Comparison of an approximate and an exact method of shear-lag analysis
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STRESSED SKIN- BEAMS, BOX↗
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Bending and shear stresses developed by the instantaneous arrest of the root of a cantilever beam rotating with constant angular velocity about a transverse axis through the root
A theoretical investigation was made of the behavior of a cantilever beam in rotational motion about a transverse axis through the root determining the stresses, the deflections, and the accelerations that occur in the beam as a result of the arrest of motion. The equations for bending and shear stress reveal that, at a given percentage of the distance from root to tip and at a given trip velocity, the bending stresses for a particular mode are independent of the length of the beam and the shear stresses vary inversely with the length. When examined with respect to a given angular velocity instead of a given tip velocity, the equations reveal that the bending stress is proportional to the length of the beam whereas the shear stress is independent of the length. Sufficient experimental verification of the theory has previously been given in connection with another problem of the same type.
BEAMS - VIBRATION↗
Inclusion of transverse shear deformation in finite element displacement formulations
A stiffness matrix is derived for a beam element with transverse shear deformation. It is shown that straightforward energy minimization yields the correct stiffness matrix in displacement formulations when transverse shear effects are considered. Since the TIM4 beam element does not represent the geometric boundary conditions for a cantilever beam the rotation of the normal must be retained as a grid point degree of freedom.
Narayanaswami, R.↗
Gravitational lensing of supernovae by dark matter candidates of mass M greater than about 0.001 solar masses
A review is presented concerning the gravitational lensing of supernovae by intervening condensed objects, including dark matter candidates such as dim stars and black holes. the expansion of the supernova beam within the lens produces characteristic time-dependent amplification and polarization which depend upon the mass of the lens. The effects of the shearing of the beam due to surrounding masses are considered, although the study of these effects is confined to isolated masses whose size is much less than that of the supernova (about 10 to the 15th cm). Equations for the effects of lensing and graphs comparing these effects in different classes of supernovae are compared. It is found that candidates for lensing would be those supernovae at least as bright as their parent galaxy, or above the range of luminosities expected for their spectral class.
Wagoner, Robert V.↗
Recurrence formulas and differential equations for stress analysis of cambered box beams
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EQUATIONS - STRESSES BEAMS↗
Stress and Distortion Analysis of a Swept Box Beam Having Bulkheads Perpendicular to the Spars
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WING SPARS, BOX - BENDING & TORSION↗
Optical propagation through a homogeneous turbulent shear flow
Effects of organized turbulent structures on the propagation of an optical beam in a homogeneous shear flow were studied. A passive-scalar field in a computed turbulent shear flow is used to represent index-of-refraction fluctuations, and phase errors induced in a coherent optical beam by turbulent fluctuations are computed. The organized vortical structures produce a scalar distribution with elongated regions of intense fluctuations which have an inclination with respect to the mean flow similar to that of the characteristic hairpin eddies. It is found that r.m.s. phase error is minimized by propagating approximately normal to the inclined vortical structures. Two-point correlations of vorticity and scalar fluctuation suggest that the regions of intense scalar fluctuation are produced primarily by the hairpin eddies.
Truman, C. Randall↗
Optical propagation through a homogeneous turbulent shear flow
Effects of organized turbulent structures on the propagation of an optical beam in a homogeneous shear flow have been studied. A passive-scalar field in a computed turbulent shear flow is used to represent index-of-refraction fluctuations, and phase errors induced in a coherent optical beam by turbulent fluctuations are computed. The organized vortical structures produce a scalar distribution with elongated regions of intense fluctuations which have an inclination with respect to the mean flow similar to that of the characteristic hairpin eddies. It is found that rms phase error is minimized by propagating approximately normal to the inclined vortical structures. Two-point correlations of vorticity and scalar fluctuation suggest that the regions of intense scalar fluctuation are produced primarily by the hairpin eddies.
Truman, C. Randall↗
Computationally Efficient Beam Elements for Accurate Stresses in Sandwich Laminates and Laminated Composites with Delaminations
Laminated composites are prone to delamination failure due to the lack of reinforcement through the thickness. Therefore, during the design process the initiation and propagation of delaminations should be accounted for as early as possible. This paper presents computationally efficient nine degree-of-freedom (dof) and eight-dof shear locking-free beam elements using the mixed form of the refined zigzag theory (RZT(sup(m))). The corresponding nine-dof and eight-dof elements use the anisoparametric and constrained anisoparametric interpolation schemes, respectively, to eliminate shear locking in slender beams. The advantage of the present element over previous RZT beam elements is that no post-processing is required to accurately model the transverse shear stress while maintaining the computational efficiency of a low-order beam element. Comparisons with high-fidelity finite element models and three-dimensional elasticity solutions show that the elements can robustly and accurately predict the displacement field, axial stress and transverse shear stress through the thickness of a sandwich beam or a composite laminate with an embedded delamination. In fact, the accuracy and computational efficiency of predicting stresses in laminates with embedded delaminations make the present elements attractive choices for RZT-based delamination initiation and propagation methodologies available in the literature.
R. M. J. Groh↗
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.↗
Dynamic Stability of Uncertain Laminated Beams Under Subtangential Loads
Because of the inherent complexity of fiber-reinforced laminated composites, it can be challenging to manufacture composite structures according to their exact design specifications, resulting in unwanted material and geometric uncertainties. In this research, we focus on the deterministic and probabilistic stability analysis of laminated structures subject to subtangential loading, a combination of conservative and nonconservative tangential loads, using the dynamic criterion. Thus a shear-deformable laminated beam element, including warping effects, is derived to study the deterministic and probabilistic response of laminated beams. This twenty-one degrees of freedom element can be used for solving both static and dynamic problems. In the first-order shear deformable model used here we have employed a more accurate method to obtain the transverse shear correction factor. The dynamic version of the principle of virtual work for laminated composites is expressed in its nondimensional form and the element tangent stiffness and mass matrices are obtained using analytical integration The stability is studied by giving the structure a small disturbance about an equilibrium configuration, and observing if the resulting response remains small. In order to study the dynamic behavior by including uncertainties into the problem, three models were developed: Exact Monte Carlo Simulation, Sensitivity Based Monte Carlo Simulation, and Probabilistic FEA. These methods were integrated into the developed finite element analysis. Also, perturbation and sensitivity analysis have been used to study nonconservative problems, as well as to study the stability analysis, using the dynamic criterion.
Goyal, Vijay K.↗
In-situ TEM observation of shear induced microstructure evolution in Cu-Nb alloy
Phase boundaries in multiphase alloys govern defect interaction and chemical intermixing across different phases during plastic deformation. Dynamic interaction of defects with phase boundaries in multiphase alloys, especially for immiscible alloys, has been topic of significant research interest in recent years. In this work, we describe a novel approach for carrying out in-situ TEM shear deformation to directly observe interfacial microstructural evolution of a Cu-Nb alloy. A unique double shear specimen geometry is microfabricated by a focused ion beam technique to apply shear deformation upon push loading inside the TEM. From the real-time observation, we discover that the phase boundary with a zigzag morphology effectively blocks stacking faults nucleated in a Cu grain from slipping into a Nb grain. Meanwhile, the Cu phase bears the most plastic deformation through slip or twinning mechanisms. This work sheds light on understanding the shear deformation and the behavior of phase boundaries in multiphase alloys during shear deformation.
36 MATERIALS SCIENCE↗
Development of polyphenylquinoxaline graphite composites
The potential of polyphenylquinoxaline (PPQ)/graphite composites to serve as structural material at 316 C (600 F)has been demonstrated using a block copolymer, BlCo(13), PPQ derivative. Initially, thirteen polyphenylquinoxalines were evaluated. From this work, four candidate polymers were selected for preliminary evaluation as matrices for HMS graphite fiber reinforced composites. The preliminary composite evaluation enabled selection of one of the four polymers for advanced composite preparation and testing. Using an experimentally established cure schedule for each of the four polymers, preliminary laminates of 50% resin volume content, prepared without postcure, were tested for flexure strength and modulus, interlaminar shear strength (short beam), and tensile strength and modulus at ambient temperature. A block copolymer (Bl Co 13) derived from one mole p-bis (phenylglyoxalyl) benzene, one fourth mole 3,3'-diaminobenzidine and three-fourths mole 3,3', 4,4'-tetraminobenzophenone was selected for extensive study. Tensile, flexural, and interlaminar shear values were obtained after aging and testing postcured BlCo(13) laminates at 316 C (600 F). The potential of PPQ/graphite laminates to serve as short term structural materials at temperatures up to 371 C (700 F) was demonstrated through weight loss experiments.
Hoggatt, J. T.↗
Development of polyphenylquinoxaline graphite composites.
The potential of polyphenylquinoxaline (PPQ)/graphite composites to serve as structural material at 316 C (600 F) has been demonstrated using a block copolymer, BICo(1:3), PPQ derivative. Initially, 13 polyphenylquinoxalines were evaluated. From this work, four candidate polymers were selected for preliminary evaluation as matrices for HMS graphite fiber reinforced composites. The preliminary composite evaluation enabled selection of one of the four polymers for advanced composite preparation and testing. Using an experimentally established cure schedule for each of the four polymers, preliminary laminates of 50% resin volume content, prepared without postcure, were tested for flexure strength and modulus, interlaminar shear strength (short beam), tensile strength, and modulus of ambient temperature. The potential of PPQ/graphite laminates to serve as short term structural materials at temperatures up to 371 C (700 F) was demonstrated through weight loss experiments.
Shdo, J. G.↗
ISOFINEL: Isoparametric finite element code for elastic analysis of two-dimensional bodies
A formulation is presented for the development of a finite element program for the elastic analysis of two-dimensional bodies using the eight-node isoparametric quadrilateral. The program solves for both plane stress and plane strain problems. The finite element formulation based on the isoparametric displacement functions is presented. The program structure is given in the form of flow diagrams with descriptions of the numerical procedure used to obtain the element stiffness matrix, and the solution method employed to solve for nodal displacements. Three numerical examples (a plate under uniaxial tension, a plate under pure shear, and a beam under pure bending) are presented to illustrate the capability and limitations of the element implementation. The first problem is solved exactly by the element, as predicted by the form of its displacement functions. In the other two problems the accuracy of the solution is highly dependent upon the slenderness of the element, the number of elements in the map, and the numerical integration scheme used to build the element stiffness matrix.
Marino, C.↗
Comparison of some optimal control methods for the design of turbine blades
This paper attempts a comparative study of some numerical methods for the optimal control design of turbine blades whose vibration characteristics are approximated by Timoshenko beam idealizations with shear and incorporating simple boundary conditions. The blade was synthesized using the following methods: (1) conjugate gradient minimization of the system Hamiltonian in function space incorporating penalty function transformations, (2) projection operator methods in a function space which includes the frequencies of vibration and the control function, (3) epsilon-technique penalty function transformation resulting in a highly nonlinear programming problem, (4) finite difference discretization of the state equations again resulting in a nonlinear program, (5) second variation methods with complex state differential equations to include damping effects resulting in systems of inhomogeneous matrix Riccatti equations some of which are stiff, (6) quasi-linear methods based on iterative linearization of the state and adjoint equation. The paper includes a discussion of some substantial computational difficulties encountered in the implementation of these techniques together with a resume of work presently in progress using a differential dynamic programming approach.
Desilva, B. M. E.↗
The structural behavior of a graphite-polymide honeycomb sandwich panel with quasi-isotropic face sheets and an orthotropic core
The results of a series of tests of graphite-polyimide honeycomb sandwich panels are presented. The panels were 1.22 m long, 0.508 m wide, and approximately 13.3 m thick. The face sheets were a T-300/PMR-15 fabric in a quasi-isotropic layup and were 0.279 mm thick. The core was Hexcel HRH 327-3/16 - 4.0 glass reinforced polyimide honeycomb, 12.7 mm thick. Three panels were used in the test: one was cut into smaller pieces for testing as beam, compression, and shear specimens; a second panel was used for plate bending tests; the third panel was used for in-plane stability tests. Presented are the experimental results of four point bending tests, short block compression tests, core transverse shear modulus, three point bending tests, vibration tests, plate bending tests, and panel stability tests. The results of the first three tests are used to predict the results of some of the other tests. The predictions and experimental results are compared, and the agreement is quite good.
Hyer, M. W.↗