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At least 91 records · Page 5

Wrinkle ridges, reverse faulting, and the depth penetration of lithospheric stress in lunae planum, Mars

Tectonic features on a planetary surface are commonly used as constraints on models to determine the state of stress at the time the features formed. Quantitative global stress models applied to understand the formation of the Tharsis province on Mars constrained by observed tectonics have calculated stresses at the surface of a thin elastic shell and have neglected the role of vertical structure in influencing the predicted pattern of surface deformation. Wrinkle ridges in the Lunae Planum region of Mars form a conentric pattern of regularly spaced features in the eastern and southeastern part of Tharsis; they are formed due to compressional stresses related to the response of the Martian lithosphere to the Tharsis bulge. As observed in the exposures of valley walls in areas such as the Kasei Valles, the surface plains unit is underlain by an unconsolidated impact-generated megaregolith that grades with depth into structurally competent lithospheric basement. The ridges have alternatively been hypothesized to reflect deformation restricted to the surface plains unit ('thin skinned deformation') and deformation that includes the surface unit, megaregolith and basement lithosphere ('thick skinned deformation'). We have adopted a finite element approach to quantify the nature of deformation associated with the development of wrinkle ridges in a vertically stratified elastic lithosphere. We used the program TECTON, which contains a slippery node capability that allowed us to explicitly take into account the presence of reverse faults believed to be associated with the ridges. In this study we focused on the strain field in the vicinity of a single ridge when slip occurs along the fault. We considered two initial model geometries. In the first, the reverse fault was assumed to be in the surface plains unit, and in the second the initial fault was located in lithospheric basement, immediately beneath the weak megaregolith. We are interested in the conditions underwhich strain in the surface layer and basement either penetrates or fails to penetrate through the megaregolith. We thus address the conditions required for an initial basement fault to propagate through the megaregolith to the surface, as well as the effect of the megareolith on the strain tensor in the vicinity of a fault that nucleates in the surface plains unit.

Zuber, M. T.↗

Thermal correction of deformations in a telescope mirror

Orbiting astronomical observatories have the potential for making observations far superior to those from earth-based mirrors. In order for this performance to be realized, the contour of the primary mirror must be very accurately controlled. A preliminary investigation of the use of thermally induced elastic strains for correcting axisymmetric deformations in space telescope mirrors has been presented. The relation between axial deformation and thermal inputs was determined by a finite difference solution of the equations for thin elastic shells. The use of this technique was demonstrated analytically on a beryllium paraboloid. This mirror had 10 equally spaced thermal inputs and results are presented which show the nature of the temperature distribution required to correct deformations due to an acceleration-type loading.

Rhodes, M. D.↗

Vibrations of incompressible liquid-plastic tank combinations using a series representation of the liquid

A series representation is presented of the dynamic behavior of incompressible non-viscous liquids contained in partially filled elastic shells of revolution. Using a series in which each term satisfies exactly Laplace's equation, the liquid portion of the problem becomes an integral equation on the wetted wall of the shell. Physical insight required in selecting the terms of the series is such that selection may be readily programed on a computer. Liquid-shell vibration interaction is investigated by modifying an existing shell of revolution vibration program with the series expansion of the liquid pressure loading on the wetted shell wall. Application of the modified program is demonstrated on a hemispherical tank and a realistic scaled model of a launch vehicle tank having a more complex geometry. Comparison of the present analysis with a NASTRAN finite element analysis for a hemispherical tank, and comparison with test results for a launch vehicle tank shows excellent agreement and rapid convergence of the series representation of the liquid to the true solution.

Housner, J. M.↗

Elastic lithosphere thickness on the moon from mare tectonic features - A formal inversion

The thickness (T) of the lunar elastic lithosphere at the time (3.6 to 3.8 billion years ago) of the earliest preserved basalt flows in circular mare basins can be estimated by inverting the observed locations of extensional tectonic features in and surrounding the maria. In performing the inversion, the lithosphere is modeled as an elastic shell with a liquid interior, and the basalt load for each mare is approximated by a set of concentric cylinders. To permit solving the forward problem of placing radial limits on the positions of the rilles around a given mare, an additional parameter F, the ratio of the radial stress at the radial limits to the maximum radial stress, is introduced. T and F are chosen to give the best weighted-squares fit of the radial limits to the observations, and are used as the initial values in a linearized matrix inversion to check the resolution and estimate errors. The application of the procedure to three maria with prominent extensional features, Humorum, Orientale, and Serenitatis, gives values of T from about 40 + or - 10 to 50 + or - 10 km, and in each case the linearized matrix equation has an exact inverse.

Comer, R. P.↗

Jump phenomena

The paper considers jump phenomena composed of large amplitude responses of nonlinear systems caused by small amplitude disturbances. Physical problems where large jumps in the solution amplitude are important features of the response are described, including snap buckling of elastic shells, chemical reactions leading to combustion and explosion, and long-term climatic changes of the earth's atmosphere. A new method of rational functions was then developed which consists of representing the solutions of the jump problems as rational functions of the small disturbance parameter; this method can solve jump problems explicitly.

Reiss, E. L.↗

Mechanics of couple-stress fluid coatings

The formal development of a theory of viscoelastic surface fluids with bending resistance - their kinematics, dynamics, and rheology are discussed. It is relevant to the mechanics of fluid drops and jets coated by a thin layer of immiscible fluid with rather general rheology. This approach unifies the hydrodynamics of two-dimensional fluids with the mechanics of an elastic shell in the spirit of a Cosserat continuum. There are three distinct facets to the formulation of surface continuum mechanics. Outlined are the important ideas and results associated with each: the kinematics of evolving surface geometries, the conservation laws governing the mechanics of surface continua, and the rheological equations of state governing the surface stress and moment tensors.

Waxman, A. M.↗

Thermal stresses in planetary elastic lithospheres

The role of thermal stresses in the tectonics of the moon is reexamined in this paper. A model is used that considers a spherical elastic shell overlying a fluid core. It is shown that the thermal stresses generated by temperature changes within the shell usually dominate over the thermal contraction or expansion of the core. During the entire evolution of the moon the cooling of the lithosphere is likely to have dominated the cooling of the interior and the result would be tensional lithospheric thermal stresses. However, during the recent evolution of the moon the change in the near surface thermal stresses is compressional. It is argued that the surface compressional features on Mercury are not due to the thermal contraction of the interior

Turcotte, D. L.↗

Tidal reorientation and the fracturing of Jupiter's moon Europa

The lineaments on Europa are discussed in terms of the orientation of the lineaments relative to the tensile stress trajectories due to tidal distortions and to nonsynchronous rotation. The cracks are noticeable by their darker albedo compared to the presumed water ice surrounding them. The stress trajectories for tidal distortion of a thin elastic shell are superimposed on Mercator projection maps of the lineaments. It is shown that the lineaments are mainly oriented at high angles to the tensile stress trajectories that would be expected for regularly occurring nonsynchronous rotation, i.e., extensional fractures would appear. The reorientation motions which would cause the fractures are estimated. It is suggested that the fractures occur episodically to release stresses built up on the tensile surface of the crust during the continuous nonsynchronous rotation of Europa.

Mcewen, A. S.↗

Stress analysis of Tellus Regio, Venus, based on gravity and topography - Comparison with Venera 15/16 radar images

The tectonics of the Tellus Region highland on Venus is examined using the altimetry and gravity data collected by Pioneer Venus, which were incorporated into a thin elastic shell model to calculate both the global (long-wavelength) and the regional (short-wavelength) stresses for various assumed values of crust, lithosphere, and mantle thickness and modes of compensation. The resultant stress fields were compared to the surface morphology observed in the Venera 15/16 radar images and interpreted in terms of stress history of Tellus Regio. The best fitting parameters were found to be consistent with minor amounts of lithospheric flexure being necessary to produce the observed surface features of this region.

Williams, David R.↗

Layout optimization using the homogenization method

A generalized layout problem involving sizing, shape, and topology optimization is solved by using the homogenization method for three-dimensional linearly elastic shell structures in order to seek a possibility of establishment of an integrated design system of automotive car bodies, as an extension of the previous work by Bendsoe and Kikuchi. A formulation of a three-dimensional homogenized shell, a solution algorithm, and several examples of computing the optimum layout are presented in this first part of the two articles.

Suzuki, Katsuyuki↗

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.↗

Remarks on the elastic axis of shell wings

The definitions of flexural center, torsional center, elastic center, and elastic axis are discussed. The calculation of elastic centers is dealt with in principle and a suggestion is made for the design of shear webs.

Kuhn, Paul↗

Large amplitude flexural vibration of thin elastic flat plates and shells

The general equations governing the large amplitude flexural vibration of any thin elastic shell using curvilinear orthogonal coordinates are derived and consist of two coupled, nonlinear, partial differential equations in the normal displacement w and the stress function F. From these equations, the governing equations for the case of shells of revolution or flat plates can be readily obtained as special cases. The material of the shell or plate is isotropic and homogeneous and Hooke's law for the two-dimensional case is valid. It is suggested that the difference between the hardening type of nonlinearity in the case of flat plates and straight beams and the softening type of nonlinearity in the case of shells and rings can, in general, be traced to the amount of curvature present in the underformed median surface of the structure concerned.

Pandalia, K. A. V.↗