Cartesian formulation of membrane theory.
Cartesian formulation of membrane theory, discussing equations of equilibrium, strain energy, variation formulation and boundary conditions
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Cartesian formulation of membrane theory, discussing equations of equilibrium, strain energy, variation formulation and boundary conditions
The objective is to study the assumed natural strain (ANS) formulation of finite elements from a variational standpoint. The study is based on two hybrid extensions of the Reissner-type functional that uses strains and displacements as independent fields. One of the forms is a genuine variational principle that contains an independent boundary traction field, whereas the other one represents a restricted variational principle. Two procedures for element level elimination of the strain field are discussed, and one of them is shown to be equivalent to the inclusion of incompatible displacement modes. Also, the 4-node C(exp 0) plate bending quadrilateral element is used to illustrate applications of this theory.
The objective of the research described in this paper is to assess the accuracy of classical linear acceleration/strain prediction theory for flat, rectangular panels excited by low level, acoustic plane waves. Predictions for both aluminum and laminated composite panels were based on the Ritz method using an orthotropic, multi-mode analysis with rotational springs on the boundaries. The measured natural frequencies and critical damping ratio of the panels were empirial inputs to the model. The comparison between measured and predicted acceleration was very good. Although a factor of three bias error was found between measured and predicted strains, the model was good for predicting the trends in the spatial variation in strain across the panel.
Probabilistic failure analysis is a tool to predict the reliability of a part or system. Probabalistic techniques were used to predict critical stresses which occur in the solid rocket booster aft-skirt during main engine buildup, immediately prior to lift-off. More than any other hold down post (HDP) load component, the Z loads are sensitive to variations in strains and calibration constants. Also, predicted aft-skirt stresses are strongly affected by HDP load variations. Therefore, the instrumented HDP are not effective load transducers for Z loads, and, when used with aft skirt stress indicator equations, yield estimates with large uncertainty. Monte Carlo simulation proved to be a straight forward way of studying the overlapping effects of multiple parameters on predicted equipment performance. An advantage of probabilistic analysis is the degree of uncertainty of each parameter as stated explicitly by its probability distribution. It was noted, however, that the choice of parameter distribution had a large effect on the simulation results. Many times these distributions must be assumed. The engineer who is designing the part should be responsible for the choice of parameter distribution.
An evaluation is made of a perturbation method devised to obtain highly accurate approximations to families of strongly nonlinear solutions which are either continuous or discontinuous, and which represent variations in some arbitrary parameter. The method first defines a unit perturbation by using two nonlinear solutions which differ from one another by a nominal change in some geometric or flow parameter, then employs this unit perturbation to predict a family of related nonlinear solutions over a range of parameter variation. Coordinate straining is incorporated into this perturbation method for determining the unit perturbation to account for the movement of discontinuities and maxima of high-gradient regions due to the perturbation. Attention is given to transonic and subsonic flows. Comparisons of the perturbation results with the corresponding 'exact' nonlinear solutions show a remarkable accuracy and range of validity of the perturbation method across the spectrum of examples considered.
This paper presents a study of pumpkin-shaped superpressure balloons, consisting of gores made from a thin polymeric film attached to high stiffness, meridional tendons. This type of design is being used for the NASA ULDB balloons. The gore film shows considerable time-dependent stress relaxation, whereas the behaviour of the tendons is essentially time-independent. Upon inflation and pressurization, the "instantaneous", i.e. linear-elastic strain and stress distribution in the film show significantly higher values in the meridional direction. However, over time, and due to the biaxial visco-elastic stress relaxation of the the material, the hoop strains increase and the meridional stresses decrease, whereas the remaining strain and stress components remain substantially unchanged. These results are important for a correct assessment of the structural integrity of a pumpkin balloon in a long-duration mission, both in terms of the material performance and the overall stability of the shape of the balloon. An experimental investigation of the time dependence of the biaxial strain distribution in the film of a 4 m diameter, 48 gore pumpkin balloon is presented. The inflated shape of selected gores has been measured using photogrammetry and the time variation in strain components at some particular points of these gores has been measured under constant pressure and temperature. The results show good correlation with a numerical study, using the ABAQUS finite-element package, that includes a widely used model of the visco-elastic response of the gore material:
A portable device for calibrating dynamic strain gages is described. The device contains a motor-driven cam, which applies alternating tensile loads to a metal strip 5/8 inch wide and 6 1/4 inches long. The cam is designed to produce a nearly sinusoidal variation of strain with time. Dynamic strain gages with gage lengths up to 5 inches may be calibrated by mounting them on the strip and by changing the frequency and the amplitude of the tensile load. The frequency may be varied from 15 to 30 cycles per second and the strain amplitude from 0 to 10x10-4 in steps of 2x10-4.
Reissner variational formulation of temperature distribution boundary value problem of axisymmetric thermal stresses in isotropic sandwich shells of revolution
Reissner variational formulation of temperature distribution boundary value problem of axisymmetric thermal stresses in isotropic sandwich shells of revolution
A method for determining highly accurate approximations to families of strongly nonlinear solutions which are either continuous or discontinuous, and which represent variations in some arbitrary parameters, is developed and evaluated. The procedure consists of defining a unit perturbation by employing two or more nonlinear solutions which differ from one another by a nominal change in some geometric or flow parameter, and then using that unit perturbation to predict a family of related nonlinear solutions over a range of parameter variation. Coordinate straining is used in determining the unit perturbation to account for the movement of discontinuities and maxima of high-gradient regions due to the perturbation. Although the procedure is generally applicable, results are presented here for nonlinear aerodynamic applications. Attention is focused in particular on transonic flows which are strongly supercritical and exhibit large surface shock movement over the parametric range studied; and on subsonic flows which display large pressure variations in the stagnation and peak suction pressure regions. Flows past both isolated airfoils and compressor cascades involving a variety of flow and geometry parameter changes are considered. Comparisons with the corresponding 'exact' nonlinear solutions indicate a remarkable accuracy and range of validity of such a procedure. Computational time is trivial.
Butt-weld joints are most commonly designed into pressure vessels which then become as reliable as the weakest increment in the weld chain. In practice, weld material properties are determined from tensile test specimen and provided to the stress analyst in the form of a stress versus strain diagram. Variations in properties through the thickness of the weld and along the width of the weld have been suspect but not explored because of inaccessibility and cost. The purpose of this study is to investigate analytical and computational methods used for analysis of welds. The weld specimens are analyzed using classical elastic and plastic theory to provide a basis for modeling the inelastic properties in a finite-element solution. The results of the analysis are compared to experimental data to determine the weld behavior and the accuracy of prediction methods. The weld considered in this study is a multiple-pass aluminum 2219-T87 butt weld with thickness of 1.40 in. The weld specimen is modeled using the finite-element code ABAQUS. The finite-element model is used to produce the stress-strain behavior in the elastic and plastic regimes and to determine Poisson's ratio in the plastic region. The value of Poisson's ratio in the plastic regime is then compared to experimental data. The results of the comparisons are used to explain multipass weld behavior and to make recommendations concerning the analysis and testing of welds.
A computer program which is being developed to analyze the heterogeneous stress and strain history variation at the 'damage critical' locations of a composite structure operating at elevated temperatures is described. The theoretical foundations behind this program are described. The relationship between Fourier series and Green's function approaches is elucidated.
An analysis of GPS data over the period 1987-91 confirms geologic and seismic evidence that the Santa Barbara Channel is a complicated actively deforming region. The data indicate north-south compression in the eastern channel, with little deformation in the west. Rotation may also be an important deformation mechanism. An analysis of strain rate variation over periods of 4.5, 17, and 100 yr suggests that deformation is nonuniform.
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A study is made of the effect of lamination and material parameters of thermally stressed multilayer composite panels on the strain energy and its sensitivity coefficients obtained by the three-dimensional thermoelasticity model. The sensitivity coefficients measure the sensitivity of the strain energy to variations in the different lamination and material parameters of the panel. The strain energy and sensitivity coefficients obtained by the three-dimensional model are used as the basis for assessing the accuracy of the corresponding quantities obtained by two-dimensional first-order shear deformation theory. Numerical results are presented for antisymmetrically laminated angle-ply panels subjected to linear temperature variation through the thickness. The numerical results demonstrate the accuracy of the strain energy and its sensitivity coefficients obtained by the first-order shear deformation theory, for the range of parameters considered, and the importance of the particular terms in the strain energy, which vanish for single-layer panels.
The subduction of the Cocos plate beneath Costa Rica is among the highest convergence rates in the world. The high subduction rate and nearness of the Nicoya Peninsula, Costa Rica to the Middle America Trench (MAT) provide a unique opportunity to map variations in interseismic strain of the crust above the seismogenic zone in response to variations in seismic coupling.
Temperature effects on electrical resistivity of metallic strain gage materials
A single-band model calculation is developed for the effect of strain on the temperature variation of the electronic density of states and the electrical onductivity of disordered binary alloys. Experimentally, strain has only a small effect on the temperature variation of the conductivity. Shifts in the Fermi level and distortions of the density of states under different strains are found from the calculations. The small change in the temperature variation of conductivity under strain is a result of competition between these two effects. Methods to extract physical parameters characterizing alloys from measurements of the strain and temperature variation of the resistivity are discussed. Suggestions are also made about materials-selection criteria for strain-gauge applications.