Critical shear stress of an infinitely long flat plate with equal elastic restraints against rotation along the parallel edges
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Design of structures for optimum geometry
A method is presented for configuration optimization of finite element structures, given a reasonable initial geometry. The objective is to minimize weight or cost. Design variables include geometric as well as member sizing parameters. The number of elements and joints, and the element-joint relationships are prescribed and are not changed during the optimization process. However, the joint locations are changed. The structure is assumed to be linearly elastic and may be statically indeterminate. Multiple loading conditions are allowed. Constraints include limits on stiffness as well as strength. The method is demonstrated with application to truss design, subject to minimum size, strength, buckling, and displacement constraints. Major design improvements are achieved through configurations changes.
Vanderplaats, G. N.↗
Structural Verification and Modeling of a Tension Cone Inflatable Aerodynamic Decelerator
Verification analyses were conducted on membrane structures pertaining to a tension cone inflatable aerodynamic decelerator using the analysis code LS-DYNA. The responses of three structures - a cylinder, torus, and tension shell - were compared against linear theory for various loading cases. Stress distribution, buckling behavior, and wrinkling behavior were investigated. In general, agreement between theory and LS-DYNA was very good for all cases investigated. These verification cases exposed the important effects of using a linear elastic liner in membrane structures under compression. Finally, a tension cone wind tunnel test article is modeled in LS-DYNA for which preliminary results are presented. Unlike data from supersonic wind tunnel testing, the segmented tension shell and torus experienced oscillatory behavior when subjected to a steady aerodynamic pressure distribution. This work is presented as a work in progress towards development of a fluid-structures interaction mechanism to investigate aeroelastic behavior of inflatable aerodynamic decelerators.
Tanner, Christopher L.↗
Performance of three ablation materials during simulation of long-duration afterbody heating
Resistance to heat penetration and deformations or buckling of three ablation materials during simulated exposure to lifting vehicle afterbody heating
HEAT RESISTANCE↗
Compression failure of angle-ply laminates
The present work deals with modes and mechanisms of failure in compression of angle-ply laminates. Experimental results were obtained from 42 angle-ply IM7/8551-7a specimens with a lay-up of ((plus or minus theta)/(plus or minus theta)) sub 6s where theta, the off-axis angle, ranged from 0 degrees to 90 degrees. The results showed four failure modes, these modes being a function of off-axis angle. Failure modes include fiber compression, inplane transverse tension, inplane shear, and inplane transverse compression. Excessive interlaminar shear strain was also considered as an important mode of failure. At low off-axis angles, experimentally observed values were considerably lower than published strengths. It was determined that laminate imperfections in the form of layer waviness could be a major factor in reducing compression strength. Previously developed linear buckling and geometrically nonlinear theories were used, with modifications and enhancements, to examine the influence of layer waviness on compression response. The wavy layer is described by a wave amplitude and a wave length. Linear elastic stress-strain response is assumed. The geometrically nonlinear theory, in conjunction with the maximum stress failure criterion, was used to predict compression failure and failure modes for the angle-ply laminates. A range of wave length and amplitudes were used. It was found that for 0 less than or equal to theta less than or equal to 15 degrees failure was most likely due to fiber compression. For 15 degrees less than theta less than or equal to 35 degrees, failure was most likely due to inplane transverse tension. For 35 degrees less than theta less than or equal to 70 degrees, failure was most likely due to inplane shear. For theta less than 70 degrees, failure was most likely due to inplane transverse compression. The fiber compression and transverse tension failure modes depended more heavily on wave length than on wave amplitude. Thus using a single parameter, such as a ratio of wave amplitude to wave length, to describe waviness in a laminate would be inaccurate. Throughout, results for AS4/3502, studied previously, are included for comparison. At low off-axis angles, the AS4/3502 material system was found to be less sensitive to layer waviness than IM7/8551-7a. Analytical predictions were also obtained for laminates with waviness in only some of the layers. For this type of waviness, laminate compression strength could also be considered a function of which layers in the laminate were wavy, and where those wavy layers were. Overall, the geometrically nonlinear model correlates well with experimental results.
Peel, Larry D.↗
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.↗
Buckling tests on eccentrically loaded beam columns
Formulas are obtained for computing the buckling load of rods eccentrically loaded at each end, the computation being extended in particular to the inelastic range. The test results are graphically presented on three sets of curves. Two of these, at least for the elastic range, are independent of the material tested. The third set, which is independent of the material, possesses greater clearness and is therefore used for comparing the test results with the theoretical.
Cassens, J↗
Buckling of structures with uncertain imperfections - Personal perspective
The previous review on stochastic buckling of structures was written by Amazigo in 1976. This review summarizes some of the developments which took place in recent two decades. A brief overview is given of the effect on uncertainty in the initial geometric imperfections, elastic moduli, applied forces, and thickness variation. For the benefit of the thinking reader, the review has a critical nature. It should be noted that this manuscript has yet to be completed.
Elishakoff, Isaac↗
Stiffness and damping characteristics of aluminum in creep
Tensile creep tests conducted at 200 C were performed on annealed commercially pure aluminum specimens in order to measure the dominant elevated temperature dislocation processes. Testing consisted of applying small lateral loads to measure flexural stiffness, and vibrating the specimens laterally in order to measure dynamic modulus and internal damping. It was concluded that (1) the strain hardening increased static stiffness and decreased internal damping during early creep, and (2) the dynamic modulus remained essentially constant at the elastic value during creep. These results imply that primary creep may constitute a mechanism of recovery of dislocatory disorder induced by yielding the material during loading, and that the inelastic modulus utilized as a mathematical concept in several creep buckling theories is not a directly measurable material property.
Berkovits, A.↗
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↗
How to Introduce the Imperfection Sensitivity Concept into Design 2
The previous review on stochastic buckling of structures was written by Amazigo in 1976. The present review summarizes some of the developments which took place in recent two decades. A brief overview is given of the effect on uncertainty in the initial geometric imperfections, elastic moduli, applied forces, and thickness variation. For the benefit of the thinking reader, the review has a critical nature. Present essay should be viewed as a direct continuation of our previous paper (1983) with the same title. In order not to repeat what was covered there, it appears instructive to read it although not necessarily prior to dwelling on this article. Accordingly the title is appended with the serial number. It is not promised that the third review will follow since the university science, both fortunately and unfortunately, stands on three things: relevance, interest, and grants.
Elishakoff, Isaac↗
Study of foldable elastic tubes for large space structure applications
Various modifications were made to the tube design. The tubes were retested and analyzed, and the results are presented. One type of modified tube, the slotted tube, deployed successfully and reliably, and became the focus of detailed tests. Optimal design criteria, taking into consideration deployment as well as strength and buckling behavior were established.
Jones, I. W.↗
A mechanical model for elastic fiber microbuckling
A two-dimensional mechanical model is presented to predict the compressive strength of unidirectional fiber composites using technical beam theory and classical elasticity. First, a single fiber resting on a matrix half-plane is considered. Next, a more elaborate analysis of a uniformly laminated, unidirectional fiber composite half-plane is presented. The model configuration incorporates a free edge which introduces a buckling mode that originates at the free edge and decays into the interior of the half-plane. It is demonstrated that for composites of low volume fraction (less than 0.3), this decay mode furnishes values of buckling strain that are below the values predicted by the Rosen (1965) model. At a higher volume fraction the buckling mode corresponds to a half-wavelength that is in violation of the usual assumptions of beam theory. Causes for deviations of the model prediction from existing experimental results are discussed.
Waas, A. M.↗
A Mechanical Model for Elastic Fiber Microbuckling
A two-dimensional mechanical model is presented to predict the compressive strength of unidirectional fiber composites using technical beam theory and classical elasticity. First, a single fiber resting on a matrix half-plane is considered. Next, a more elaborate analysis of a uniformly laminated, unidirectional fiber composite half-plane is presented. The model configuration incorporates a free edge which introduces a buckling mode that originates at the free edge and decays into the inferior of the half-plane. It is demonstrated that for composites of low volume fraction (less than 0.3), this decay mode furnishes values of buckling strain that are below the values predicted by the Rosen (1965) model. At a higher volume fraction the buckling mode corresponds to a half wavelength that is in violation of the usual assumptions of beam theory. Causes for deviations of the model prediction froi?i existing experimental results are discussed.
Waas, M. A.↗
Investigation of Fiber Waviness in a Thick Glass Composite Beam Using THz NDE
Fiber waviness in laminated composite material is introduced during manufacture because of uneven curing, resin shrinkage, or ply buckling caused by bending the composite lay-up into its final shape prior to curing. The resulting waviness has a detrimental effect on mechanical properties, therefore this condition is important to detect and characterize. Ultrasonic characterization methods are difficult to interpret because elastic wave propagation is highly dependent on ply orientation and material stresses. By comparison, the pulsed terahertz response of the composite is shown to provide clear indications of the fiber waviness. Pulsed Terahertz NDE is an electromagnetic inspection method that operates in the frequency range between 300 GHz and 3 THz. Its propagation is influenced by refractive index variations and interfaces. This work applies pulsed Terahertz NDE to the inspection of a thick composite beam with fiber waviness. The sample is a laminated glass composite material approximately 15mm thick with a 90-degree bend. Terahertz response from the planar section, away from the bend, is indicative of a homogeneous material with no major reflections from internal plies, while the multiple reflections at the bend area correspond to the fiber waviness. Results of these measurements are presented for the planar and bend areas.
Anastasi, Robert F.↗
Nonlinear Analysis of the Space Shuttle Superlightweight LO2 Tank: Bahavior Under Booster Ascent Loads - Part 1
Results of linear bifurcation and nonlinear analyses of the Space Shuttle superlightweight (SLWT) external liquid-oxygen (LO2) tank for an important early booster ascent loading condition are presented. These results for thin-walled linear elastic shells that are subjected to combined mechanical and thermal loads illustrate an important type of response mode that may be encountered in the design of other liquid-fuel launch vehicles. Linear bifurcation analyses are presented that predict several nearly equal eigenvalues that correspond to local buckling modes in the forward ogive section of the LO2 tank. In contrast, the nonlinear response phenomenon is shown to consist of short-wavelength bending deformations in the forward ogive and barrel sections of the LO2 tank that growing amplitude in a stable manner increasing load. Imperfection sensitivity analyses are presented that show that the presence of several nearly equal eigenvalues does not lead to a premature general instability mode for the forward ogive section. For the linear bifurcation and nonlinear analyses, the results show that accurate predictions of the response of the shield generally require a large-scale, high-fidelity finite-element model. Results are also presented that show that the SLWT LO2 tank can support loads in excess of approximately 2.6 times the values of the operational loads considered.
Young, Richard D.↗
Titanium/beryllium laminates - Fabrication, mechanical properties, and potential aerospace applications
The paper describes an investigation to assess the fabricability, mechanical properties, and possible aerospace applications of adhesively-bonded titanium/beryllium Tiber laminates. The results of the investigation indicate that structural laminates can be made which have: a modulus of elasticity comparable to steel, fracture strength comparable to the yield strength of titanium, density comparable to aluminum, impact resistance comparable to titanium, and little or no notch sensitivity. These laminates can have stiffness and weight advantages over other materials, including advanced fiber composites, in some aerospace applications where buckling resistance, vibration frequencies, and weight considerations control the design.
Chamis, C. C.↗
Titanium/beryllium laminates: Fabrication, mechanical properties, and potential aerospace applications
The investigation indicated that structural laminates can be made which have: a modulus of elasticity comparable to steel, fracture strength of comparable to the yield strength of titanium, density comparable to aluminum, impact resistance comparable to titanium, and little or no notch sensitivity. These laminates can have stiffness and weight advantages over other materials including advanced fiber composites, in some aerospace applications where buckling resistance, vibration frequencies, and weight considerations control the design.
Chamis, C. C.↗