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DESAP 2 synthesizes linear-elastic structures under static loads. Objective is to find element sizes (cross-sectional areas, plate thicknesses, and the like) that minimize total structural weight without changing layout of structure. Weight is minimized for given layout subject to prescribed contstraints.
The complex failure behavior exhibited by bolted joints of graphite epoxy (Hercules AS/3501) was investigated for the net tension, bearing and shearout failure modes using combined analytical and experimental techniques. Plane stress, linear elastic, finite element methods were employed to determine the two dimensional state of stress resulting from a loaded hole in a finite width, semiinfinite strip. The stresses predicted by the finite element method were verified by experiment to lend credence to the analysis. The influence of joint geometric parameters on the state of stress and resultant strength of the joint was also studied. The resulting functional relationships found to exist between bolted joint strength and the geometric parameters, were applied in the formulation of semiempirical strength models for the basic failure modes. A point stress failure criterion was successfully applied as the failure criterion for the net tension and shearout failure modes.
A simple, versatile, and efficient computational technique has been developed for dynamic analysis of linear elastic beam and rod type of structures. Moreover, the method provides a rather general solution approach for two-point boundary value problems that are described by a single independent spatial variable. For structural problems, the method is implemented by a mixed state vector formulation of the differential equations, combined with an integrating matrix solution procedure. Highly accurate solutions are easily achieved with this approach. Example solutions are given for beam vibration problems including discontinuous stiffness and mass parameters, elastic restraint boundary conditions, concentrated inertia loading, and rigid body modes
Two dimensional and quasi-three dimensional, linear elastic finite element models for the prediction of crack growth characteristics, including crack growth direction, in laminated composite materials are presented. Mixed mode crack growth in isotropic materials, unidirectional and laminated composites is considered. The modified crack closure method is used to predict the applied load level for crack extension and two failure theories, modifications of the point stress and the Hashin failure criteria, are proposed to predict the direction of crack extension in composites. Comparisons are made with the Tsai-Wu failure criterion and the Sih strain energy density criterion as well as with experimental results. It is shown that the modified versions of point stress and Hashin criteria compare well with experiment.
Development of a simplified method for estimating structural inelastic stress and strain response to cyclic thermal loading is presented. The method assumes that high temperature structural response is the sum of time independent plastic and time dependent elastic/creep components. The local structural stress and strain response predicted by linear elastic analysis is modified by the simplified method to predict the inelastic response. The results with simulations by a nonlinear finite element analysis and used time independent plasticity and unified time dependent material model are compared.
The validity of linear elastic fracture mechanics and other fracture criteria was investigated with laminates of boron fiber reinforced aluminum (R/A1) and of carbon fiber reinforced epoxide (CFRP). Cracks are assessed by fracture strength Kc or Kmax (critical or maximum value of the stress intensity factor). The Whitney and Nuismer point stress criterion and average stress criterion often show that Kmax of fiber composite materials increases with increasing crack length; however, for R/A1 and CFRP the curve showing fracture strength as a function of crack length is only applicable in a small domain. For R/A1, the reason is clearly the extension of the plastic zone (or the damage zone n the case of CFRP) which cannot be described with a stress intensity factor.
The approach for the method development assumes that, for a thermally loaded structure, the overall strain history is defined by linear elastic analysis. The local stress history at a fatigue critical location is then determined from a one dimensional material behavior model and the local strain and temperature conditions. Three material models are currently being evaluated to assess their ability to predict relevant high temperature cyclic material response characteristics. They are: a time independent classical plasticity and creep representation, a time dependent viscoplastic model capable of predicting combined creep and plasticity effects, and an approximate elastic analysis approach that uses a series of stress-strain curves and a cyclic hardening model to determine reverse plasticity.
The nonlinear strain-displacement and velocity-displacement relations of spinning imperfect rotational paraboloidal thin shell antennas are derived for nonaxisymmetrical deformations. Using these relations with the admissible trial functions in the principle functional of dynamics, the nonlinear equations of stress inducing motion are expressed in the form of a set of quasi-linear ordinary differential equations of the undetermined functions by means of the Rayleigh-Ritz procedure. These equations include all nonlinear terms up to and including the third degree. Explicit expressions are given for the coefficient matrices appearing in these equations. Both translational and rotational off-sets of the axis of revolution (and also the apex point of the paraboloid) with respect to the spin axis are considered. Although the material of the antenna is assumed linearly elastic, it can be anisotropic.
The tensile fracture behavior of 15 center-notched hybrid laminates was studied. Three basic laminate groups were tested: (1) a baseline group with graphite/epoxy plies, (2) a group with the same stacking sequence but where the zero-deg plies were one or two plies of S-glass or Kevlar, and (3) a group with graphite plies but where the zero-deg plies were sandwiched between layers of perforated Mylar. Specimens were loaded linearly with time; load, far field strain, and crack opening displacement (COD) were monitored. The loading was stopped periodically and the notched region was radiographed to reveal the extent and type of damage (failure progression). Results of the tests showed that the hybrid laminates had higher fracture toughnesses than comparable all-graphite laminates. The higher fracture toughness was due primarily to the larger damage region at the ends of the slit; delamination and splitting lowered the stress concentration in the primary load-carrying plies. A linear elastic fracture analysis, which ignored delamination and splitting, underestimated the fracture toughness. For almost all of the laminates, the tests showed that the fracture toughness increased with crack length. The size of the damage region at the ends of the slit and COD measurements also increased with crack length.
The minimum weight optimum design of damped linearly elastic structural systems subjected to periodic loading with behavior constraints on maximum deflections and side constraints on design variables is addressed. Attention is focused on the two major impediments to an optimal solution: (1) the time parametric nature of the behavior constraints; and (2) the severe nonconvexity of the design space. A solution method based on upper bound approximations for the behavior constraints and an innovative mathematical programming scheme for seeking the optimal frequency subspace is set forth. Numerical results for several test problems illustrate the effectiveness of the method reported.
The determination of the elastodynamic fields of an ellipsoidal inhomogeneity is studied in detail via the eigenstrain approach. A complete formulation and a treatment of both types of eigenstrains for equivalence between the inhomogeneity problem and the inclusion problem are given. This approach is shown to be mathematically identical to other approaches such as the direct volume integral formulation. Expanding the eigenstrains and applied strains in the polynomial form in the position vector and satisfying the equivalence conditions at every point, the governing simultaneous algebraic equations for the unknown coefficients in the eigenstrain expansion are derived. The elastodynamic field outside an ellipsoidal inhomogeneity in a linear elastic isotropic medium is given as an example. The angular and frequency dependence of the induced displacement field, as well as the differential and total cross sections are formally given in series expansion form for the case of uniformly distributed eigenstrains.
Stable crack-growth and fracture-toughness experiments were conducted using precracked specimens machined from LI-900 reusable surface insulation (RSI) tiles of the Space Shuttle thermal protection system (TPS) at room temperature. Similar fracture experiments were conducted on fracture specimens with preexisting cracks at the interface of the tile and the strain isolation pad (SIP). Stable crack growth was not observed in the LI-900 tile fracture specimens which had a fracture toughness of 12.0 kPa sq rt of m. The intermittent subcritical crack growth at the tile-pad interface of the fracture specimens was attributed to successive local pull-outs due to tensile overload in the LI-900 tile and cannot be characterized by linear elastic fracture mechanics. No subcritical interfacial crack growth was observed in the fracture specimens with densified LI-900 tiles where brittle fracture initiated at an interior point away from the densification.
Fatigue crack growth patterns and lives for surface cracks, surface cracks at holes, and corner cracks at holes in three dimensional bodies were predicted using linear-elastic fracture mechanics concepts that were modified to account for crack-closure behavior. The predictions were made by using stress intensity factor equations for these crack configurations and the fatigue crack-growth (delta K against rate) relationship for the material of interest. The crack configurations were subjected to constant-amplitude fatigue loading under either remote tension or bending loads. The predicted crack growth patterns and crack growth lives for aluminum alloys agreed well with test data from the literature.
A new method for experimental determination of the modal parameters of a structure is presented. The method allows for multiple input forces to be applied simultaneously, and for an arbitrary number of acceleration response measurements to be employed. These data are used to form the equations of motion for a damped linear elastic structure. The modal parameters are then obtained through an eigenvalue technique. In conjunction with the development of the equations, an extensive computer simulation study was performed. The results of the study show a marked improvement in the mode shape identification for closely-spaced modes as the number of applied forces is increased. Also demonstrated is the influence of noise on the method's ability to identify accurate modal parameters. Here again, an increase in the number of exciters leads to a significant improvement in the identified parameters.
The development of test methodology for characterizing matrix dominated failure modes is discussed emphasizing issues of matrix cracking, delamination under static loading, and the relationship of composite properties to matrix properties. Both strength characterization and classical techniques of linear elastic fracture mechanics were examined. Materials development studies are also discussed. Major areas of interest include acetylene-terminated and bismaleimide resins for 350 to 450 deg use, thermoplastics development, and failure resistant composite concepts.
The free-edge delamination of graphite/epoxy laminates under static loading is being analyzed to obtain fundamental understanding of the continuum mechanics involved. The analyses are conducted by idealizing the material response of each ply in the laminate as homogenous, linear elastic, and anisotropic. A generalized plane strain elastic boundary value problem was formulated to investigate the energy variation of such a body.
The behavior of tensile coupons with surface notches of various semi-elliptical shapes were evaluated for specimens obtained from a filament wound graphite/epoxy cylinder. The quasi-static test results, in some instances, are inadequate for defining complete trend curves and the interpretive analysis is considered to be preliminary. Specimens with very shallow notches were observed to be notch insensitive and the unnotched strength from these specimens was determined to be 54.97 Ksi. The failure strain of the laminate was found to be 1.328%. Specimens with deeper notches were sensitive to notch depth, notch aspect ratio, and specimen width. Using the unnotched strength of 54.97 Ksi and Poe's general toughness parameter, the fracture toughness was estimated to be 27.2 Ksi square root of In. Isotropic linear elastic fracture mechanics together with the estimated fracture toughness correctly predicted the influence of notch depth, aspect ratio, and specimen finitewidth.
Simplified inelastic analysis procedures were developed at NASA Lewis and Pratt & Whitney Aircraft for predicting the stress-strain response at the critical location of a thermomechanically cycled structure. These procedures are intended primarily for use as economical structural analysis tools in the early design stages of aircraft engine hot section components where nonlinear finite-element analyses would be prohibitively expensive. Both simplified methods use as input the total strain history calculated from a linear elastic analysis. The elastic results are modified to approximate the characteristics of the inelastic cycle by incremental solution techniques. A von Mises yield criterion is used to determine the onset of active plasticity. The fundamental assumption of these methods is that the inelastic strain is local and constrained from redistribution by the surrounding elastic material.