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Shell structures are important components of airplanes, missiles, and space vehicles, but present capabilities for predicting the local and general instability of many such structures are inadequate. A large effort continues to be devoted to the stability analysis of shell structures, and considerable progress has been made. Results are slowly disseminated, however, and many engaged in research are not fully cognizant of the problems and practices of the vehicle designers who utilize research results. Therefore, an NASA SYMPOSIUM ON INSTABILITY OF SKELL STRUCTURES was organized by the Langley Research Center with sessions held there on October 24 and 25, 1962. Participants were limited to persons contributing papers and to certain officials of the U.S. Government. This symposium was planned to provide those persons concerned with shell instability at research laboratories, at educational institutions, and in the aerospace industry with a comprehensive view of the present state of the art, including the voids in present knowledge, important current problems, and the most fruitful directions for future theoretical and experimental research on the instability of all types of shell structures. Individuals actively engaged in research on shell stability or design were invited to contribute written papers for inclusion in a compilation to be distributed to the participants prior to the symposium. A few papers were selected by a steering committee for oral presentation at the symposium. Provision was made, also, for a discussion of all papers.

Engineering science in space - Conference, Huntsville, Alabama, October-November 1967

Design, engineering, and flight history of mariner ii space probe

Conference on aircraft loads, flutter, buffeting, and structures

Conference on aircraft loads, flutter, and structures

The design of lightweight, efficient structures is one of the fundamental requirements for achievement of high performance in military aircraft. In this paper some of the structural and materials considerations that are important to the strength, weight, and integrity of aircraft structures are reviewed. A comparison of some structural materials is made on the basis of weight-strength and tear resistance. In the area of structural design, the relative weights of several types of construction that are of current interest are reviewed and the influence of different materials and the effects of the related temperatures on structural weight are indicated. Lastly, other factors that are of importance in structural design of future aircraft are discussed. These include strength under nonuniform temperatures, creep, sonic fatigue, and panel flutter.

Equations of motion are derived for use in simulating a spacecraft or other complex electromechanical system amenable to idealization as a set of hinge-connected rigid bodies of tree topology, with rigid axisymmetric rotors and nonrigid appendages attached to each rigid body in the set. In conjunction with a previously published companion paper on finite-element appendage vibration equations, this paper provides a complete minimum-dimension formulation suitable for generic programming for digital computer numerical integration.

The results are presented of a study to obtain a computer program for the penetration of a thin plate of aluminum by a sphere of rock. The study was divided into two projects. One project covers the initial impact, the crushing of the sphere of rock, the break up of the aluminum sheet, and the conversion of the sufficiently shock-compressed regions of rock and aluminum into a plasma. The other project considers the ejection of a cone of plasma with entrained particles from the impact zone, its expansion as it traverses a region of free space, and its impact on a stack of paper sheets. The ablation of fragments in penetrating the stack of paper sheets is also considered.

The Space Shuttle represents the focus of NASA development endeavors for the next decade. The purpose of the shuttle is to provide a general launch capability for a variety of payloads ranging in weight to as high as 65,000 pounds. This paper concentrates on one aspect of the shuttle development, namely, dynamics and aeroelasticity. The objective of our research during the first year of activity has been directed at searching out problems peculiar to the Space Shuttle, reviewing the state of the art, and developing a program to satisfy the needs. Some of the specific items covered in this paper are vibration modes, thermal protection system dynamics, fluid dynamics, ground winds, flutter, buffet, and noise.

Two test incidents involving instability of large scale commercially built structures are described. Two classes of structure are discussed; the first, a fuselage with skin designed to buckle at low stress, and the second, a wing whose surface remains unbuckled to failure. The structure in the region of failure is defined and the failures described and illustrated. Insofar as possible, the stresses in the critical area at the time of failure are reported and compared to strength determined by analysis. Both fuselage and wing surfaces were observed to fail in the mode of a medium range column when adequate support was provided by ribs and frames. Initial failure in the wing example was premature due to a design deficiency in rib strength. A clear illustration is given of the effect of rib stiffness on wing surface stability. Adding stiffness to wing ribs increases the limit of surface stability to the theoretical flat panel value.

The differential equations which must be solved to predict the buckling load are reviewed. The different possible physical interpretations of these equations are discussed.

A brief discussion is presented of three structural shell stability studies in progress at Lockheed Missiles & Space Company: the stabilizing influence of solid propellants, the effect of cushion stiffness on buckling under cushion loading, and the snap-through buckling of axially loaded cylinders. Recent analytical results are compared with test data. Also included is a brief description of a few shell stability problems of present interest to LMSC for which satisfactory methods of analysis are not available.

A presentation is made which highlights several current shell stability problems. A searching reappraisal of shell stability research is advocated in the light of the current rapidly mounting intensity of shell research which in many cases is disproportionately academic and non-design orientated.

General instability in shell type structures is a relatively infrequent phenomenon. By general instability is meant that a complete section of a structure becomes elastically unstable, as compared with local crippling or buckling. The first step in design is to rough size the structure and determine its compatibility with air vehicle configuration and system instillations. After this step has been completed, it is possible to survey the layouts to determine whether general instability is likely to occur. The general parameters of length, diameter, frame spacing, element stiffness, etc., are than investigated to determine if a general failing stress exists which is less than any local column, beam column, or panel failing stress. In this way, a well-balanced design is determined and general stability failing modes eliminated.

Some theoretical investigations of buckling of elastic shells are surveyed in this report. Only geometrically perfect shells are considered; initial dents and out-of-roundness are not taken into account. Several questions raised by the studies are: (a) Under what conditions is the infinitesimal theory of buckling of shells adequate? (b) How does the energy theory of buckling of shells correlate with the method based on equilibrium equations for bending moments, tensions, and shears in a buckled configuration? (c) How important are nonlinear terms in the tangential displacements u, v in the strain-displacement relations for buckling and post-buckling studies? (d) How important are the boundary conditions for u, v in affecting stability? (e) If a condition of snap-through is approached, how much external work is required to push the shell "over the hump" into the buckled configuration? (f) How reliable are mathematical approximations used previously in the infinitesimal theory of buckling of shells? Tentative and incomplete answers to some of these questions are suggested.

Techniques have been developed for making essentially "perfect" thin cylindrical shells and for making shells with definite types of initial deformations. The "perfect" shells give buckling stresses much higher than have previously been obtained. Initial deformations of the form ∆R= a(o) sin ((πx)/L) have been tested and ranges of positive a(o) were found in which there was no lowering of the buckling stress. Negative values of a(o) caused a decrease in the failure load. A theoretical solution which indicated the same trends as were found experimentally has been carried out.

The problem of optimum design of axially compressed cylinders stiffened by rings and stringers is discussed. Particular attention is devoted to configurations suitable for large launch vehicles. Consideration is given to the analytical techniques for determining strength as well as the procedure for optimization.

Investigations carried out at STL on three current problems involving instability of thin shells in applications to aerospace vehicles are discussed. The first concerns the experimental determination of the buckling behavior of longitudinally stiffened pressurized cylinders; the second, the analytic prediction and experimental confirmation of the buckling behavior of multi-layer cylinders and the third involves the behavior of cylinders under combined axial load and lateral pressure. In each case the background of the application is reviewed, followed by a short description of the work. It is indicated that the longitudinally stiffened cylinder shows considerable promise in taking maximum advantage of the strengthening effect of internal pressure, that the use of an external low modulus layer as an insulator can have a significant effect on the buckling capability of a shell, and that the assumption of a linear interaction for pressure and axial load is unnecessarily conservative.

An account of the approach used in design of a large sandwich construction nose cone is given. The areas in which analytical methods are needed are discussed and a theoretical procedure is proposed.

Design relationships have been derived for the determination of elastic buckling strength levels for unpressurized monocoque truncated cones under axial compression. Theoretical implications have been considered in the establishment of a semi-empirical analysis leading to the development of probability based design expressions. Data from 170 tests by various investigators were statistically evaluated for the expected mean, 90%, and 99% probability strength levels. Dispersion of data was found to be slightly less than that of monocoque cylinders. Non-linear effects of radius to thickness ratio or strength deterioration with length to radius ratio were not discernible.

A discussion of the current methods used to design the Saturn type booster shell structures is presented covering bending and axial compression, with and without internal pressure. Problem areas encountered in the application of available shell stability data to these designs are delineated; as well as, suggested areas of future research for shell configurations anticipated in advanced designs.

In the present paper is examined the method of investigating the stability of plates and shells beyond the elastic limit, that proceeds from the generalization of the Hencky-Mises theory of elastico-plastic deformations given in the works of Smirnov-Alyayev, Schmidt, and in our papers.

The paper discusses the application of the variational equation to nonlinear finite element analysis. The problem of beam vibration with large deflection is considered. The variational equation is shown to be flexible in both the solution of a general problem and in the finite element formulation. Difficulties are shown to arise when Galerkin's equations are used in the consideration of the finite element formulation of two-dimensional linear elasticity and of the linear classical beam.

Experiments have shown that fatigue cracks close at positive loads during constant-amplitude load cycling. The crack-closure phenomenon is caused by residual plastic deformations remaining in the wake of an advancing crack tip. The present paper is concerned with the application of a two-dimensional, nonlinear, finite-element analysis for predicting crack-closure and crack-opening stresses during cyclic loading. A two-dimensional finite-element computer program, which accounts for both elastic-plastic material behavior and changing boundary conditions associated with crack extension and intermittent contact of the crack surfaces under cyclic loading, has been developed. An efficient technique to account for changing boundary conditions was also incorporated into the nonlinear analysis program. This program was subsequently used to study crack extension and crack closure under constant-amplitude and two-level block loading. The calculated crack-closure and crack-opening stresses were qualitatively consistent with experimental observations.

Vibroacoustic testing was performed on the orbital workshop dynamic test article and the payload assembly, the two major elements of the Skylab payload. The testing was conducted on each of the Skylab elements separately in the reverberation chamber at the Johnson Space Center. The two test configurations were high fidelity flight article simulations. The testing was conducted in two phases; in the first phase, acoustic tests were performed at levels simulating the lift-off and atmospheric flight acoustic criteria. In the second phase, low frequency sinusoidal vibration tests were conducted to obtain modal response data. The objectives of the Skylab vibroacoustic test program were to: verify the vibration design and test criteria; qualify selected flight components to the vibroacoustic criteria; and verify analytical models used for dynamic load analyses. This paper describes the vibroacoustic testing and discusses the results.

A summary of papers is presented which covers the following broad aspects of high temperature metal fatigue: (1) materials development and characterization; (2) environmental factors, including air, vacuum, helium, iodine, sodium, and radiation environments; (3) general fatigue life relationships; (4) crack growth laws; (5) design code activities; and (6) design and service experience. Illustrative tables accompany the summary.

The plane elastostatic problem for two bonded half planes containing an arbitrarily oriented crack in the neighborhood of the interface is considered. Using Mellin Transforms the problem is formulated as a system of singular integral equations. The equations are solved for various crack orientations, material combinations, and external loads. The numerical results given in the paper include the stress intensity factors, the strain energy release rates, and the probable clevage angles giving the direction of crack propagation.

This paper presents the formulation and check-out problems for a computer code DYNAPLAS, which analyzes the large deflection elastic-plastic dynamic response of stiffened shells of revolution. The formulation for spacial discretization is by the finite element method with finite differences being used for the evaluation of the pseudo forces due to material and geometric nonlinearities. Time integration is by the Houbolt method or central differences. The stiffeners may be due to concentrated or distributed eccentric rings and spring supports at arbitrary angles around the circumference of the elements. Check-out problems include the comparison of solutions from DYNAPLAS with experimental and other computer solutions for rings and conical and cylindrical shells. A hypothetical submarine including stiffeners and missile tube is studied under a combination of hydrostatic and dynamically applied asymmetrical pressure loadings.

This paper describes the latest addition to the STARS system of computer programs, STARS-2P, for the plastic, large deflection analysis of axisymmetrically loaded shells of revolution. The STARS system uses a numerical integration scheme to solve the governing differential equations. Several unique features for shell of revolution programs that are included in the STARS-2P program are described. These include orthotropic nonlinear kinematic hardening theory, a variety of shell wall cross sections and discrete ring stiffeners, cyclic and nonproportional mechanical and thermal loading capability, the coupled axisymmetric large deflection elasto-plastic torsion problem, an extensive restart option, arbitrary branching capability, and the provision for the inelastic treatment of smeared stiffeners, isogrid, and waffle wall constructions. To affirm the validity of the results, comparisons with available theoretical and experimental data are presented.

The paper deals with the initiation, growth, and possible arrest of fracture in shell structures containing initial defects which may be approximated by an isolated part-through crack. The main study is restricted to the structures in which the net section of the shell wall around the defect zone is fully yielded. The problem is solved by using an 8th order shallow shell theory with a conventional plastic strip model to account for the plastic deformations. Using the critical COD or the plastic instability as fracture criterion, the results are applied to the fracture propagation and arrest in shells. The calculated results are then compared with those obtained from the experiments on zircaloy, aluminum, and steel pipes.

Several aspects of adhesive-bonded joint analysis and design are presented from the reference of size of structure or load intensity. This integrates the individual characterizations of double-lap, single-lap, stepped-lap, tapered-lap and scarf joints. The paper includes an overview of bonded joint selection from the standpoints of design, fabrication, and processing, each bearing in mind the influence of such considerations on the strength of the joint. A case study is presented of the optimization of a specific relatively thick titanium-to-graphite epoxy stepped-lap joint, using the digital computer analysis program A4EG. The factors accounted for are adhesive plasticity, adherend stiffness imbalance, adherend thermal mismatch, and change of material properties within the range of temperature environment and with load direction. The strength increases obtainable by refining the initial design are demonstrated.

A review and assessment of the state of the art in automated aeroelastic design is presented. Most of the aeroelastic design studies appearing in the literature deal with flutter, and, therefore, this paper also concentrates on flutter. The flutter design problem is divided into three cases: as isolated flutter mode, neighboring flutter modes, and a hump mode which can rise and cause a sudden, discontinuous change in the flutter velocity. Synthesis procedures are presented in terms of techniques that are appropriate for problems of various levels of difficulty. Current trends, which should result in more efficient, powerful and versatile design codes, are discussed. Approximate analysis procedures and the need for simultaneous consideration of multiple design requirements are emphasized.

The buckling of shallow spherical shells under pressure has been the subject of many theoretical and experimental papers. Experimental data above the theoretical buckling load of Huang have given rise to speculation that shallow shell theory may not adequately predict the stability of nonsymmetric modes in higher-rise shells which are normally classified as shallow by the Reissner criterion. This article considers holographic interferometry as a noncontact, high-resolution method of measuring prebuckling deformations. Prebuckling deformations of a lambda = 9, h/b = 0.038 shell are Fourier-analyzed. Buckling is found to occur in an N = 5 mode as predicted by Huang's theory. The N = 4 mode was unusually stable, suggesting that even at this low value of h/b, stabilizing effects may be at work.

This paper reviews some recent applications of the concept of reinforcing metal structures with advanced filamentary composites, and presents some results of an experimental investigation of the tensile behavior of aluminum and titanium reinforced with unidirectional boron/epoxy. Results are given for tubular and flat specimens, bonded at either room temperature or elevated temperature. The composite reinforced metals showed increased stiffness over the all-metal counterpart, as predicted by the rule of mixtures, and the results were independent of specimen geometry. The tensile strength of the born/epoxy reinforced metals is shown to be a function of the geometry of the test specimen and the method of bonding the composite to the metal.

Two aspects of the geometrically nonlinear analysis of laminated composite shells are considered in this paper. The first pertains to the simplifications and computational advantages resulting from the use of group-theoretic methods in conjunction with computerized symbolic (algebraic) manipulation in the element development. The second aspect pertains to the combined effects of shear deformation and nonlinearity on the accuracy and convergence of two-dimensional, shear-flexible stiffness finite element models.

The present paper provides a unified, general presentation of the basic theory of the buckling and post-buckling behavior of elastic structures in a form suitable for application to a wide variety of special problems. The notation of functional analysis is used for this purpose. Before the general analysis, simple conceptual models are used to elucidate the basic concepts of bifurcation buckling, snap buckling, imperfection sensitivity, load-shortening relations, and stability. The energy approach, the virtual-work approach, and mode interaction are discussed. The derivations and results are applicable to continua and finite-dimensional systems. The virtual-work and energy approaches are given separate treatments, but their equivalence is made explicit. The basic concepts of stability occupy a secondary position in the present approach.

This paper gives an overview of the development and status of an improved numerical process for the solution of solid mechanics problems. The proposed process uses a mixed formulation with the fundamental unknowns consisting of both stress and displacement parameters. The problem is formulated either by means of first-order partial differential equations or in a variational form by using a Hellinger-Reissner-type mixed variational principle. For presentation purposes, the components of a numerical process are characterized and the criteria for an ideal process are outlined. Commonly used finite-difference and finite-element procedures are examined in the light of these criteria and it is shown that they fall short in a number of ways. The proposed numerical process, on the other hand, satisfies most of the optimality criteria and appears to be particularly suited for use with the forthcoming generation computers.

The weights of major structural components of hypersonic, liquid hydrogen fueled aircraft are estimated and discussed. The major components are the body structure, body thermal protection system tankage and wing structure. The method of estimating body structure weight is presented in detail while the weights of the other components are estimated by methods given in referenced papers. Two nominal vehicle concepts are considered. The advanced concept employs a wing-body configuration and hot structure with a nonintegral tank, while the potential concept employs an all body configuration and cold, integral pillow tankage structure. Characteristics of these two concepts are discussed and parametric data relating their weight fractions to variations in vehicle shape and size design criteria and mission requirements, and structural arrangement are presented. Although the potential concept is shown to have a weight advantage over the advanced, it involves more design uncertainties since it is farther removed in design from existing aircraft.

A closed cylindrical shell under uniform internal pressure has a slit around a portion of its circumference. Linear shallow shell theory predicts inverse square-root-type singularities in certain of the stresses at the crack tips. This paper reports the computed strength of these singularities for different values of a dimensionless parameter based on crack length, shell radius and shell thickness.

This paper summarizes and evaluates the work done on the elastic analysis of the surface flaw problem by the application of the alternating method. An attempt is made to describe the alternating method and to present the history of its application to the surface flaw problem and to related problems in fracture mechanics. Stress intensity factors obtained by this method are summarized and compared. Results are also compared to those obtained by investigators using other methods of analysis. An evaluation of the use of the alternating method is presented with the purpose of pointing out the advantages and disadvantages in the application of this technique to the surface flaw problem.

Based on selected topics, the paper is broadly aimed to indicate achievements of the past decade, the state of the art, and trends in aeroelasticity. Topics selected for this end include: brief orientation into the history of the subject, roles of active controls and the concept of aerodynamic energy in load alleviation and in flutter suppression, computerized aeroelastic analysis, aeroelastic effects in stability, aeroelastic optimization, the use of composites, recent applications of lifting surface theory to interfering surfaces and control surfaces, transonic flow considerations, and some problems related to the space shuttle.

The excitation of a Love surface wave guided by a thin film layer deposited on a semiinfinite substrate is studied in this paper. Both the thin film and the substrate are considered to be elastically isotropic. Amplitudes of the surface wave in the thin film region and the substrate are found in terms of the strength of a line source vibrating in a direction transverse to the propagating wave. In addition to the surface wave, the bulk shear wave excited by the source is also studied. Analytical expressions for the bulk wave amplitude as a function of the direction of propagation, the acoustic powers transported by the surface and bulk waves, and the efficiency of surface wave excitation are obtained. A numerical example is given to show how the bulk wave radiation pattern depends upon the source frequency, the film thickness and other important parameters of the problem. The efficiency of surface wave excitation is also calculated for various parameter values.

This paper presents a survey of four aspects of nonlinear analysis - basic formulation, plasticity relations, computational procedures, and methods of solution. This survey is for the most part limited to static geometric and material nonlinear analysis under the assumption of small strains. The two formulations covered are the total Lagrangian and the incremental moving coordinate formulations. A comparison of the two formulations is presented and an attempt is made to clarify the underlying basis of each formulation. The survey of computational procedures reveals that most researchers are now using some form of numerical integration to evaluate nonlinear contributions.

The paper defines the experimental phase of an objective to obtain the mechanical characteristics and coefficients required by the generalized form of Hooke's law for nylon-polyurethane-coated fabric. Test specimens were cylindrical fabric sleeves and were loaded in axial tension by an Instron, in hoop tension by pressurizing, and in shear by a torquing fixture. An extensive amount of strain data is included for a wide combination of the three membrane loads. The tests indicate highly nonlinear stress-strain characteristics of the fabric and a strong dependency on all three membrane loads.

This paper examines some basic considerations underlying dynamic shell response analysis and the impact of these considerations upon the practical aspects of solution by numerical methods. Emphasis is placed on the solution of linear problems. The present states of development of the finite difference and finite element methods are reviewed, and techniques for the treatment of temporal variation are discussed. An examination is made of the frequency parameters characteristic of thin shell theory, applied excitations, and spatial mesh geometries, and the significance of these parameters with respect to computational convergence is illustrated.

Fatigue and fracture of cylindrical and spherical shells containing a through crack and subjected to internal pressure or torsion are considered. The stress intensity factor ratios giving the effect of curvature are obtained as functions of a dimensionless shell parameter. By using the conventional plastic strip model the plastic zone size around the crack tip and the crack opening displacement are calculated. The calculated COD values are shown to be in good agreement with the experimental results. The fracture criterion of critical COD is verified by using the results of the burst tests in titanium and aluminum alloy cryogenic pressure vessels. Modified fatigue crack propagation models taking into account the bending effect in shells are introduced and are applied to the analysis of experimental data obtained from flat plates, and cylindrical shells under axial tension, internal pressure, and torsion. Finally, the paper includes the effect of humidity on the crack growth rate and the effect of load biaxiality on the rupture strength.