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NASA NTRS2005

Failure Analysis of Discrete Damaged Tailored Extension-Shear-Coupled Stiffened Composite Panels

The results of an analytical and experimental investigation of the failure of composite is tiffener panels with extension-shear coupling are presented. This tailored concept, when used in the cover skins of a tiltrotor aircraft wing has the potential for increasing the aeroelastic stability margins and improving the aircraft productivity. The extension-shear coupling is achieved by using unbalanced 45 plies in the skin. The failure analysis of two tailored panel configurations that have the center stringer and adjacent skin severed is presented. Finite element analysis of the damaged panels was conducted using STAGS (STructural Analysis of General Shells) general purpose finite element program that includes a progressive failure capability for laminated composite structures that is based on point-stress analysis, traditional failure criteria, and ply discounting for material degradation. The progressive failure predicted the path of the failure and maximum load capability. There is less than 12 percent difference between the predicted failure load and experimental failure load. There is a good match of the panel stiffness and strength between the progressive failure analysis and the experimental results. The results indicate that the tailored concept would be feasible to use in the wing skin of a tiltrotor aircraft.

Baker, Donald J.↗

NASA NTRS1988

A mixed formulaton of C(0)-linear triangular plate/shell element - The role of edge shear constraints

A simple and effective linear C(0)-tiangular element for plates and shells is developed on the basis of the Hellinger-Reissner mixed variational principle with independently assumed stress and displacement fields. Two main features are emphasized in this development concerning the assumed transverse shear stress field. First, this assumption results in edge-type penalty constraints in the thin plate/shell regimes. Second, the element is used in the form of a four-triangle, cross-diagonal macroelement mesh. As a result, the element is shown to be free from shear locking in thin plate/shell applications, and it satisfies all the appropriate patch tests required for Kirchhoff plate models. In addition, the element exhibits good overall convergence properties in a variety of test problems for plates and shells. Finally, from the computational standpoint, the element is very efficient since all stiffness component matrices are derived in explicit forms.

Saleeb, A. F.↗

NASA NTRS1990

Elastic/viscoplastic behavior of fiber-reinforced thermoplastic composites

An elastic/viscoplastic constitutive model was used to characterize the nonlinear and rate dependent behavior of a continuous fiber-reinforced thermoplastic composite. This model was incorporated into a finite element program for the analysis of laminated plates and shells. Details on the finite element formulation with the proposed constitutive model were presented. The numerical results were compared with experimental data for uniaxial tension and three-point bending tests of (+ or - 45 deg)3s APC-2 laminates.

Wang, C.↗

NASA NTRS1988

Hierarchic plate and shell models based on p-extension

Formulations of finite element models for beams, arches, plates and shells based on the principle of virtual work was studied. The focus is on computer implementation of hierarchic sequences of finite element models suitable for numerical solution of a large variety of practical problems which may concurrently contain thin and thick plates and shells, stiffeners, and regions where three dimensional representation is required. The approximate solutions corresponding to the hierarchic sequence of models converge to the exact solution of the fully three dimensional model. The stopping criterion is based on: (1) estimation of the relative error in energy norm; (2) equilibrium tests, and (3) observation of the convergence of quantities of interest.

Szabo, Barna A.↗

NASA NTRS1985

Mixed models and reduction method for dynamic analysis of anisotropic shells

A time-domain computational procedure is presented for predicting the dynamic response of laminated anisotropic shells. The two key elements of the procedure are: (1) use of mixed finite element models having independent interpolation (shape) functions for stress resultants and generalized displacements for the spatial discretization of the shell, with the stress resultants allowed to be discontinuous at interelement boundaries; and (2) use of a dynamic reduction method, with the global approximation vectors consisting of the static solution and an orthogonal set of Lanczos vectors. The dynamic reduction is accomplished by means of successive application of the finite element method and the classical Rayleigh-Ritz technique. The finite element method is first used to generate the global approximation vectors. Then the Rayleigh-Ritz technique is used to generate a reduced system of ordinary differential equations in the amplitudes of these modes. The temporal integration of the reduced differential equations is performed by using an explicit half-station central difference scheme (Leap-frog method). The effectiveness of the proposed procedure is demonstrated by means of a numerical example and its advantages over reduction methods used with the displacement formulation are discussed.

Noor, A. K.↗

NASA NTRS1995

A kinematically driven anisotropic viscoelastic constitutive model applied to tires

Aircraft tires are composite structures manufactured with viscoelastic materials such as carbon black filled rubber and nylon cords. When loaded they experience large deflections and moderately large strains. Detailed structural models of tires require the use of either nonlinear shell or nonlinear three dimensional solid finite elements. Computational predictions of the dynamic response of tires must consider the composite viscoelastic material behavior in a realistic fashion. We describe a modification to a nonlinear anisotropic shell finite element so it can be used to model viscoelastic stresses during general deformations. The model is developed by introducing internal variables of the type used to model elastic strain energy. The internal variables are strains, curvatures, and transverse shear angles which are in a one-to-one correspondence with the generalized coordinates used to model the elastic strain energy for nonlinear response. A difference-relaxation equation is used to relate changes in the observable strain field to changes in the internal strain field. The internal stress state is introduced into the equilibrium equations by converting it to nodal loads associated with the element's displacement degrees of freedom. In this form the tangent matrix in the Newton-Raphson solution algorithm is not modified from its form for the nonlinear statics problem. Only the gradient vector is modified and the modification is not computationally costly. The existing finite element model for the Space Shuttle nose gear tire is used to provide examples of the algorithm. In the first example, the tire's rim is displaced at a constant rate up to a fixed value. In the second example, the tire's rim is enforced to follow a saw tooth load and unload curve to generate hysteresis loops.

Johnson, Arthur R.↗

NASA NTRS1976

Buckling of structures; Proceedings of the Symposium, Harvard University, Cambridge, Mass., June 17-21, 1974

The papers deal with such topics as the buckling and post-buckling behavior of plates and shells; methods of calculating critical buckling and collapse loads; finite element representations for thin-shell instability analysis; theory and experiment in the creep buckling of plates and shells; creep instability of thick shell structures; analytical and numerical studies of the influence of initial imperfections on the elastic buckling of columns; mode interaction in stiffened panels under compression; imperfection-sensitivity in the interactive buckling of stiffened plates; buckling of stochastically imperfect structures; and the Liapunov stability of elastic dynamic systems. A special chapter is devoted to design problems, including the design of a Mars entry 'aeroshell', and buckling design in vehicle structures. Individual items are announced in this issue.

Budiansky, B.↗

NASA NTRS1980

Thermal stress analysis of symmetric shells subjected to asymmetric thermal loads

The performance of the NASTRAN level 16.0 axisymmetric solid elements when subjected to both symmetric and asymmetric thermal loading was investigated. A ceramic radome was modeled using both the CTRAPRG and the CTRAPAX elements. The thermal loading applied contained severe gradients through the thickness of the shell. Both elements were found to be more sensitive to the effect of the thermal gradient than to the aspect ratio of the elements. Analysis using the CTRAPAX element predicted much higher thermal stresses than the analysis using the CTRAPRG element, prompting studies of models for which theoretical solutions could be calculated. It was found that the CTRAPRG element solutions were satisfactory, but that the CTRAPAX element was very geometry dependent. This element produced erroneous results if the geometry was allowed to vary from a rectangular cross-section. The most satisfactory solution found for this type of problem was to model a small segment of a symmetric structure with isoparametric solid elements and apply the cyclic symmetry option in NASTRAN.

Negaard, G. R.↗

NASA NTRS1979

Computer design synthesis of a below knee-Syme prosthesis

A detailed design synthesis analysis of the BK Syme prosthesis is provided, to determine the socket's cutout orientation size and shape, cutout fillet shape, socket wall thickness distribution and the reinforced fiber distribution in the socket wall, for a minimally stressed structurally safe lightweight prosthesis. For analysis purposes, the most adverse socket loading is obtained at the push-off stage of gait; this loading is idealized as an axial in-plane loading on the bottom edge of the circular cylindrical socket shell whose top edge is considered fixed. Finite element stress analysis of the socket shell (with uniform and graded wall thickness) are performed for various orientations of the cutout and for various types of corner fillets. A lateral cutout with a streamline fillet is recommended. The wall material (i.e., thickness) distribution is determined so as to minimize the stresses, while ensuring that the wall material's stress limits are not exceeded. For such a maximally stressed lightweight socket shell, the panels in the neighborhood of the cutout are checked to ensure that they do not buckle under their acquired stresses. A fiber-reinforced laminated composite socket shell is also analyzed in order to recommend optimum variables in orientations and densities of reinforcing fibers.

Elangovan, P. T.↗

NASA NTRS1976

Vibration characteristics of 1/8-scale dynamic models of the space-shuttle solid-rocket boosters

Vibration tests and analyses of six 1/8 scale models of the space shuttle solid rocket boosters are reported. Natural vibration frequencies and mode shapes were obtained for these aluminum shell models having internal solid fuel configurations corresponding to launch, midburn (maximum dynamic pressure), and near endburn (burnout) flight conditions. Test results for longitudinal, torsional, bending, and shell vibration frequencies are compared with analytical predictions derived from thin shell theory and from finite element plate and beam theory. The lowest analytical longitudinal, torsional, bending, and shell vibration frequencies were within + or - 10 percent of experimental values. The effects of damping and asymmetric end skirts on natural vibration frequency were also considered. The analytical frequencies of an idealized full scale space shuttle solid rocket boosted structure are computed with and without internal pressure and are compared with the 1/8 scale model results.

Leadbetter, S. A.↗

NASA NTRS1983

Wrinkling phenomenon in structures. II - Wrinkling criteria

The wrinkling phenomenon in elasticity is mathematically defined and described as a special type of instability associated with the loss of hyperbolicity of the governing equations when some of the characteristic speeds of elastic wave propagation become imaginary. The developed criteria of wrinkling are applied to such structural elements as membranes, strings, soft shells, soft rods, and laminated material. The cause of wrinkling in these elements is due to compression in longitudinal directions that exceeds the through-the-thickness shear modulus. For elements with internal fluid flow the critical compression is reduced due to the destabilizing effect of the flow. The most effective mathematical analysis technique is a combination of tensor analysis and index notations.

Zak, M.↗

NASA NTRS1987

Advances in computational structural and solid mechanics; Proceedings of the First World Congress on Computational Mechanics, University of Texas, Austin, Sept. 22-26, 1986

Papers are presented on the nonlinear dynamic analysis of quasi-symmetric anisotropic structures, the analysis of large deformations of membrane shells by the generalized finite difference method, the vibration of shear-deformable laminated plate structures by the finite strip method, and Coon's surface method for the formulation of finite elements for plates and shells. Other topics include an evaluation of higher-order modal methods for calculating the transient structural response, a nonlinear dynamic analysis of frame structures, and a nonlinear analysis of a truss by energy minimization. Also considered are an incremental Galerkin method for plates and stiffened plates, a comparison of the postbuckling behavior of plates and shells, and a general solution of bending in a cylindrical shell.

Noor, Ahmed K.↗

NASA NTRS1995

Alaska Crustal Deformation: Finite Element Modeling Constrained by Geologic and Very Long Baseline Interferometry Data

We compute crustal motions in Alaska by calculating the finite element solution for an elastic spherical shell problem. The method we use allows the finite element mesh to include faults and very long baseline interferometry (VLBI) baseline rates of change. Boundary conditions include Pacific-North American (PA-NA) plate motions. The solution is constrained by the oblique orientation of the Fairweather-Queen Charlotte strike-slip faults relative to the PA-NA relative motion direction and the oblique orientation from normal convergence of the eastern Aleutian trench fault systems, as well as strike-shp motion along the Denali and Totschunda fault systems. We explore the effects that a range of fault slip constraints and weighting of VLBI rates of change has on the solution. This allows us to test the motion on faults, such as the Denali fault, where there are conflicting reports on its present-day slip rate. We find a pattern of displacements which produce fault motions generally consistent with geologic observations. The motion of the continuum has the general pattern of radial movement of crust to the NE away from the Fairweather-Queen Charlotte fault systems in SE Alaska and Canada. This pattern of crustal motion is absorbed across the Mackenzie Mountains in NW Canada, with strike-slip motion constrained along the Denali and Tintina fault systems. In south central Alaska and the Alaska forearc oblique convergence at the eastern Aleutian trench and the strike-shp motion of the Denali fault system produce a counterclockwise pattern of motion which is partially absorbed along the Contact and related fault systems in southern Alaska and is partially extruded into the Bering Sea and into the forearc parallel the Aleutian trench from the Alaska Peninsula westward. Rates of motion and fault slip are small in western and northern Alaska, but the motions we compute are consistent with the senses of strike-slip motion inferred geologically along the Kaltag, Kobuk Trench, and Thompson Creek faults and with the normal faulting observed in NW Alaska near Nome. The nonrigid behavior of our finite element solution produces patterns of motion that would not have been expected from rigid block models: strike-slip faults can exist in a continuum that has motion mostly perpendicular to their strikes, and faults can exhibit along-strike differences in magnitudes and directions.

Lundgren, Paul↗

NASA NTRS1992

Coupled 2D-3D finite element method for analysis of a skin panel with a discontinuous stiffener

This paper describes a computationally efficient analysis method which was used to predict detailed stress states in a typical composite compression panel with a discontinuous hat stiffener. A global-local approach was used. The global model incorporated both 2D shell and 3D brick elements connected by newly developed transition elements. Most of the panel was modeled with 2D elements, while 3D elements were employed to model the stiffener flange and the adjacent skin. Both linear and geometrically nonlinear analyses were performed on the global model. The effect of geometric nonlinearity induced by the eccentric load path due to the discontinuous hat stiffener was significant. The local model used a fine mesh of 3D brick elements to model the region at the end of the stiffener. Boundary conditions of the local 3D model were obtained by spline interpolation of the nodal displacements from the global analysis. Detailed in-plane and through-the-thickness stresses were calculated in the flange-skin interface near the end of the stiffener.

Wang, J. T.↗

NASA NTRS1981

On Hybrid and mixed finite element methods

Three versions of the assumed stress hybrid model in finite element methods and the corresponding variational principles for the formulation are presented. Examples of rank deficiency for stiffness matrices by the hybrid stress model are given and their corresponding kinematic deformation modes are identified. A discussion of the derivation of general semi-Loof elements for plates and shells by the hybrid stress method is given. It is shown that the equilibrium model by Fraeijs de Veubeke can be derived by the approach of the hybrid stress model as a special case of semi-Loof elements.

Pian, T. H. H.↗

NASA NTRS1991

Improved finite-element methods for rotorcraft structures

An overview of the research directed at improving finite-element methods for rotorcraft airframes is presented. The development of a modification to the finite element method which eliminates interelement discontinuities is covered. The following subject areas are discussed: geometric entities, interelement continuity, dependent rotational degrees of freedom, and adaptive numerical integration. This new methodology is being implemented as an anisotropic, curvilinear, p-version, beam, shell, and brick finite element program.

Hinnant, Howard E.↗

NASA NTRS2012

The Effects of Geometric and Loading Imperfections on the Response and Lower-Bound Buckling Load of a Compression-Loaded Cylindrical Shell

Results from a numerical study of the buckling response of a thin-walled compressionloaded isotropic circular cylindrical shell with initial geometric and loading imperfections are used to determine a lower bound buckling load estimate suitable for preliminary design. The lower bound prediction techniques presented herein include an imperfection caused by a lateral perturbation load, an imperfection in the shape of a single stress-free dimple (similar to the lateral pertubation imperfection), and a distributed load imperfection that induces a nonuniform load in the shell. The ABAQUS finite element code is used for the analyses. Responses of the cylinders for selected imperfection amplitudes and imperfection types are considered, and the effect of each imperfection is compared to the response of a geometrically perfect cylinder. The results indicate that compression-loaded shells subjected to a lateral perturbation load or a single dimple imperfection, and a nonuniform load imperfection, exhibit similar buckling behavior and lower bound trends and the predicted lower bounds are much less conservative than the corresponding design recommendation NASA SP-8007 for the design of buckling-critical shells. In addition, the lateral perturbation technique and the distributed load imperfection produce response characteristics that are physically meaningful and can be validated via laboratory testing.

Kriegesmann, Benedikt↗

NASA NTRS1981

Deep anistropic shell program for tire analysis

A finite element program was constructed to model the mechanical response of a tire, treated as a deep anisotropic shell, to specified static loads. The program is based on a Sanders Budiansky type shell theory with the effects of transverse shear deformation and bending-extensional coupling included. A displacement formulation is used together with a total Lagrangian description of the deformation. Sixteen-node quadrilateral elements with bicubic shape functions are employed. The Noor basis reduction technique and various type of symmetry considerations serve to improve the computational efficiency.

Andersen, C. M.↗