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Simple, accurate buckling interaction formulae are presented for long orthotropic plates with either simply supported or clamped longitudinal edges and under combined loading that are suitable for design studies. The loads include 1) combined uniaxial compression (or tension) and shear, 2) combined pure inplane bending and 3) shear and combined uniaxial compression (or tension) and pure inplane bending. The interaction formulae are the results of detailed regression analysis of buckling data obtained from a very accurate Rayleigh-Ritz method.

Nondimensional parameters and equations governing the buckling behavior of rectangular symmetrically laminated plates are presented that can be used to represent the buckling resistance, for plates made of all known structural materials, in a very general, insightful, and encompassing manner. In addition, these parameters can be used to assess the degree of plate orthotropy, to assess the importance of anisotropy that couples bending and twisting deformations, and to characterize quasi-isotropic laminates quantitatively. Bounds for these nondimensional parameters are also presented that are based on thermodynamics and practical laminate construction considerations. These bounds provide insight into potential gains in buckling resistance through laminate tailoring and composite-material development. As an illustration of this point, upper bounds on the buckling resistance of long rectangular orthotropic plates with simply supported or clamped edges and subjected to uniform axial compression, uniform shear,...

A special-purpose, semi-analytical solution method for determining the stress and deformation fields in a thin laminated-composite cylindrical shell with an elliptical cutout is presented. The analysis includes the effects of cutout size, shape, and orientation; non-uniform wall thickness; oval-cross-section eccentricity; and loading conditions. The loading conditions include uniform tension, uniform torsion, and pure bending. The analysis approach is based on the principle of stationary potential energy and uses Lagrange multipliers to relax the kinematic admissibility requirements on the displacement representations through the use of idealized elastic edge restraints. Specifying appropriate stiffness values for the elastic extensional and rotational edge restraints (springs) allows the imposition of the kinematic boundary conditions in an indirect manner, which enables the use of a broader set of functions for representing the displacement fields. Selected results of parametric studies are presented for several geometric parameters that demonstrate that analysis approach is a powerful means for developing design criteria for laminated-composite shells.

An analysis-based approach for developing shell-buckling design criteria for laminated-composite cylindrical shells that accurately account for the effects of initial geometric imperfections is presented. With this approach, measured initial geometric imperfection data from six graphite-epoxy shells are used to determine a manufacturing-process-specific imperfection signature for these shells. This imperfection signature is then used as input into nonlinear finite element analyses. The imperfection signature represents a first-approximation mean imperfection shape that is suitable for developing preliminary-design data. Comparisons of test data and analytical results obtained by using several different imperfection shapes are presented for selected shells. These shapes include the actual measured imperfection shape of the test specimens, a first-approximation mean imperfection shape, with and without plus or minus one standard deviation, and the linear-bifurcation-mode imperfection shape. In addition, buckling interaction curves for composite shells subjected to combined axial compression and torsion loading are presented that were obtained by using the various imperfection shapes in the analyses. A discussion of the nonlinear finite element analyses is also presented. Overall, the results indicate that the analysis-based approach presented for developing reliable preliminary-design criteria has the potential to provide improved, less conservative buckling-load estimates and to reduce the weight and cost of developing buckling-resistant shell structures.

A combined complex potential-variational solution method is developed for the analysis of unsymmetrically laminated plates with finite planform geometry, subjected to arbitrary edge loads, and with an inclined elliptical cutout. This method uses complex potentials and their Laurent series expansions to reduce the potential energy of a plate to a contour integral that is evaluated numerically by the trapezoidal rule. A variational statement of equilibrium is applied to the potential energy to obtain a linear system of equations in terms of the unknown coefficients of the Laurent series, whose solutions yield the stress and displacement fields for a given problem. This approach represents a computationally efficient alternative to boundary collocation procedures that are typically used to solve problems based on complex potential theory. Comparisons are made with corresponding results obtained from finite element analysis for a square unsymmetrically laminated plate with a central inclined elliptical cutout and subjected to biaxial tension. The results confirm the validity of the solution method.

An approach for synthesizing buckling results and behavior for thin balanced and unbalanced symmetric laminates that are subjected to nondestabilizing mechanical preloads, uniform heating or cooling, and elastically or totally restrained axial thermal expansion or contraction is presented. This approach uses a nondimensional analysis for infinitely long, flexurally anisotropic plates that are subjected to combined loads and is based on useful nondimensional parameters. In addition, a stiffness-weighted laminate coefficient of thermal expansion is derived and used to determine critical temperatures in terms of physically intuitive mechanical buckling coefficients, and the effects of membrane orthotropy and membrane anisotropy are included. Many results are presented for some common laminates that are intended to facilitate a structural designer's transition to the use of the generic buckling design curves that are presented in the article. Several generic buckling design curves are presented that provide p...

The new Space Shuttle superlightweight external fuel tank e ew for the e rst time on 2 June 1998 (Space Transportation System-mission 91 ). We present results of elastic linear-bifurcation buckling and nonlinear analyses of one of its major components; that is, the liquid-oxygen tank. The contents include an overview of the structure and a brief description of the e nite element code that was used to conduct the analyses. Results are presented that illustrate three distinctly different types of nonlinearresponsephenomena for thin-walled shells that aresubjected to combined mechanical and thermal loads that launch-vehicle shell designers may encounter. A procedure is demonstrated that can beused by structural analysts and designers to obtain reasonable, conservative estimates of linear-bifurcation, buckling-load knockdown factors for shells that are subjected to complex loading conditions or to characterize the effects of initial geometric imperfections on nonlinear shell response phenomena. Results are also presented that show that the superlightweight liquid-oxygen tank can carry loads in excess of twice the values of the operational prelaunch loads considered and that a e uid-e lled launch-vehicle shell can be highly sensitive to initial geometric imperfections. Presentedherearee vepapersonlarge-scaleanalysesofacomplexshellstructure.Thee rst,longerpaper,“ NonlinearBehaviorofSpaceShuttleSuperlightweight Liquid-OxygenTankUnderPrelaunchLoads,” coversthestructure,theanalysistechnique,someloading cases,andexperimentalverie cationonthemethod.Itis followed by a companion paper, “ Modeling and NonlinearStructural Analysis of a Large-ScaleLaunch Vehicle,” which goes into greaterdepth on themethods, and then by three shorter papers, “ Effects of Welding-Induced Imperfections on Behavior of Space Shuttle Superlightweight Tank,” “ Nonlinear Behavior of Space Shuttle Superlightweight Tank Under Booster Ascent Loads,” and “ Nonlinear Behavior of Space Shuttle Superlightweight Tank Under End-of-Flight Loads,” covering interesting behaviorunder differing load cases. Thesepapersare intended to stand ontheir own (and hencehavesomeredundant introductory material) but are complementary to one another, and so they are presented here together.

Results of linear-bifurcation and nonlinear analyses of the Space Shuttle superlightweight (SLWT) external liquid-oxygen (LO2) tank for an important early booster ascent loading condition are presented. These results for thin-walled linear elastic shells that are subjected to combined mechanical and thermal loads illustrate an important type of response mode that may be encountered in the design of other liquid-fuel launch vehicles. Linear-bifurcation analyses are presented that predict several nearly equal eigenvalues that correspond to local buckling modes in the forward ogive section of the LO 2 tank. In contrast, the nonlinear response phenomenon is shown to consist of short-wavelength bending deformations in the forward-ogive and barrel sections of the LO2 tank that grow in amplitude in a stable manner with increasing load. Imperfection sensitivity analyses are presented that show that the presence of several nearly equal eigenvalues does not lead to a premature general instability mode for the forward-ogive section. For the linear-bifurcation and nonlinear analyses, the results show that accurate predictions of the response of the shell generally require a large-scale, high-e delity, e nite element model, and that a design based on a linear-bifurcation buckling analysis and a buckling-load knockdown factor is overly conservative. Results are presented that show that the SLWT LO 2 tank can support loads in excess of approximately 2.6 timesthevaluesof theoperationalloads considered. In addition, results are presented that show that local bending deformations may cause failure of the thermal protection system (TPS) at load levels less than the load level corresponding to structural collapse. Results are presented that can be used to estimate the load level at which TPS failure is likely to occur.

Results of linear-bifurcation buckling and nonlinear analyses of the Space Shuttle superlightweight external liquid-oxygen tank are presented for an important prelaunch loading condition. These results show the effects of actual, measured welding-induced initial geometric imperfections on an important response mode for thin-walled shellsthataresubjectedtocombinedmechanicalandthermalloads.Thistypeofinitialgeometricimperfectionmay be encountered in the design of other liquid-fuel launch vehicles. Results are presented that show that the liquidoxygen tank will buckle in the barrel section, but at load levels nearly four times the magnitude of the operational load level, and will exhibit stable postbuckling behavior. The actual measured imperfections are located in this sectionofthetank. Resultsofimperfection sensitivity analysesarepresented thatshowthat thelargestdegradation in the apparent membrane stiffnesses of the liquid-oxygen tank barrel section is caused by an imperfection shape that is in the form of the linear-bifurcation buckling mode with a relatively small amplitude. These results also show that the effect of the relatively large-amplitude measured imperfection is benign.

Results of elastic, linear-bifurcation buckling and nonlinear analyses of the new Space Shuttle superlightweight external liquid-oxygen tank are presented for an important end-of-e ight loading condition. These results illustrate an important type of response mode for thin-walled shells subjected to combined mechanical and thermal loads that may be encountered in the design of other liquid-fuel launch vehicles. Linear-bifurcation buckling analyses are presented that predict several nearly equal eigenvalues that correspond to local buckling modes in the aft dome of the liquid-oxygen tank. In contrast, the nonlinear response phenomenon is shown to consist of a shortwavelength bending deformation in the aft elliptical dome of the liquid-oxygen tank that grows in amplitude in a stable manner with increasing load. Imperfection sensitivity analyses are presented that show that the presence of several nearly equal eigenvalues does not lead to a premature general instability mode for the aft dome. For the linear-bifurcation and nonlinear analyses, the results show that accurate predictions of the response of the shell generally require a large-scale, high-e delity, e nite element model, and that a design based on a linear-bifurcation buckling analysis and a buckling-load knockdown factor is overly conservative. Results are also presented that showthatthesuperlightweightliquid-oxygentankcansupportloadsin excessofapproximately1.9 timesthevalues of the operational loads considered.

The results of a study of the vibration response of transversely isotropic flat and curved panels subjected to temperature fields and to mechanical loads into the postbuckling load range are presented. The results were obtained using a higher-order transverse-shear-deformation theory of shallow shells that includes the effects of geometric nonlinearities and initial geometric imperfections. The results focus on the interaction between the temperature field, the applied mechanical load, and the fundamental frequency associated with small vibrations about the prebuckling and postbuckling equilibrium states. Results are presented for a wide range of temperatures and mechanical load magnitudes and of geometric parameters. The results show that transverse-shear flexibility has a significant effect on the analytical prediction of panel response and that the fundamental frequency of a panel may be substantially overestimated in the prebuckling load range and underestimated in the postbuckling load range. Results are also presented that indicate that the fundamental frequency of flat panels generally increases as the initial geometric imperfection amplitude increases for both the prebuckling and postbuckling load ranges. The results, however, also indicate that the fundamental frequency of curved panels generally decreases in the prebuckling load range and increases in the postbuckling load ranges.

The results of a parametric study of the vibration behavior of flat and shallow curved panels subjected to temperature fields and mechanical loads are presented. The mechanical loads include uniform axial-compression prebuckling loads and transverse lateral pressure. The temperature fields include spatially nonuniform heating over the panel surfaces and a linear through-the-thickness temperature gradient. The structural analysis used for the study is based on a higher order transverse-shear-deformation shallow-shell theory that includes the effects of geometric nonlinearities and initial geometric imperfections. Analytical results are presented for simply supported single-layer and three-layer panels made from transversely isotropic materials. The results identify the interaction of the applied thermal and mechanical loads with the fundamental frequencies in both the prebuckling and postbuckling equilibrium states. The results indicate that initial geometric imperfections, transverse-shear flexibility, and changes in curvature are important contributors to the response of a panel for a wide range of structural and loading parameters.

Buckling loads for long isotropic and laminated cylinders are calculated based on Euler, Fluegge and Donnell's equations. Results from these methods are presented using simple parameters useful for fundamental design work. Buckling loads for two types of simply supported boundary conditions are calculated using finite element methods for comparison to select cases of the closed form solution. Results indicate that relying on Donnell theory can result in an over-prediction of buckling loads by as much as 40% in isotropic materials.

Structural stability is a major consideration in the design of lightweight shell structures. However, the theoretical predictions of geometrically perfect structures often considerably over predict the buckling loads of inherently imperfect real structures. It is reasonably well understood how the shell geometry affects the imperfection sensitivity of axially compressed cylindrical shells; however, the effects of shell anisotropy on the imperfection sensitivity is less well understood. In the present paper, the development of an analytical model for assessing the imperfection sensitivity of axially compressed orthotropic cylinders is discussed. Results from the analytical model for four shell designs are compared with those from a general-purpose finite-element code, and good qualitative agreement is found. Reasons for discrepancies are discussed, and potential design implications of this line of research are discussed.

A parametric study of the buckling behavior of infinitely long symmetrically laminated anisotropic plates subjected to combined loadings is presented. The loading conditions considered are pure in-plane bending, transverse tension and compression, and shear. Results obtained using a special purpose analysis that is well suited for parametric studies are presented for clamped and simply supported plates. Moreover, results are presented for some common laminate constructions, and generic buckling design charts are presented for a wide range of useful nondimensional parameters.

The Space Shuttle Challenger (STS 51-L) accident led to an intense investigation of the structural behavior of the solid rocket booster (SRB) tang and clevis field joints. Results are presented of axisymmetric shell analyses that parametrically assess the structural behavior of SRB field joints subjected to quasi-steady-state internal pressure loading for both the original joint flown on mission STS 51-L and the redesigned joint flown for the first time after the STS 51-L accident on the Space Shuttle Discovery. Discussion of axisymmetric shell modeling issues and details is presented and a generic method for simulating contact between adjacent shells of revolution is described. Results are presented that identify the performance trends of the joints for a wide range of joint parameters. An important finding is that the redesigned joint exhibits significantly smaller O-ring gap changes and much less sensitivity to joint clearances than the original joint. For a wide range of joint parameters, the result presented indicate that the redesigned joint provides a much better pressure seal than the original joint.

Results that illustrate the use of a video-image-correlation-based displacement and strain measurement system to assess the effects of material nonuniformities on the behavior of the sprayed-on foam insulation (SOFI) used for the thermal protection system on the Space Shuttle External Tank are presented. Standard structural verification specimens for the SOFI material with and without cracks and subjected to mechanical or thermal loading conditions were tested. Measured full-field displacements and strains are presented for selected loading conditions to illustrate the behavior of the foam and the viability of the measurement technology. The results indicate that significant strain localization can occur in the foam because of material nonuniformities. In particular, elongated cells in the foam can interact with other geometric or material discontinuities in the foam and develop large-magnitude localized strain concentrations that likely initiate failures. Furthermore, some of the results suggest that continuum mechanics and linear elastic fracture mechanics might not adequately represent the physical behavior of the foam, and failure predictions based on homogeneous linear material models are likely to be inadequate.

A multi-scale analysis of the structural stability of a carbon nanotube-polymer composite material is developed. The influence of intrinsic molecular structure, such as nanotube length, volume fraction, orientation and chemical functionalization, is investigated by assessing the relative change in critical, in-plane buckling loads. The analysis method relies on elastic properties predicted using the hierarchical, constitutive equations developed from the equivalent-continuum modeling technique applied to the buckling analysis of an orthotropic plate. The results indicate that for the specific composite materials considered in this study, a composite with randomly orientated carbon nanotubes consistently provides the highest values of critical buckling load and that for low volume fraction composites, the non-functionalized nanotube material provides an increase in critical buckling stability with respect to the functionalized system.

An approach for synthesizing buckling results and behavior for thin balanced and unbalanced symmetric laminates that are subjected to uniform axial compression loads and elastically restrained against inplane expansion, contraction, and shear deformation is presented. This approach uses a nondimensional analysis for infinitely long, flexurally anisotropic plates (coupling between bending and twisting) that are subjected to combined mechanical loads and is based on nondimensional parameters. In addition, nondimensional loading parameters are derived that account for the effects of the elastic inplane deformation restraints, membrane orthotropy, and membrane anisotropy on the induced prebuckling stress state. The loading parameters are used to determine buckling coefficients that include the effects of flexural orthotropy and flexural anisotropy. Many results are presented, for some selected laminates, that are intended to facilitate a structural designer’s transition to the use of the generic buckling-design curves that are presented and discussed in the paper. Several buckling response curves are presented that provide physical insight into the behavior for combined loads, in addition to providing useful design data. An example is presented that demonstrates the use of the generic design curves, which are applicable to a wide range of laminate constructions. The analysis approach and generic results indicate the effects and characteristics of laminate orthotropy and anisotropy in a very general and unifying manner.

An approach for synthesizing buckling results for, and behavior of, thin balanced and unbalanced symmetric laminates that are subjected to uniform heating or cooling and elastically restrained against thermal expansion or contraction is presented. This approach uses a nondimensional analysis for infinitely long, flexurally anisotropic plates that are subjected to combined mechanical loads and is based on useful nondimensional parameters. In addition, stiffness-weighted laminate thermal-expansion parameters and compliance coefficients are derived that are used to determine critical temperatures in terms of physically intuitive mechanical-buckling coefficients. The effects of membrane orthotropy and membrane anisotropy are included in the general formulation. Many results are presented for some common laminates that are intended to facilitate a structural designer's transition to the use of generic buckling design curves. Several curves that illustrate the fundamental parameters used in the analysis are presented, for nine contemporary material systems, that provide physical insight into the buckling response in addition to providing useful design data. Examples are presented that demonstrate the use of generic design curves. The analysis approach and generic results indicate the effects and characteristics of elastically restrained laminate thermal expansion or contraction, membrane orthotropy and anisotropy, and flexural orthotropy and anisotropy in a very general and unifying manner.

Results from a numerical and experimental study that illustrate the effects of selected cutout reinforcement configurations on the buckling and failure response of compression-loaded composite cylindrical shells with a cutout are presented. The effects of reinforcement size, thickness, and orthotropy on the overall response of compression-loaded shells are described. In general, reinforcement around a cutout in a compression-loaded shell can retard or eliminate the local buckling response and material failure near the cutout and increase the buckling load of the shell. However, some results show that certain reinforcement configurations can cause a significant increase in the local interlaminar failures that can accumulate near the free edges of a cutout during a local buckling event.

An approach for synthesizing buckling results and behavior for thin balanced and unbalanced symmetric laminates that are subjected to uniform heating or cooling and fully restrained against thermal expansion or contraction is presented. This approach uses a nondimensional analysis for infinitely long, flexurally anisotropic plates that are subjected to combined mechanical loads and is based on useful nondimensional parameters. In addition, stiffness-weighted laminate thermal-expansion parameters are derived that are used to determine critical temperatures in terms of physically intuitive mechanical buckling coefficients, and the effects of membrane orthotropy and membrane anisotropy are included. Many results are presented for some common laminates that are intended to facilitate a structural designer's transition to the use of the generic buckling design curves that are presented in the paper. Several generic buckling design curves are presented that provide physical insight into the buckling response in addition to providing useful design data. Examples are presented that demonstrate the use of the generic design curves. The analysis approach and generic results indicate the effects and characteristics of laminate thermal expansion, membrane orthotropy and anisotropy, and flexural orthotropy and anisotropy in a very general and unifying manner.

The results of an analytical study of the nonlinear and buckling response characteristics of curved panels subjected to combined loads are presented. Aluminum and laminated composite panels are considered in the study and a flat and shallow curved panel configurations are considered as well. The panels are subjected to combined axial compression and transverse tension or compression loads or combined axial compression and inplane shear loads. Results illustrating the effects of various combined load states on the buckling response of the panels are presented. In addition, results illustrating the effects of laminate orthotropy and anisotropy and panel curvature on the panel response are presented. The results indicate that panel curvature can have a significant effect on the nonlinear and buckling behavior of the panels subjected to combined loads. Results are included that show that geometrically perfect panels do not exhibit bifurcation points for some combined loads. Results are also presented that show the effects of laminate orthotropy and anisotropy on the interaction of combined loads.

An analytical, parametric study of the attenuation of bending boundary layers or edge effects in balanced and unbalanced, symmetrically and unsymmetrically laminated thin cylindrical shells is presented for nine contemporary material systems. The analysis is based on the linear Sanders-Koiter shell equations and specializations to the Love-Kirchhoff shell equations and Donnell's equations are included. Two nondimensional parameters are identified that characterize and quantify the effects of laminate orthotropy and laminate anisotropy on the bending boundary-layer decay length in a very general and encompassing manner. A substantial number of structural design technology results are presented for a wide range of laminated-composite cylinders. For all the laminate constructions considered, the results show that the differences between results that were obtained with the Sanders-Koiter shell equations, the Love-Kirchhoff shell equations, and Donnell's equations are negligible. The results also show that the effect of anisotropy in the form of coupling between pure bending and twisting has a negligible effect on the size of the bending boundary-layer decay length of the balanced, symmetrically laminated cylinders considered. Moreover, the results show that coupling between the various types of shell anisotropies has a negligible effect on the calculation of the bending boundary-layer decay length in most cases. The results also show that in some cases neglecting the shell anisotropy results in underestimating the bending boundary-layer decay length and in other cases it results in an overestimation.

The advantages of using a hierarchical analysis approach to calculate the buckling load of an axially compressed composite cylindrical shell is demonstrated using an example taken from a recent experimental program. The Delft Interactive Shell DEsign COde (DISDECO) shell design code is used for this hierarchical analysis approach to provide an accurate prediction of the critical buckling load of the actual shell structure. DISDECO includes the influence of the boundary conditions, initial geometric imperfections, the effects of stiffener and load eccentricities, and the effects of prebuckling deformations caused by edge constraints in the analysis. It is shown that the use of DISDECO makes it relatively simple to proceed step by step from simple to more complex models and solution procedures. As a final step in the hierarchical analysis approach, the critical buckling load and the estimated imperfection sensitivity of the shell are verified by conducting an analysis of a large finite element model with one of the current generation two-dimensional shell analysis codes with advanced capabilities needed to represent both geometric and material nonlinearities.

Results from a numerical and experimental study of the response of compression-loaded quasi-isotropic curved panels with a centrally located circular cutout are presented. The numerical results were obtained by using a geometrically nonlinear finite element analysis code. The effects of cutout size, panel curvature and initial geo- metric imperfections on the overall response of compression-loaded panels are described. In addition, results are presented from a numerical parametric study that indicate the effects of elastic circumferential edge restraints on the prebuckling and buckling response of a selected panel and these numerical results are compared to experimentally measured results. These restraints are used to identify the effects of circumferential edge restraints that are introduced by the test fixture that was used in the present study. It is shown that circumferential edge restraints can introduce substantial nonlinear prebuckling deformations into shallow compression-loaded curved panels that can results in a significant increase in buckling load.

NONLINEAR ANALYSIS OF THE SPACE SHUTTLE SUPERLIGHTWEIGHTLO 2 TANK: PART I - BEHAVIOR UNDER BOOSTER ASCENT LOADSRichard D. Young, Michael P. Nemeth, Timothy J. Collins, and James. H. Starnes, Jr.NASA Langley Research CenterHampton, Virginia 23681-0001Presented at the 39th AIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics, and Material ConferenceAIAA Paper No. 98-1838Long Beach, CahforniaApril 20-23, 1998

A parametric study is presented of the buckling behavior of infinitely long symmetrically laminated anisotropic plates subjected to combined loads. The study focuses on the interaction of a subcritical (stable) secondary loading state of constant magnitude and a primary destabilizing load that is increased in magnitude until buckling occurs. The loads, considered in this report are uniform axial compression, pure in-plane bending, transverse tension and compression, and shear. Results are presented that were obtained by using a special purpose nondimensional analysis that is well suited for parametric studies of clamped and simply supported plates. In particular, results are presented for a +/- 45(sub S) graphite-epoxy laminate that is highly anisotropic and representative of a laminate used for spacecraft applications. In addition, generic buckling-design charts are presented for a wide range of nondimensional parameters that are applicable to a broad class of laminate constructions. These results show the general behavioral trends of specially orthotropic plates and the effects of flexural anisotropy on plates subjected to various combined loading conditions. An important finding of the present study is that the effects of flexural anisotropy on the buckling resistance of a plate can be significantly more important for plates subjected to combined loads than for plates subjected to single-component loads.

The buckling and postbuckling behaviour of thin plates with a cut-out and made of advanced composite materials are research topics of great practical importance. For example, composite plate-like subcomponents with cut-outs are being considered for use in many types of aerospace structures owing to their high stiffness-to-weight and strength-to-weight properties. These properties could ultimately yield substantial weight savings for aircraft structures.

A parametric study of the buckling behavior of infinitely long symmetrically laminated anisotropic plates subjected to combined loadings are presented. The loading conditions considered are pure inplane bending, transverse tension and compression, and shear. Results obtained using a special purpose analysis are presented for clamped and simply supported plates. An important finding of the study is that the effects of anisotropy are much more pronounced in shear-loaded plates than in axial compression-loaded plates and plates loaded by pure inplane bending.

An experimental study of the buckling and postbuckling behavior of square and rectangular compression loaded aluminum plates with centrally located circular, square, and elliptical cutouts is presented. Experimental results indicate that the plates exhibit overall trends of increasing buckling strain and decreasing initial postbuckling stiffness with increasing cutout width. Corresponding plates with circular and square cutouts of the same width buckle at approximately the same strain level, and exhibit approximately the same initial postbuckling stiffness. Results show that the reduction in initial postbuckling stiffness due to a cutout generally decreases as the plate aspect ratio increases. Other results presented indicate that square plates with elliptical cutouts having a large cutout-width-to-plate-width ratio generally lose prebuckling and initial postbuckling stiffness as the cutout height increases. However, the plates buckle at essentially the same strain level. Results also indicate that postbuckling stiffness is more sensitive to changes in elliptical cutout height than are prebuckling stiffness and buckling strain.

A simple, rational approach is presented for developing micropolar beam models for large repetitive beam-like planar lattices with rigid joints. The micropolar beam models have independent microrotation, and displacement fields and are characterized by their strain and kinetic energies, from which the equations of motion and boundary conditions can be derived. The procedure for developing the expression for the strain energy of the micropolar beam involves introducing basic assumptions regarding the variation of the displacement and microrotation components in the plane of the cross-section and obtaining effective elastic coefficients of the continuum in terms of the material properties and geometry of the original lattice structure. The high accuracy of the solutions obtained by the micropolar beam models is demonstrated by means of numerical examples.

Micropolar beam models are developed for the static, free vibration and buckling analysis of repetitive spatial beamlike lattices with rigid joints. The micropolar beam models have independent microrotation and displacement fields and are characterized by their strain energy, potential energy due to initial stresses and kinetic energy from which the governing differential equations and boundary conditions can be derived. The procedure for developing the expression for the strain energy of the micropolar beam involves introducing basic assumptions regarding the variation of the displacement and microrotation components in the plane of the cross-section, and obtaining effective elastic coefficients of the continuum in terms of the material properties and geometry of the original lattice structure. The high accuracy of the solutions obtained by the micropolar beam models is demonstrated by means of numerical examples for vierendeel and double-laced lattice girders with triangular cross-sections.