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NASA NTRS1985

ISAAC (integrated Structural Analysis and Control) via Continuum Modeling and Distributed Frequency Domain Design Techniques

A methodology is proposed for the integrated design of structures and their controls. The integration of design is accomplished through simultaneous selection, via optimization, of designer-specified parameters governing the structure and its controller. The cost function is chosen to address the primary structural and control goals. Inequality constraints are added to insure that additional design requirements are met. The methodology is illustrated through development of an example involving a cantilever beam. A distributed transfer function is derived from the Bernoulli-Euler beam equation. A controller parameterization is then chosen, and performance requirements specified. A controller is then obtained via optimization, which is shown to give good performance.

Gustafson, C. L.↗

NASA NTRS1984

Multiobjective optimization in structural design with uncertain parameters and stochastic processes

The application of multiobjective optimization techniques to structural design problems involving uncertain parameters and random processes is studied. The design of a cantilever beam with a tip mass subjected to a stochastic base excitation is considered for illustration. Several of the problem parameters are assumed to be random variables and the structural mass, fatigue damage, and negative of natural frequency of vibration are considered for minimization. The solution of this three-criteria design problem is found by using global criterion, utility function, game theory, goal programming, goal attainment, bounded objective function, and lexicographic methods. It is observed that the game theory approach is superior in finding a better optimum solution, assuming the proper balance of the various objective functions. The procedures used in the present investigation are expected to be useful in the design of general dynamic systems involving uncertain parameters, stochastic process, and multiple objectives.

Rao, S. S.↗

NASA NTRS1984

The characterization of Mode I delamination failure in non-woven, multidirectional laminates

The uniform double cantilever beam test and SEM are presently used for the characterization of Mode I delamination behavior in fiber-reinforced epoxy laminates. Delamination failure assumes forms that depend on ply orientation, test specimen geometry, and matrix toughness, but the calculated fracture energy is noted to be heavily dependent on fracture surface morphology. A material property concept that is independent of both test specimen geometry and the orientation of the plies constituting the delaminating interface is elucidated, through the definition of interlaminar fracture solely in terms of an interlaminar separation that includes no fiber breakage or pull-out. This value, which dissipates the lowest possible amount of energy during crack growth, is the controlling factor for laminate toughness.

Chai, H.↗

NASA NTRS1984

Composite interlaminar fracture - Effect of matrix fracture energy

A major result of the use of the double cantilever beam test to provide a measure of the interlaminar fracture energy in composites subjected to simple Mode I-type loading is the observation that increasing the toughness of the matrix resin by as much as a factor of 20 produced a major (approximately four-fold) increase in interlaminar fracture energy. The data presently analyzed show that, with brittle polymers, resin toughness is fully transferred to the composite, while in the case of tougher polymers the resin toughness is only partially transferred due to the fibers' restriction of the crack tip deformation zone in the polymer, together with their changing of local stress field details. Factors which tend to increase interlaminar toughness are fiber nesting and bridging, as well as fiber breakage and pull-out during crack growth.

Hunston, D. L.↗

NASA NTRS1984

Fracture of composite-adhesive-composite systems

This program was undertaken to initiate the development of a test method for testing adhesive joints in metal-adhesive-composite systems. The uniform double cantilever beam (UDCB) and the width tapered beam (WTB) specimen geometries were evaluated for measuring Mode I fracture toughness in these systems. The WTB specimen is the preferred geometry in spite of the fact that it is more costly to machine than the UDCB specimen. The use of loading tabs attached to thin sheets of composites proved to be experimentally unsatisfactory. Consequently, a new system was developed to load thin sheets of adherends. This system allows for the direct measurement of displacement along the load line. In well made joints separation occurred between the plies rather than in the adhesive.

Ripling, E. J.↗

NASA NTRS1984

Ultrasonic probing of the fracture process zone in rock using surface waves

A microcrack process zone is frequently suggested to accompany macrofractures in rock and play an important role in the resistance to fracture propagation. Attenuation of surface waves propagating through mode I fractures in wedge-loaded double-cantilever beam specimens of Westerly granite has been recorded in an attempt to characterize the structure of the fracture process zone. The ultrasonic measurements do not support the generally accepted model of a macroscopic fracture that incrementally propagates with the accompaniment of a cloud of microcracks. Instead, fractures in Westerly granite appear to form as gradually separating surfaces within a zone having a width of a few millimeters and a length of several tens of millimeters. A fracture process zone of this size would necessitate the use of meter-sized specimens in order for linear elastic fracture mechanics to be applicable.

Swanson, P. L.↗

NASA NTRS1985

Delamination growth in composite materials

Research related to growth of an imbedded through-width delamination (ITWD) in a compression loaded composite structural element is presented. Composites with widely different interlaminar fracture resistance were examined, viz., graphite/epoxy (CYCOM 982) and graphite/PEEK (APC-2). The initial part of the program consisted of characterizing the material in tension, compression and shear mainly to obtain consistent material properties for analysis, but also as a check of the processing method developed for the thermoplastic APC-2 material. The characterization of the delamination growth in the ITWD specimen, which for the unidirectional case is essentially a mixed Mode 1 and 2 geometry, requires verified mixed-mode growth criteria for the two materials involved. For this purpose the main emphasis during this part of the investigation was on Mode 1 and 2 fracture specimens, namely the Double Cantilever Beam (DCB) and End Notched Flexure (ENF) specimens.

Gillespie, J. W., Jr.↗

NASA NTRS1985

Application of variable metric methods to structural synthesis

Powell (1977, 1978), Biggs (1972, 1975), and Han (1976, 1977) have developed a class of variable metric methods which create an explicit, quadratic, subproblem which is to be solved for finding a search direction for design improvement. A one-dimensional search is then performed. The present paper has the objective to present this variable metric approach in the context of structural synthesis. The variable metric algorithm is modified for application to the structural synthesis problem. The application of the new procedure is illustrated with the aid of examples, taking into account a 10-bar planar truss, a 17-bar planar tower, and a cantilever beam.

Vanderplaats, G. N.↗

NASA NTRS1984

Bonded joint strength - Static versus fatigue

Adhesives are commonly characterized only by their static strength even though they are used in structural joints that are subjected to fatigue loads. This paper reviews the relationship between static and fatigue strength for four different specimen types: single-lap-shear, edge-delamination, double cantilever beam, and cracked-lap-shear. It was found that the ratio of static strength to fatigue strength varied from 2.3 to 4.7, depending on the adhesive and specimen configuration.

Johnson, W. S.↗

NASA NTRS1985

An elastic strip with multiple cracks and applications to tapered specimens

In this paper an infinite elastic strip containing arbitrarily oriented cracks and subjected to uniform tension and a pair of concentrated forces is formulated in terms of a system of singular integral equations. Even though the technique is sufficiently general to solve new multiple crack problem, with the objective of applying the results to tapered specimens, only a certain symmetric crack geometry and loading conditions are considered. The stress intensity factors are calculated for edge cracks in the strip under uniform tension and for a 'compact' and a 'slender' tapered specimen (the latter simulating the double cantilever beam) under concentrated forces or crack surface wedge forces.

Liu, X.-H.↗

NASA NTRS1985

Characterization of Mode I and mixed-mode delamination growth in T300/5208 graphite/epoxy

The roles played by Mode I and Mode II strain-energy release rates (G-I and G-II, respectively) in inducing delamination growth under static and fatigue loading were investigated, using T300/5208 graphite/epoxy specimens. Double cantilever beam (DCB) specimens and cracked lap shear (CLS) specimens were used for pure Mode I and mixed-mode tests, respectively. Fatigue-induced delamination growth was characterized by constant-amplitude fatigue tests at a minimum to maximum cyclic load ratio of 0.05 and a frequency of 10 Hz. During the tests, the maximum and minimum strain-energy release rates (Gmax, Gmin) and the delamination growth rate (da/dN) were monitored. Static tests on mixed-mode CLS specimens measured the total strain-energy release rate, which was broken into G-I and G-II components using finite-element analysis. A power-law relationship between da/dN and G-Imax, and da/dN and Gmax were obtained from fatigue test results on DCB and CLS specimens, respectively. The power law for a pure Mode II delamination was derived from CLS results by subtracting the contribution due to G-I.

Ramkumar, R. L.↗

NASA NTRS1986

Fracture toughness tests on plasma-sprayed coatings

Fracture toughness measurements have been performed on plasma-sprayed coatings. The intrinsic fracture toughness of plasma-sprayed coatings may be ascertained by means of a double cantilever beam (DCB) test. Emphasis is placed on calibration of the specimen geometry. Representative values for alumina coatings are presented.

Berndt, C. C.↗

NASA NTRS1986

Tetraglycidyl epoxy resins and graphite fiber composites cured with flexibilized aromatic diamines

Studies were performed to synthesize new ether modified, flexibilized aromatic diamine hardeners for curing epoxy resins. The effect of moisture absorption on the glass transition temperatures of a tetraglycidyl epoxy, MY 720, cured with flexibilized hardeners and a conventional aromatic diamine was studied. Unidirectional composites, using epoxy-sized Celion 6000 graphite fiber as the reinforcement, were fabricated. The room temperature and 300 F mechanical properties of the composites, before and after moisture exposure, were determined. The Mode I interlaminar fracture toughness of the composites was characterized using a double cantilever beam technique to calculate the critical strain energy release rate.

Delvigs, P.↗

NASA NTRS1986

Computer aided derivation of equations for composite mechanics problems and finite element analyses

Explicit equations are derived for analysis of multilayered fiber composites and for finite element analyses. The equations are obtained using a symbolic program and tested for various composite properties as well as for different fiber orientations. In order to analyze multilayered fiber composite structures, a variable thickness finite element is formulated. Examples of an airfoil geometry, simulated in a form of a cantilevered beam with various fiber orientations are studied.

Sarigul, N.↗

NASA NTRS1986

Impact resistance and interlaminar fracture toughness of through-the-thickness reinforced graphite/epoxy

Five through-the-thickness stitch configurations are analyzed to determine the effect of impact resistance and interlaminar fracture toughness on T3000/3501-6 graphite/epoxy. The test specimens were stitched with either polyester or Kevlar yarns and with various stitch parameters. Tension and compression mechanical, impact and compression-after-impact, and double cantilever beam tests were conducted. It is observed that the stitched laminates have tension and compression strengths 20-25 percent lower than the strengths of unstitched laminates, the tension strength of stitched laminates is reduced with increasing number of stitches, and the compression strength increases as the number of stitches are increased. The impact data reveal that the Kevlar stitched laminates have less damage than unstitched laminates; the most effective configuration for suppressing impact damage and improving interlaminar fracture toughness consists of Kevlar yarns 1/4 inch apart with eight stitches per inch. The mode 1 critical strain energy release rate for the 1/4 inch Kevlar eight stitch laminate was calculated as 30 times higher than that of the unstitched.

Dexter, H. B.↗

NASA NTRS1986

A comparison of several methods for the calculation of vibration mode shape derivatives

Four methods for the calculation of derivatives of vibration mode shapes (eigenvectors) with respect to design parameters are reviewed and compared. These methods (finite difference method, Nelson's method, modal method and a modified modal method) are implemented in a general-purpose commercial finite element program and applied to a cantilever beam and a stiffened cylinder with a cutout. A beam tip mass, a beam root height and specific dimensions of the cylinder model comprise the design variables. Data are presented showing the amount of central processor time used to compute the first four eigenvector derivatives for each example problem; errors and rapidity of convergence of the approximate derivative to the exact derivative are taken into account. Nelson's method proved to be most reliable and efficient.

Sutter, T. R.↗

NASA NTRS1986

Characterization of mode I and mixed-mode failure of adhesive bonds between composite adherends

A combined experimental and analytical investigation of an adhesively bonded composite joint was conducted to characterize both the static and fatigue beyond growth mechanism under mode 1 and mixed-mode 1 and 2 loadings. Two bonded systems were studied: graphite/epoxy adherends bonded with EC 3445 and FM-300 adhesives. For each bonded system, two specimen types were tested: a double-cantilever-beam specimen for mode 1 loading and a cracked-lapshear specimen for mixed-mode 1 and 2 loading. In all specimens tested, failure occurred in the form of debond growth. Debonding always occurred in a cohesive manner with EC 3445 adhesive. The FM-300 adhesive debonded in a cohesive manner under mixed-mode 1 and 2 loading, but in a cohesive, adhesive, or combined cohesive and adhesive manner under mode 1 loading. Total strain-energy release rate appeared to be the driving parameter for debond growth under static and fatigue loadings.

Mall, S.↗

NASA NTRS1985

Structural parameter identification of distributed systems using finite element approximation

A system identification technique is developed for classes of distributed systems using finite element approximations. Vibrating systems represented by partial differential equations have physical parameters associated with mass, stiffness, and damping distributions which need to be known in order to properly control and design mathematical models of the system. In order to identify these parameters a weighted least-squares algorithm and modified Newton-Raphson method is used for the identification process. The theory and technique is demonstrated by estimating the system parameters of a vibrating cantilever beam made up of several different structural properties.

Lee, K. Y.↗