digital computer procedure is presented for the accurate and efficient solution of the plastic buckling problem of structures. This is achieved by a Sturm sequence method employing a bisection strategy, which eliminates the need for having to solve the buckling eigenvalue problem at each incremental (decremental) loading stage that is associated with the usual solution techniques. The plastic buckling mode shape is determined by a simple inverse iteration process, once the buckling load has been established. Numerical results are presented for plate problems with various edge conditions. The resulting computer program written in FORTRAN V for the JPL UNIVAC 1108 machine proves to be most economical in comparison with other existing methods of such analysis.

Gupta, K. K.↗

NASA NTRS1978

Application of a trigonometric finite difference procedure to numerical analysis of compressive and shear buckling of orthotropic panels

A numerical analysis developed for the buckling of rectangular orthotropic layered panels under combined shear and compression is described. This analysis uses a central finite difference procedure based on trigonometric functions instead of using the conventional finite differences which are based on polynomial functions. Inasmuch as the buckle mode shape is usually trigonometric in nature, the analysis using trigonometric finite differences can be made to exhibit a much faster convergence rate than that using conventional differences. Also, the trigonometric finite difference procedure leads to difference equations having the same form as conventional finite differences; thereby allowing available conventional finite difference formulations to be converted readily to trigonometric form. For two-dimensional problems, the procedure introduces two numerical parameters into the analysis. Engineering approaches for the selection of these parameters are presented and the analysis procedure is demonstrated by application to several isotropic and orthotropic panel buckling problems. Among these problems is the shear buckling of stiffened isotropic and filamentary composite panels in which the stiffener is broken. Results indicate that a break may degrade the effect of the stiffener to the extent that the panel will not carry much more load than if the stiffener were absent.

Stein, M.↗

NASA NTRS1982

Tensile buckling of advanced turboprops

Theoretical studies were conducted to determine analytically the tensile buckling of advanced propeller blades (turboprops) in centrifugal fields, as well as the effects of tensile buckling on other types of structural behavior, such as resonant frequencies and flutter. Theoretical studies were also conducted to establish the advantages of using high performance composite turboprops as compared to titanium. Results show that the vibration frequencies are not affected appreciably prior to 80 percent of the tensile speed. Some frequencies approach zero as the tensile buckling speed is approached. Composites provide a substantial advantage over titanium on a buckling speed to weight basis. Vibration modes change as the rotor speed is increased and substantial geometric coupling is present.

Chamis, C. C.↗

NASA NTRS1981

Bifurcation and post-buckling analysis of laminated composite plates via reduced basis technique

A reduced basis technique and a problem-adaptive computational algorithm are presented for the bifurcation and post-buckling analysis of laminated anisotropic plates. The computational algorithm can be conveniently divided into three distinct stages. The first stage is that of determining the bifurcation point. The plate is discretized by using displacement finite element (or finite difference) models. The special symmetries exhibited by the response of the anisotropic plate are used to reduce the size of the analysis region. The vector of unknown nodal parameters is expressed as a linear combination of a small number of basis vectors, and a Rayleigh-Ritz technique is used to approximate the finite element equations by a small system of algebraic equations. The reduced equations are used to determine the bifurcation point and the associated eigenmode of the panel. In the second stage of the bifurcation buckling mode is used to obtain a nonlinear solution in the vicinity of the bifurcation point and new (updated) sets of basis vectors and reduced equations are generated. In the third stage the reduced equations are used to trace the post-buckling paths. The effectiveness of the proposed technique for predicting the bifurcation and post-buckling behavior of plates is demonstrated by means of numerical examples for plates loaded by means of prescribed edge displacements.

Noor, A. K.↗

NASA NTRS1983

Generic buckling curves for specially orthotropic rectangular plates

Using a double affine transformation, the classical buckling equation for specially orthotropic plates and the corresponding virtual work theorem are presented in a particularly simple fashion. These dual representations are characterized by a single material constant, called the generalized rigidity ratio, whose range is predicted to be the closed interval from 0 to 1 (if this prediction is correct then the numerical results using a ratio greater than 1 in the specially orthotropic plate literature are incorrect); when natural boundary conditions are considered a generalized Poisson's ratio is introduced. Thus the buckling results are valid for any specially orthotropic material; hence the curves presented in the text are generic rather than specific. The solution trends are twofold; the buckling coefficients decrease with decreasing generalized rigidity ratio and, when applicable, they decrease with increasing generalized Poisson's ratio. Since the isotropic plate is one limiting case of the above analysis, it is also true that isotropic buckling coefficients decrease with increasing Poission's ratio.

Brunnelle, E. J.↗

NASA NTRS1985

Short-wavelength buckling and shear failures for compression-loaded composite laminates

The short-wavelength buckling (or the microbuckling) and the interlaminar and inplane shear failures of multi-directional composite laminates loaded in uniaxial compression are investigated. A laminate model is presented that idealizes each lamina. The fibers in the lamina are modeled as a plate, and the matrix in the lamina is modeled as an elastic foundation. The out-of-plane w displacement for each plate is expressed as a trigonometric series in the half-wavelength of the mode shape for laminate short-wavelength buckling. Nonlinear strain-displacement relations are used. The model is applied to symmetric laminates having linear material behavior. The laminates are loaded in uniform end shortening and are simply supported. A linear analysis is used to determine the laminate stress, strain, and mode shape when short-wavelength buckling occurs. The equations for the laminate compressive stress at short-wavelength buckling are dominated by matrix contributions.

Shuart, M. J.↗

NASA NTRS1986

An approximate buckling analysis for rectangular orthotropic plates with centrally located cutouts

An approximate analysis for predicting buckling of rectangular orthotropic composite plates with centrally located cutouts is presented. In this analysis, prebuckling and buckling problems are converted from a two-dimensional to a one-dimensional system of linear differential equations with variable coefficients. The conversion is accomplished by expressing the displacements as series with each element containing a trigonometric function of one coordinate and a coefficient that is an arbitrary function of the other coordinate. Ordinary differential equations are then obtained from a variational principle. Analytical results obtained from the approximate analysis are compared with finite element analyses for isotropic plates and for specially orthotropic plates with central circular cutouts of various sizes. Experimental results for the specially orthotropic plates are also presented. In nearly all cases, the approximate analysis predicts the buckling mode shapes correctly and predicts the buckling loads to within a few percent of the finite element and experimental results.

Nemeth, M. P.↗

NASA NTRS1987

Thermal stresses and buckling of elastic plates with reinforced edges

An approximation method based on the method of Kantorovich is used to calculate the critical thickness necessary to prevent thermal buckling of a rectangular cantilever plate with edge stiffeners. The case where no external loads are applied is considered, and the only stresses are those due to the prescribed thermal profile. Stiffeners are found to play an important role in the thermal buckling by affecting the overall distribution of the in-plane stresses within the plate. Results show that edge stiffeners can cause less or more buckling, and that in most situations the edge stiffeners hinder buckling because a thicker plate is required than if the stiffeners were not present.

Ahmed, M.↗

NASA NTRS1987

Measurement of impact-induced delamination buckling in composite laminates

High-velocity impact tests were performed on graphite/epoxy laminates with embedded delaminations. High-speed photography of the transversely impacted laminates shows that dynamic local buckling of the sublaminate region formed by the delamination can cause a mode-I-dominated propagation of that delamination. Simultaneous recordings of the dynamic strain histories at several locations in the buckled sublaminate region are used to measure the laminate and sublaminate responses to the impact loading. Flexural motion resulting from transverse impact is shown to reduce local buckling of the sublaminate. This buckling causes a progressive separation of the delaminated surfaces and subsequent extension of the delamination in a mode-I dominated fashion.

Grady, J. E.↗

NASA NTRS1988

Non-isothermal buckling behavior of viscoplastic shell structures

Described are the mathematical model and solution methodologies for analyzing the structural response of thin, metallic elasto-viscoplastic shell structures under large thermomechanical loads and their non-isothermal buckling behavior. Among the system responses associated with these loads and conditions are snap-through, buckling, thermal buckling, and creep buckling. This geometric and material nonlinearities (of high order) can be anticipated and are considered in the model and the numerical treatment.

Riff, Richard↗

NASA NTRS1986

Buckling characteristics of hypersonic aircraft wing tubular panels

The buckling characteristics of Rene 41 tubular panels installed as wing panels on a hypersonic wing test structure (HWTS) were determined nondestructively through use of a force/stiffness technique. The nondestructive buckling tests were carried out under different combined load conditions and different temperature environments. Two panels were subsequently tested to buckling failure in a universal tension compression testing machine. In spite of some data scattering because of large extrapolations of data points resulting from termination of the test at a somewhat low applied load, the overall test data correlated fairly well with theoretically predicted buckling interaction curves. The structural efficiency of the tubular panels was slightly higher than that of the beaded panels which they replaced.

Ko, William L.↗

NASA NTRS1991

Combined-load buckling behavior of metal-matrix composite sandwich panels under different thermal environments

Combined compressive and shear buckling analysis was conducted on flat rectangular sandwich panels with the consideration of transverse shear effects of the core. The sandwich panel is fabricated with titanium honeycomb core and laminated metal matrix composite face sheets. The results show that the square panel has the highest combined load buckling strength, and that the buckling strength decreases sharply with the increases of both temperature and panel aspect ratio. The effect of layup (fiber orientation) on the buckling strength of the panels was studied in detail. The metal matrix composite sandwich panel was much more efficient than the sandwich panel with nonreinforced face sheets and had the same specific weight.

Ko, William L.↗

NASA NTRS1991

Thermal buckling and postbuckling of symmetrically laminated composite plates

The thermal buckling and postbuckling response of symmetrically laminated composite plates are discussed. Using variational methods in conjunction with a Rayleigh-Ritz formulation, thermal buckling and postbuckling are investigated for two laminates, a (+/- 45/0/90) and a (+/- 45/02), under two different simple support conditions, fixed and sliding. These laminates are subjected to the condition of a uniform temperature change. The effects of the principal material axis not being aligned with the edges of the plate, referred to here as material axis skewing, are also investigated. Although differences between buckling temperatures for the two support conditions were small, support conditions can have a large influence on thermal postbuckling response. In general, plates with fixed simple supports deflect more than plates with sliding simple supports. In addition, support conditions can influence modal interaction. Skewing of the material axis decreases the buckling temperatures of both laminates and, like fixed support conditions, causes increased postbuckling deflections. Skewing also influences modal interaction.

Meyers, C. A.↗

NASA NTRS1991

Thermal-structural panel buckling tests

A titanium-matrix-composite (TMC) hat-stiffened panel of 61 cm sq area and 3.175 cm thick was nondestructively tested to 649 C to examine its buckling characteristics. Compressive loads were applied to the panel in a 978.6 kN uniaxial load frame system. High-temperature testing was performed using quartz lamp heating. A single-strain-age force/stiffness buckling prediction technique was developed to predict panel buckling loads. For the monolithic panel, these test predictions correlated within 10 percent with a finite-element buckling analyses performed elsewhere. Comparisons between force/stiffness predictions and analyses for the TMC panel are in progress.

Thompson, Randolph C.↗

NASA NTRS1992

Scaling laws for buckling instability in monolayer networks

In this comment a power law is argued to govern the thickening of cell widths relative to their lengths in buckling monolayer networks. A scaling relation is derived for general instabilities in cellular networks, and a reply is given that questions the use of the amplitude of the buckling undulation in an already buckled wall in the Euler relation. Both treatments provided shed light on the stability/instability of wavelengths for buckling monolayer networks.

Noever, David A.↗

NASA NTRS1993

Compressive and shear buckling analysis of metal matrix composite sandwich panels under different thermal environments

Combined inplane compressive and shear buckling analysis was conducted on flat rectangular sandwich panels using the Raleigh-Ritz minimum energy method with a consideration of transverse shear effect of the sandwich core. The sandwich panels were fabricated with titanium honeycomb core and laminated metal matrix composite face sheets. The results show that slightly slender (along unidirectional compressive loading axis) rectangular sandwich panels have the most desirable stiffness-to-weight ratios for aerospace structural applications; the degradation of buckling strength of sandwich panels with rising temperature is faster in shear than in compression; and the fiber orientation of the face sheets for optimum combined-load buckling strength of sandwich panels is a strong function of both loading condition and panel aspect ratio. Under the same specific weight and panel aspect ratio, a sandwich panel with metal matrix composite face sheets has much higher buckling strength than one having monolithic face sheets.

Ko, William L.↗

NASA NTRS1991

Thermal buckling of symmetrically laminated composite plates

This paper discusses an investigation into the thermal buckling of symmetrically laminated composite plates. In this study thermal buckling is investigated for laminates under two different simple support conditions, fixed and sliding. These laminates are subjected to the conditions of a uniform temperature change, and a temperature change varying linearly along the length of the plate. The effects of the principal material axes not being aligned with the edges of the plate are also investigated. The buckling response is studied using variational methods, specifically the Trefftz criterion. A Rayleigh-Ritz formulation is used to obtain numerical results from the formulations for the prebuckling response and the buckling response.

Meyers, C. A.↗