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NASA NTRS1995

Sensitivity analysis for the dynamic response of thermoviscoplastic shells of revolution

A computational procedure is presented for evaluating the sensitivity coefficients of the dynamic axisymmetric, fully-coupled, thermoviscoplastic response of shells of revolution. The analytical formulation is based on Reissner's large deformation shell theory with the effects of large-strain, transverse shear deformation, rotatory inertia and moments turning around the normal to the middle surface included. The material model is chosen to be viscoplasticity with strain hardening and thermal hardening, and an associated flow rule is used with a von Mises effective stress. A mixed formulation is used for the shell equations with the fundamental unknowns consisting of six stress resultants, three generalized displacements and three velocity components. The energy-balance equation is solved using a Galerkin procedure, with the temperature as the fundamental unknown. Spatial discretization is performed in one dimension (meridional direction) for the momentum and constitutive equations of the shell, and in two dimensions (meridional and thickness directions) for the energy-balance equation. The temporal integration is performed by using an explicit central difference scheme (leap-frog method) for the momentum equation; a predictor-corrector version of the trapezoidal rule is used for the energy-balance equation; and an explicit scheme consistent with the central difference method is used to integrate the constitutive equations. The sensitivity coefficients are evaluated by using a direct differentiation approach. Numerical results are presented for a spherical cap subjected to step loading.

Kulkarni, Makarand↗

NASA NTRS2012

Asymmetric Magnetosphere Deformation Driven by Hot Flow Anomaly(ies)

We present a case study of a large deformation of the magnetopause on November 26, 2008. The investigation is based on observations of five THEMIS spacecraft located at the dawn flank in the magnetosphere and magnetosheath, on Cluster measurements at the dusk magnetosheath, and is supported by ACE solar wind monitoring. The main revelation of our study is that the interaction of the IMF discontinuity with the bow shock creates either one very elongated hot flow anomaly (HFA) or a pair of them that is (are) simultaneously observed at both flanks. Whereas the dusk HFA is weak and does not cause observable deformation of the magnetopause, the pressure variations connected with the dawn HFA lead to a magnetopause displacement by approx. = 5 R(sub E) outward from its nominal position. This is followed by a rapid inward motion of the magnetopause approx. = 4 R(sub E) inward with respect to the model location. The surface deformation is so large that the outermost THEMIS spacecraft was in the magnetosphere, whereas the spacecraft located 9 R(sub E) inbound entered into the magnetosheath at the same time. The whole event lasted about 5 minutes.

hot flow anomaly↗

NASA NTRS1965

Testing device subjects elastic materials to biaxial deformations

Testing device stretches elastic materials biaxially over large deformation ranges and varies strain ratios in two perpendicular directions. The device is used in conjunction with a tensile testing machine, which holds the specimen and permits control over the direction and magnitude of the stresses applied.

Becker, G. W.↗

NASA NTRS1989

Some comments on global-local analyses

The main theme concerns methods that may be classified as global (approximate) and local (exact). Some specific applications of these methods are found in: fracture and fatigue analysis of structures with 3-D surface flaws; large-deformation, post-buckling analysis of large space trusses and space frames, and their control; and stresses around holes in composite laminates.

Atluri, Satya N.↗

NASA NTRS1977

An experimental-theoretical correlation study of non-linear bending and torsion deformations of a cantilever beam

An experimental study of the large deformation of a cantilevered beam under a gravity tip load has been made. The beam root is rotated so that the tip load is oriented at various angles with respect to the beam principal axes. Static twist and bending deflections of the tip and bending natural frequencies have been measured as a function of tip load magnitude and orientation. The experimental data are compared with the results of a recently developed non-linear structural theory. Agreement is reasonably good when bending deflections are small compared to the beam span, but systematic differences occur for larger deflections.

Dowell, E. H.↗

NASA NTRS1987

Interseismic deformation for normal fault earthquakes

Comparison between the coseismic vertical deformation associated with normal fault earthquakes and permanent deformation indicated by geologic structure indicates that large deformation must occur during the period between earthquakes. When sufficient geodetic and geologic information is available it is possible to estimate the spatial character of this interseismic deformation. A case in point is the 1983 Borah Peak, Idaho earthquake. This normal fault earthquake produced roughly 5 times as much basin subsidence as it did uplift of the adjacent mountain ranges. In contrast, geophysical and geological observations show that the basin is roughly as deep as the bounding range is high. A similar normal fault event in the Basin and Range, the 1959 Hebgen Lake earthquake, was also accompanied by substantially larger subsidence than uplift. In this case, postseismic geodetic measurements show broad regional uplift with a spatial pattern which is roughly consistent with that proposed for the Borah Peak event. Modeling suggests that postseismic viscoelastic relaxation and strain accumulation in an elastic lithosphere overlying a viscoelastic asthenosphere are possible physical mechanisms to generate interseismic uplift. These mechanisms may be the contemporary expression of those processes responsible for the high elevation of the Basin and Range Province.

Reilinger, Robert↗

NASA NTRS2022

Cable Decoupling and Cable-Based Stiffening of Continuum Robots

Cable-driven continuum robots, which are robots with a continuously flexible backbone and no identifiable joints that are actuated by cables, have shown great potential for many applications in unstructured, uncertain environments. However, the standard design for a cable-driven continuum robot segment, which bends a continuous backbone along a circular arc, has many compliant modes of deformation which are uncontrolled, and which may result in buckling or other undesirable behaviors if not ameliorated. In this paper, we detail an approach for using additional cables to selectively stiffen planar cable-driven robots with-out substantial coupling to the actuating cables. A mechanics-based model based on the planar Cosserat equations is used to find the design conditions under which additional cables can be routed without coupling of the cable lengths for small deformations. Simulations show that even for relatively large deformations, coupling remains small. A prototype is evaluated, and it is demonstrated that the compliance of the robot is substantially modified relative to the same robot without stiffening cables. Additional stiffening cables are shown to increase the end-effector output stiffness by a factor of approximately 10 over a typical design with actuating cables.

Tendon/wire mechanism↗

NASA NTRS2004

Characterization of bending EAP beams

Electroactive polymers are attractive actuation materials because of their large deformation, flexibility, and lightweight. A CCD camera system was constructed to record the curved shapes of bending during the activation of EAP films and image-processing software was developed to digitize the bending curves. A computer program was developed to solve the invese problem of cantilever EAP beams with tip position limiter. using the developed program and acquired curves without tip position limiter as well as the corresponding tip force, the EAP material properties of voltage-strain sensitivity and Young's modulus were determined.

large deformation↗

NASA NTRS1975

An Experimental Study of the Nonlinear Stiffness of a Rotor Blade Undergoing Flap, Lag and Twist Deformations

This is an addendum to an experimental study of the large deformation of a cantilevered beam under a gravity tip load. It adds higher quality and new data on the static twist and bending deflections of the beam. The experimental data are compared with a recently developed nonlinear structural theory. Agreement is good for deflections that are small compared to the beam span and has systematic deviations for larger deflections.

Dowell, E. H.↗

NASA NTRS1982

Deformation-Induced Anisotropy of Polymers

New theory calculates anisotropies induced by large deformations in polymers. Theory was developed primarily for calculating anistropy of thermal expansivity, but is also applicable to thermal conductivity, elastic moduli and other properties. Theory assumes that in isotropic state, long polymer chains are randomly coiled and not oriented in particular direction. They acquire an orientation when material is deformed. As average molecular orientation increases with deformation, properties of bulk material exhibit averaging of the microscopic anistropies of the oriented molecular segments.

Peng, S. T. J.↗

NASA NTRS1976

Dynamic response of membranes with finite elements

A general set of finite-element equations is developed for treating the nonlinear dynamic response of membranes consisting of complex nonlinear materials. The approach proposed by Key (1974) for a most complete treatment of the finite-element method to the nonlinear dynamic analysis of solids is used in developing the nonlinear equations of motion for membranes with cubic quadrilateral finite elements. The computations are kept general with respect to material modeling by computing the deformation gradient and requiring a constitutive subroutine to supply the Cauchy stress. An example calculation of the vibration of a square membrane demonstrates the accuracy of the formulation for small deformation theory and shows the nonlinear effect of large deformations.

Benzley, S. E.↗

NASA NTRS1987

Significance of foundation-soil separation in dynamic soil-structure interaction

THe dynamic response of flexible surface strip-foundations allowed to uplift is numerically obtained for externally applied forces of a transient time variation. The soil medium is represented by an isotropic, homogeneous and linear half-space. The soil is treated by a time domain boundary element method, while the flexible foundation is treated by the finite element method. It was concluded that intermediate relative stiffness leads to moderate deformations when uplift is permitted. Very flexible footings produce higher deformations in unilateral contact compared to bilateral contact, and thus should be considered in their design. Unilateral contact does not significantly increase deformations for stiff footings subjected to concentrated central loading. However, relatively large deformation differences occur when the loading is eccentric, necessitating consideration of uplift in their design.

Spyrakos, Constantine C.↗

NASA NTRS1997

ZIP2DL: An Elastic-Plastic, Large-Rotation Finite-Element Stress Analysis and Crack-Growth Simulation Program

ZIP2DL is a two-dimensional, elastic-plastic finte element program for stress analysis and crack growth simulations, developed for the NASA Langley Research Center. It has many of the salient features of the ZIP2D program. For example, ZIP2DL contains five material models (linearly elastic, elastic-perfectly plastic, power-law hardening, linear hardening, and multi-linear hardening models), and it can simulate mixed-mode crack growth for prescribed crack growth paths under plane stress, plane strain and mixed state of stress conditions. Further, as an extension of ZIP2D, it also includes a number of new capabilities. The large-deformation kinematics in ZIP2DL will allow it to handle elastic problems with large strains and large rotations, and elastic-plastic problems with small strains and large rotations. Loading conditions in terms of surface traction, concentrated load, and nodal displacement can be applied with a default linear time dependence or they can be programmed according to a user-defined time dependence through a user subroutine. The restart capability of ZIP2DL will make it possible to stop the execution of the program at any time, analyze the results and/or modify execution options and resume and continue the execution of the program. This report includes three sectons: a theoretical manual section, a user manual section, and an example manual secton. In the theoretical secton, the mathematics behind the various aspects of the program are concisely outlined. In the user manual section, a line-by-line explanation of the input data is given. In the example manual secton, three types of examples are presented to demonstrate the accuracy and illustrate the use of this program.

Deng, Xiaomin↗

NASA NTRS1990

Innovative design of composite structures: Axisymmetric deformations of unsymmetrically laminated cylinders loaded in axial compression

The study focuses on the axisymmetric deformation response of unsymmetrically laminate cylinders loaded in axial compression by known loads. A geometrically nonlinear analysis is used. Though buckling is not studied, the deformations can be considered to be the prebuckling response. Attention is directed at three 16 layer laminates: a (90 sub 8/0 sub 8) sub T; a (0 sub 8/90 sub 8) sub T and a (0/90) sub 4s. The symmetric laminate is used as a basis for comparison, while the two unsymmetric laminates were chosen because they have equal but opposite bending-stretching effects. Particular attention is given to the influence of the thermally-induced preloading deformations that accompany the cool-down of any unsymmetric laminate from the consolidation temperature. Simple support and clamped boundary conditions are considered. It is concluded that: (1) The radial deformations of an unsymmetric laminate are significantly larger than the radial deformations of a symmetric laminate, although for both symmetric and unsymmetric laminates the large deformations are confined to a boundary layer near the ends of the cylinder; (2) For this nonlinear problem the length of the boundary layer is a function of the applied load; (3) The sign of the radial deformations near the supported end of the cylinder depends strongly on the sense (sign) of the laminate asymmetry; (4) For unsymmetric laminates, ignoring the thermally-induced preloading deformations that accompany cool-down results in load-induced deformations that are under predicted; and (5) The support conditions strongly influence the response but the influence of the sense of asymmetry and the influence of the thermally-induced preloading deformations are independent of the support conditions.

Hyer, M. W.↗

NASA NTRS2003

Thermocapillary-Induced Phase Separation with Coalescence

Research has been undertaken on interactions of two or more deformable drops (or bubbles) in a viscous fluid and subject to a temperature, gravitational, or flow field. An asymptotic theory for nearly spherical drops shows that small deformations reduce the coalescence and phase separation rates. Boundary-integral simulations for large deformations show that bubbles experience alignment and enhanced coalescence, whereas more viscous drops may break as a result of hydrodynamic interactions. Experiments for buoyancy motion confirm these observations. Simulations of the sedimentation of many drops show clustering phenomena due to deformations, which lead to enhanced phase separation rates, and simulations of sheared emulsions show that deformations cause a reduction in the effective viscosity.

Davis, Robert H.↗

NASA NTRS1993

A combined experimental and finite element study to predict the failure mechanisms in SiC coated carbon/carbon composites at room and elevated temperatures under flexural loading

Response of quasi-isotropic laminates of SiC coated Carbon/Carbon (C/C) composites have been investigated under flexural loading at various temperatures. Variation of load-deflection behavior with temperatures are studied. Increase in flexural strength and stiffness are observed with the rise in temperature. Extensive analyses through Optical Microscope (OM) and Non-Destructive Evaluation (NDE) have been performed to understand the failure mechanisms. Damage zone is found only within the neighborhood of the loading plane. Isoparametric layered shell elements developed on the basis of the first order shear deformation theory have been used to model the thin laminates of C/C under flexural loading. Large deformation behavior has been considered in the finite element analysis to account for the non-linearities encountered during the actual test. Data generated using finite element analysis are presented to corroborate the experimental findings, and a comparison in respect of displacement and stress-strain behavior are given to check the accuracy of the finite element analysis. Reasonable correlation between the experimental and finite element results have been established.

Mahfuz, Hassan↗

NASA NTRS1980

Straightening of a wavy strip: An elastic-plastic contact problem including snap-through

The nonlinear behavior of a wave like deformed metal strip during the levelling process were calculated. Elastic-plastic material behavior as well as nonlinearities due to large deformations were considered. The considered problem lead to a combined stability and contact problem. It is shown that, despite the initially concentrated loading, neglecting the change of loading conditions due to altered contact domains may lead to a significant error in the evaluation of the nonlinear behavior and particularly to an underestimation of the stability limit load. The stability was examined by considering the load deflection path and the behavior of a load-dependent current stiffness parameter in combination with the determinant of the current stiffness matrix.

Fischer, D. F.↗

NASA NTRS1985

Geometry of miocene extensional deformation, lower Colorado River Region, Southeastern California and Southwestern Arizona: Evidence for the presence of a regional low-angle normal fault

The geometry of Miocene extensional deformation, which changes along a 120 km-long, northeast-trending transect from the southestern Chocolate Mountains, southeastern California, to the Trigo and southern Dome Rock Mountains, southwestern Arizona is discussed. Based upon regional differences in the structural response to extension and estimated extensional strain, the transet can be divided into three northwesterly-trending structural domains. From southwest to northeast, these domains are: (1) southestern Chocolate-southernmost Trigo Mountains; (2) central to northern Trigo Mountains; and (3) Trigo Peaks-southern Dome Rock Mountains. All structures formed during the deformation are brittle in style; fault rocks are composed of gouge, cohesive gouge, and local microbreccia. In each structural domain, exposed lithologic units are composed of Mesozoic crystalline rocks unconformably overlain by Oligocene to Early Miocene volcanic and minor interbedded sedimentary rocks. Breccia, conglomerate, and sandstone deposited synchronously with regional extension locally overlie the volcanic rocks. Extensional deformation largely postdated the main phase of volcanic activity, but rare rhyolitic tuff and flows interbedded with the syndeformational clastic rocks suggest that deformation began during the waning stages of valcanism. K-Ar isotopic ages indicate that deformation occurred in Miocene time, between about 22 and m.y. ago.

Tosdal, R. M.↗