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NASA NTRS1991

Finite element structural redesign by large admissible perturbations

In structural redesign, two structural states are involved; the baseline (known) State S1 with unacceptable performance, and the objective (unknown) State S2 with given performance specifications. The difference between the two states in performance and design variables may be as high as 100 percent or more depending on the scale of the structure. A Perturbation Approach to Redesign (PAR) is presented to relate any two structural states S1 and S2 that are modeled by the same finite element model and represented by different values of the design variables. General perturbation equations are derived expressing implicitly the natural frequencies, dynamic modes, static deflections, static stresses, Euler buckling loads, and buckling modes of the objective S2 in terms of its performance specifications, and S1 data and Finite Element Analysis (FEA) results. Large Admissible Perturbation (LEAP) algorithms are implemented in code RESTRUCT to define the objective S2 incrementally without trial and error by postprocessing FEA results of S1 with no additional FEAs. Systematic numerical applications in redesign of a 10 element 48 degree of freedom (dof) beam, a 104 element 192 dof offshore tower, a 64 element 216 dof plate, and a 144 element 896 dof cylindrical shell show the accuracy, efficiency, and potential of PAR to find an objective state that may differ 100 percent from the baseline design.

Bernitsas, Michael M.↗

NASA NTRS1991

A finite element program for postbuckling calculations (PSTBKL)

The object of the research reported herein was to develop a general mathematical model and solution methodologies for analyzing the structural response of thin, metallic shell structures under large transient, cyclic, or static thermochemical loads. This report describes the computer program resulting from the research. Among the system responses associated with these loads and conditions are thermal buckling, creep buckling, and ratcheting. Thus geometric and material nonlinearities (of high order) have been anticipated and are considered in developing the mathematical model. The methodology is demonstrated through different problems of extension, shear, and of planar curved beams. Moreover, importance of the inclusion of large strains is clearly demonstrated, through the chosen applications.

Simitses, G. T.↗

NASA NTRS1991

Formulation of the nonlinear analysis of shell-like structures, subjected to time-dependent mechanical and thermal loading

The object of the research reported herein was to develop a general mathematical model and solution methodologies for analyzing the structural response of thin, metallic shell structures under large transient, cyclic, or static thermomechanical loads. Among the system responses associated with these loads and conditions are thermal buckling, creep buckling, and ratcheting. Thus geometric and material nonlinearities (of high order) can be anticipated and must be considered in developing the mathematical model. The methodology is demonstrated through different problems of extension, shear, and of planar curved beams. Moreover, importance of the inclusion of large strain is clearly demonstrated, through the chosen applications.

Simitses, George J.↗

NASA NTRS1991

Probabilistic structural analysis of adaptive/smart/intelligent space structures

A three-bay, space, cantilever truss is probabilistically evaluated for adaptive/smart/intelligent behavior. For each behavior, the scatter (ranges) in buckling loads, vibration frequencies, and member axial forces are probabilistically determined. Sensitivities associated with uncertainties in the structure, material and load variables that describe the truss are determined for different probabilities. The relative magnitude for these sensitivities are used to identify significant truss variables that control/classify its behavior to respond as an adaptive/smart/intelligent structure. Results show that the probabilistic buckling loads and vibration frequencies increase for each truss classification, with a substantial increase for intelligent trusses. Similarly, the probabilistic member axial forces reduce for adaptive and intelligent trusses and increase for smart trusses.

Pai, Shantaram S.↗

NASA NTRS1992

Experimental behavior of graphite-epoxy Y-stiffened specimens loaded in compression

An experimental investigation of the behavior of graphite-epoxy Y-stiffened specimens loaded in compression is presented. Experimental results are presented for element specimens with a single stiffener and for panel specimens with three stiffeners. Response and failure characteristics of the specimens are described. Effects of impact damage on structural response for both specimen configurations are also presented. Experimental results indicate that impact location may significantly affect the residual strength of the Y-stiffened specimens. The failure results indicate that the critical failure mode is buckling of the stiffener webs for Y-stiffened element specimens and buckling of the stiffener webs and other stiffener blades for the Y-stiffened panel specimens.

Sydow, P. Daniel↗

NASA NTRS1992

Integrating aerodynamics and structures in the minimum weight design of a supersonic transport wing

An approach is presented for determining the minimum weight design of aircraft wing models which takes into consideration aerodynamics-structure coupling when calculating both zeroth order information needed for analysis and first order information needed for optimization. When performing sensitivity analysis, coupling is accounted for by using a generalized sensitivity formulation. The results presented show that the aeroelastic effects are calculated properly and noticeably reduce constraint approximation errors. However, for the particular example selected, the error introduced by ignoring aeroelastic effects are not sufficient to significantly affect the convergence of the optimization process. Trade studies are reported that consider different structural materials, internal spar layouts, and panel buckling lengths. For the formulation, model and materials used in this study, an advanced aluminum material produced the lightest design while satisfying the problem constraints. Also, shorter panel buckling lengths resulted in lower weights by permitting smaller panel thicknesses and generally, by unloading the wing skins and loading the spar caps. Finally, straight spars required slightly lower wing weights than angled spars.

Barthelemy, Jean-Francois M.↗

NASA NTRS1991

Elastoviscoplastic snap-through behavior of shallow arches subjected to thermomechanical loads

The problem of snap-through buckling of clamped shallow arches under thermomechanical loads is investigated. The analysis is based on nonlinear kinematic relations and nonlinear rate-dependent unified constitutive equations. A finite element approach is employed to predict the, in general, inelastic buckling behavior. The construction material is alloy B1900 + Hf, which is commonly utilized in high-temperature environments. The effect of several parameters is assessed. These parameters include the rise parameter and temperature. Comparison between elastic and elastoviscoplastic responses is also presented.

Simitses, George J.↗

NASA NTRS1992

The behavior of a liquid drop levitated and drastically flattened by an intense sound field

The deformation and break-up are studied of a liquid drop in levitation through the radiation pressure. Using high-speed photography ripples are observed on the central membrane of the drop, atomization of the membrane by emission of satellite drops from its unstable ripples, and shattering of the drop after upward buckling like an umbrella, or after horizontal expansion like a sheet. These effects are captured on video. The ripples are theorized to be capillary waves generated by the Faraday instability excited by the sound vibration. Atomization occurs whenever the membrane becomes so thin that the vibration is sufficiently intense. The vibration leads to a destabilizing Bernoulli correction in the static pressure. Buckling occurs when an existent equilibrium is unstable to a radial (i.e., tangential) motion of the membrane because of the Bernoulli effect. Besides, the radiation stress at the rim of the drop is a suction stress which can make equilibrium impossible, leading to the horizontal expansion and the subsequent break-up.

Lee, C. P.↗

NASA NTRS1992

The nonlinear bending response of thin-walled laminated composite cylinders

The geometrically nonlinear Donnell shell theory is applied to the problem of stable bending of thin-walled circular cylinders. Responses are computed for cylinders with a radius-to-thickness ratio of 50 and length-to-radius ratios of 1 and 5. Four laminated composite cylinders and an aluminum cylinder are considered. Critical moment estimates are presented for short cylinders for which compression-type buckling behavior is important, and for very long cylinders for which the cross-section flattening, i.e., Brazier effect, is important. A finite element analysis is used to estimate the critical end rotation in addition to establishing the range of validity of the prebuckling analysis. The radial displacement response shows that the character of the boundary layer is significantly influenced by the geometric nonlinearities. Application of a first ply failure analysis using the maximum stress criterion suggests that in nearly all instances material failure occurs before buckling. Failure of the composite cylinders can be attributed to fiber breakage. Striking similarities are seen between the prebuckling displacements of the bending problem and axial compression problem for short cylinders.

Fuchs, Hannes P.↗

NASA NTRS1992

Stacking sequence optimization of simply supported laminates with stability and strain constraints

An integer programming formulation for the design of symmetric and balanced rectangular composite laminates with simply supported boundary conditions subject to buckling and strain constraints is presented. The design variables that define the stacking sequence of the laminate are ply-identity zero-one integers. The buckling constraint is linear in terms of the ply-identity design variables, but strains are nonlinear functions of these variables. A linear approximation is developed for the strain constraints so that the problem can be solved by sequential linearization using the branch and bound algorithm. Examples of graphite-epoxy plates under biaxial compression are presented. Optimum stacking sequences obtained using the linear approximation are compared with global optimum designs obtained using a genetic search procedure.

Nagendra, S.↗

NASA NTRS1993

Effect of bow-type initial imperfection on reliability of minimum-weight, stiffened structural panels

Computations were performed to determine the effect of an overall bow-type imperfection on the reliability of structural panels under combined compression and shear loadings. A panel's reliability is the probability that it will perform the intended function - in this case, carry a given load without buckling or exceeding in-plane strain allowables. For a panel loaded in compression, a small initial bow can cause large bending stresses that reduce both the buckling load and the load at which strain allowables are exceeded; hence, the bow reduces the reliability of the panel. In this report, analytical studies on two stiffened panels quantified that effect. The bow is in the shape of a half-sine wave along the length of the panel. The size e of the bow at panel midlength is taken to be the single random variable. Several probability density distributions for e are examined to determine the sensitivity of the reliability to details of the bow statistics. In addition, the effects of quality control are explored with truncated distributions.

Stroud, W. Jefferson↗

NASA NTRS1993

Hypersonic panel flutter in a rarefied atmosphere

Panel flutter is a form of dynamic aeroelastic instability resulting from the interaction between motion of an aircraft structural panel and the aerodynamic loads exerted on that panel by air flowing past one of the faces. It differs from lifting surface flutter in the sense that it is not usually catastrophic, the panel's motion being limited by nonlinear membrane stresses produced by the transverse displacement. Above some critical airflow condition, the linear instability grows to a limit cycle . The present investigation studies panel flutter in an aerodynamic regime known as 'free molecule flow', wherein intermolecular collisions can be neglected and loads are caused by interactions between individual molecules and the bounding surface. After collision with the panel, molecules may be reflected specularly or reemitted in diffuse fashion. Two parameters characterize this process: the 'momentum accommodation coefficient', which is the fraction of the specularly reflected molecules; and the ratio between the panel temperature and that of the free airstream. This model is relevant to the case of hypersonic flight vehicles traveling at very high altitudes and especially for panels oriented parallel to the airstream or in the vehicle's lee. Under these conditions the aerodynamic shear stress turns out to be considerably larger than the surface pressures, and shear effects must be included in the model. This is accomplished by means of distributed longitudinal and bending loads. The former can cause the panel to buckle. In the example of a simply-supported panel, it turns out that the second mode of free vibration tends to dominate the flutter solution, which is carried out by a Galerkin analysis. Several parametric studies are presented. They include the effects of (1) temperature ratio; (2) momentum accommodation coefficient; (3) spring parameters, which are associated with how the panel is connected to adjacent structures; (4) a parameter which relates compressive end load to its value which would cause classical column buckling; (5) a parameter proportional to the pressure differential between the front and back faces; and (6) initial curvature. The research is completed by an investigation into the possibility of accounting for molecular collisions, which proves to be infeasible given the speeds of current mainframe supercomputers.

Resende, Hugo B.↗

NASA NTRS1993

Probabilistic assessment of composite structures

A methodology and attendant computer code were developed and are used to computationally simulate the uncertain behavior of composite structures. The uncertain behavior includes buckling loads, stress concentration factors, displacements, stress/strain, etc., which are the consequences of the inherent uncertainties (scatter) in the primitive (independent random) variables (constituent, ply, laminate, and structural) that describe the composite structures. The computer code is IPACS (Integrated Probabilistic Assessment of Composite Structures). IPACS can simulate both composite mechanics and composite structural behavior. Application to probabilistic composite mechanics is illustrated by its use to evaluate the uncertainties in the major Poisson's ratio and in laminate stiffness and strength. IPACS' application to probabilistic structural analysis is illustrated by its used to evaluate the uncertainties in the buckling of a composite plate, the stress concentration factor in a composite panel, and the vertical displacement and ply stress in a composite aircraft wing segment. IPACS' application to probabilistic design is illustrated by its use to assess the thin composite shell (pipe).

Chamis, C. C.↗

NASA NTRS1991

Experimental behavior of graphite-epoxy Y-stiffened specimens loaded in compression

An experimental investigation of the behavior of graphite-epoxy Y-stiffened specimens loaded in compression is presented. Experimental results are presented for element specimens with a single stiffener and for panel specimens with three stiffeners. Response and failure characteristics of the specimens are described. Effects of impact damage on structural response for both specimen configurations are also presented. Results indicate that impact location may significantly affect the residual strength of the Y-stiffened specimens. The failure results indicate that the critical failure mode is buckling of the stiffener webs for Y-stiffened element specimens and buckling of both stiffener web and stiffener blade for the Y-stiffened panel specimens.

Sydow, P. D.↗

NASA NTRS1992

Probabilistic structural analysis of adaptive/smart/intelligent space structures

Pai, Shantaram S.↗

NASA NTRS1993

Shell stability analysis in a computer aided engineering (CAE) environment

The development of 'DISDECO', the Delft Interactive Shell DEsign COde is described. The purpose of this project is to make the accumulated theoretical, numerical and practical knowledge of the last 25 years or so readily accessible to users interested in the analysis of buckling sensitive structures. With this open ended, hierarchical, interactive computer code the user can access from his workstation successively programs of increasing complexity. The computational modules currently operational in DISDECO provide the prospective user with facilities to calculate the critical buckling loads of stiffened anisotropic shells under combined loading, to investigate the effects the various types of boundary conditions will have on the critical load, and to get a complete picture of the degrading effects the different shapes of possible initial imperfections might cause, all in one interactive session. Once a design is finalized, its collapse load can be verified by running a large refined model remotely from behind the workstation with one of the current generation 2-dimensional codes, with advanced capabilities to handle both geometric and material nonlinearities.

Arbocz, J.↗

NASA NTRS1993

Thermomechanical postbuckling analysis of laminated composite shells

The nonlinear response of laminated composite structures subjected to thermal loads is investigated. Analysis is performed using a refined theory and an associated finite element model for geometrically nonlinear analysis of laminated composite shell structures. The model is based on a third-order displacement field which accounts for both transverse shear and transverse normal deformations. Numerical studies of simply-supported plates and cylindrical panels indicate that when the panels are free to expand or contract in the transverse direction, the predicted critical buckling temperatures do not depend significantly upon whether or not transverse normal deformations are explicitly accounted for in the analysis model. However, the critical buckling temperatures are strongly dependent upon whether or not the transverse normal deformations are restrained along the boundaries of the panels.

Averill, R. C.↗

NASA NTRS1930

Strength in Shear of the Thin Curved Sheets of Alclad

This note is on an investigation made to obtain information on the strength of thin curved sheets of Alclad in shear. Designers may utilize this material as a strength member as well as for a covering for the wings and fuselages. A reduction may then be made in the size of the internal strength members. These experiments were undertaken with the object of securing the maximum value from the metal in this respect. The point at which buckling occurs is of primary importance. The buckling shear of a curved thin plate was determined mathematically and also experimentally. The following formula was obtained mathematically: s=K E t/r in which s is the unit shear, K is a constant, E is the modulus of elasticity, t is the thickness of the material, and r is the radius of curvature. The value of K as determined by the experiments was found to be .075. This formula applies only when s is within the elastic limit of the material. The breaking point of the material was obtained in most of the tests as a matter of information and the results are included in this report. The effect of the supporting ribs was determined by varying the number used.

Smith, George Michael↗