Rigid Deformation Research Articles

Large displacement analysis of inelastic frame structures by convected material frame approach

This paper presents the convected material frame approach to study the nonlinear behavior of inelastic frame structures. The convected material frame approach is a modification of the co-rotational approximation by incorporating an adaptive convected material frame in the basic definition of the displacement vector and strain tensor. In the formulation, each discrete element is associated with a local coordinate system that rotates and translates with the element. For each load increment, the corresponding strain-displacement and nodal force-stress relationships are defined in the updated local coordinates, and based on the updated element geometry. The rigid body motion and deformation displacements are decoupled for each increment. This modified approach incorporates the geometrical nonlinearities through the continuous updating of the material frame geometry. A generalized nonlinear function is used to derive the inelastic constitutive relation and the kinematic hardening is considered. The equation of motion is integrated by an explicit procedure and it involves only vector assemblage and vector storage in the analysis by assuming a lumped mass matrix of diagonal form. Several numerical examples are demonstrated in close agreement with the solutions obtained by the ANSYS code. Numerical studies show that the proposed approach is capable of investigating large deflection of inelastic planar structures and providing an excellent numerical performance.

Modeling and Control of Elastic Bodies. 1st Report. Proposals the Extended Reduced Order Physical Model.

This paper proposes a new modeling method of elastic body to represent the rigid motion and elastic deformation. This model can be used to control flexible multibody systems like flexible manipulators, vehicles, and space structures etc. The model consists of mass particles, springs, and rigid bodies and the behavior of mass particles represents rigid motion and deformation of elastic bodies. The mass and stiffness matrices are calculated using the modal mass, natural frequencies, and mode shapes. The efficacy of the model is verified by considering an example of an elastic car body supported by a rectangular plate. This modeling procedure is also extended to represent the dynamics of flexible multibody systems.

Stability of oblate shapes in the vicinity ofN=Z=3468Se:Bands in69Seand67As

The $\ensuremath{\gamma}$-ray decay schemes of ${}^{69}\mathrm{Se}$ and ${}^{67}\mathrm{As}$ have been considerably extended using the ${}^{40}\mathrm{Ca}{(}^{32}\mathrm{S}{,2pn)}^{69}\mathrm{Se}$ and ${}^{40}\mathrm{Ca}{(}^{32}\mathrm{S},\ensuremath{\alpha}{p)}^{67}\mathrm{As}$ reactions at 100 MeV and ${}^{40}\mathrm{Ca}{(}^{36}\mathrm{Ar},\ensuremath{\alpha}{2pn)}^{69}\mathrm{Se}$ and ${}^{40}\mathrm{Ca}{(}^{36}\mathrm{Ar},2\ensuremath{\alpha}{p)}^{67}\mathrm{As}$ reactions at 145 MeV, with the aim of studying oblate bands arising from the strong coupling of a valence ${g}_{9/2}$ particle (or hole) to the oblate deformed ground state band of ${}^{68}\mathrm{Se}.$ A new ${T}_{1/2}=12\ifmmode\pm\else\textpm\fi{}2 \mathrm{ns} {J}^{\ensuremath{\pi}}{=9/2}^{+}$ isomeric bandhead was identified in ${}^{67}\mathrm{As}.$ A transitional quadrupole moment of ${Q}_{0}=\ensuremath{-}2.7(6) e\mathrm{b}$ was deduced for the band built on the ${9/2}^{+}$ isomer in ${}^{69}\mathrm{Se},$ corresponding to a rigid oblate deformation of ${\ensuremath{\beta}}_{2}=\ensuremath{-}0.4(1),$ consistent with theoretical predictions. However, it appears that the relevant oblate configurations in ${}^{69}\mathrm{Se}$ and ${}^{67}\mathrm{As}$ are not nearly so favored as they are in ${}^{68}\mathrm{Se},$ and are rapidly crossed by prolate configurations that form the high spin yrast lines.

ON THE MECHANICAL BEHAVIOUR OF THIN-WALLED BEAMS OF OPEN CROSS-SECTION: AN ELASTIC NON-LINEAR THEORY

A general one-dimensional model able to study thin-walled beams of open cross-section, exhibiting moderate angles of twist, is presented. It is derived from the 3-D continuous model assuming that the beam cross-section presents a rigid deformation in, and warps out, its own plane. Comparisons with a previous model proposed by Ghobarah and Tso are also made.

Sickle cell anemia.

Sickle cell anemia (SCA) is a disease caused by production of abnormal hemoglobin, which binds with other abnormal hemoglobin molecules within the red blood cell to cause rigid deformation of the cell. This deformation impairs the ability of the cell to pass through small vascular channels; sludging and congestion of vascular beds may result, followed by tissue ischemia and infarction. Infarction is common throughout the body in the patient with SCA, and it is responsible for the earliest clinical manifestation, the acute pain crisis, which is thought to result from marrow infarction. Over time, such insults result in medullary bone infarcts and epiphyseal osteonecrosis. In the brain, white matter and gray matter infarcts are seen, causing cognitive impairment and functional neurologic deficits. The lungs are also commonly affected, with infarcts, emboli (from marrow infarcts and fat necrosis), and a markedly increased propensity for pneumonia. The liver, spleen, and kidney may experience infarction as well. An unusual but life-threatening complication of SCA is sequestration syndrome, wherein a considerable amount of the intravascular volume is sequestered in an organ (usually the spleen), causing vascular collapse; its pathogenesis is unknown. Finally, because the red blood cells are abnormal, they are removed from the circulation, resulting in a hemolytic anemia. For the patient with SCA, however, the ischemic complications of the disease far outweigh the anemia in clinical importance.

DYNAMIC ANALYSIS AND NUMERICAL SIMULATION OF FLEXIBLE MULTIBODY SYSTEMS1*

Numerous studies about the modelization of multibody systems with flexible parts undergoing large rigid body motions and small elastic deformations have recently been performed [[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]]. Some of them [[10][11][12][13][14][15][16][17]], [[20], [[25][26]], [[28]] focused on the influence of geometric nonlinearities, and others [[18][19]], [[21][22][23][24]], [[30][31]] focused on the terms describing dynamic nonlinearities. In this work [[30][31]], we look at the dynamic nonlinearities. The method usually used to model the motion of such systems consists of separating the motion of each component of the system of rigid body motion and small elastic deformations and keeps only the linear terms connected to them. In some cases of fast motion, the problem of the accuracy of this linearization occurs. Precisely, it has been noted that small deformations do not imply small rates of deformation or small accelerations of deformation [[18]]. The question then raised is to know if this linearization is too premature. After establishing a method to allow the evaluation of the relative importance of nonlinearity terms, it appears that these terms must be kept in some cases. The obtained method is general and does not concern only the dynamic terms. A slider-crank mechanism was used to test the theory. Kane's method [[32]] was used to establish the equations of motion, and the software AUTOLEV (Online Dynamics, Sunnyvale, CA) was used for numerical study. *Communicated by E. Haug.

Bicrystal-Based Modeling of Plasticity in FCC Metals

In this paper, intermediate modeling of polycrystalline plasticity is proposed for rigid viscoplatic large deformations. This approach is based on the use of a bicrystal as the elementary local element representing the polycrystal. The local homogenization is obtained by considering the bicrystal volume-averaging and the jump conditions at the assumed planar interface between the two crystals. Two interaction laws based on Taylor and Sachs type assumptions are proposed. These bicrystal-based averaging schemes are different from the classical Taylor and Sachs models since they allow for stresses and strains to vary from one single crystal to the other. We simulate uniaxial tension and compression as well as plane strain compression tests. Results in terms of stress-strain curves are shown in comparison to those of the pure Taylor and Sachs models. We also show results for texture evolution and discuss their comparison with the experimental measurements.

Cenozoic normal faulting and regional doming in the southern Hangay region, Central Mongolia: implications for the origin of the Baikal rift province

The Hangay Dome in central Mongolia is a mountainous region covering more than 200,000km2 with numerous flat-topped peaks over 3000m that preserve a Late Cretaceous–Paleogene erosion surface. Doming began in the middle Oligocene producing more than 2000m of regional topographic uplift. The range represents an important kinematic link between the Baikal rift province to the north and Altai transpressional ranges to the south and west. Structural field investigations of major faults visible on satellite imagery indicate that the southern Hangay Dome region is dominated by Late Cenozoic normal faults that bound small half-graben. Most faults are NE-striking and faults at the highest elevations are the most recently active. Most graben appear to be isolated systems that constitute small sediment sinks perched on the flanks and crests of the dome. The first-order feature is the dome itself and most sediment eroded off of the dome is deposited in the Mongolian Valley of Lakes or is carried northwards by the Selenga river and its extensive tributaries.The basement of the dome is a Precambrian craton although the shape and dimensions of the craton are poorly constrained to the north and east. Late Cenozoic uplift of the southern dome region appears to be confined to the area underlain by cratonic basement whereas the Altai region to the south and west is underlain by mechanically weaker Palaeozoic arc and accretionary belts. With respect to the regional northeast directed SHmax, the Hangay craton appears to have acted as a rigid passive indentor focusing Late Cenozoic transpressional deformation around its west and southern margins. Models invoking a Late Cenozoic plume as the driving force for doming and widespread alkaline volcanism on the dome are not strongly supported by geochemical and isotopic data on Neogene–Recent volcanics and the spatial correlation between areas that are domed and older cratonic crust appears too coincidental to be ignored. Convective removal of an overthickened lithospheric root leading to adiabatically decompressed asthenosphere could explain regional doming and volcanism, however major crustal thickening last occurred in the Permian in the southern Hangay region and the time lag between thickening and postulated root removal and plateau uplift (>200Myr) appears too long. An alternative model is explored based on speculated lithospheric mantle flow patterns driven by India's continued northeastward indentation. It is suggested that lithospheric mantle flow diversion around the overthickened Hangay craton crustal keel could cause lithospheric thinning beneath the craton and passive asthenospheric upwarp leading to regional topographic uplift and decompression melting/alkali volcanism. In general, the angular relationship between Precambrian craton boundaries and the prevailing northeasterly SHmax appears to control the kinematics of late Cenozoic deformation throughout the Hangay, Altai, Sayan and Baikal regions.

The Computer Simulation of Lubricated Cold Rolling Processes

A realistic friction model for lubricated cold rolling process with front and back tension is developed. The model combines a rigid-plasticity finite element code with a lubrication analysis. The rolls are assumed to be rigid and uniform deformation and isothermal conditions are assumed to prevail. The surface roughness effect on lubricant flow is included by using a average Reynolds equation. The active lubrication regime and appropriate friction factor can then be expressed in terms of internal interface variables in addition to the more traditional external variables. These internal variables include mean lubricant film thickness, workpiece roughness and roll roughness. The external variables are interface pressure and sliding speed. Numerical results using the coupled code such as roll separating force and roll torque under different rolling conditions are compared with experimental investigation. The simulation results are in good agreement with experimental data. Presented as a Society of Tribologists and Lubrication Engineers paper at the ASME/STLE Tribology Conference in Toronto, Ontario, Canada, October 26–28, 1998

Effect of shape and orientation on rigid particle rotation and matrix deformation in simple shear flow

The rotation behaviour of rigid particles from a wide range of symmetry classes was analysed in a series of three-dimensional analogue experiments, in which the particles were embedded in a transparent linear–viscous matrix deformed to large shear strains. Comparison of the measured trajectories with theoretical periodic paths for rigid ellipsoids shows that quadratic, slightly orthorhombic and monoclinic particles have trajectory paths and rotation rates closest to theory. Orthorhombic and monoclinic particles, with a minimum aspect ratio >1.5, develop non-periodic trajectories. The results establish that the simplified theoretical model for ellipsoidal forms is a good approximation for a wide range of natural particle shapes. The relationship between the rotation of a rigid particle and deformation of the adjacent matrix was also determined in a series of experiments by placing the particle at different depths relative to an imprinted grid. The results are well illustrated by the surface passing through the centre of the particle and initially parallel to the shear plane. Two deformed regions in the matrix are recognised. In the first region, the matrix rotates with the particle, together forming an approximately ellipsoidal object. The second region is dominated by folds, of limited extent along the rotation axis and greatest extent in a direction that rotates asymptotically toward the shear direction. The folds rotate more slowly than the principal direction of maximum finite stretch.

A block-fault model for deformation of the Japanese Islands derived from continuous GPS observation

We interpret the continuous GPS data for the Japanese islands from 1996 to 1999 using the model of Hashimoto and Jackson (1993). In this model crustal deformation is represented by a combination of rigid block motions and deformation due to slip deficits along the fault-bounding blocks. Hashimoto and Jackson used 19 blocks, 104 faults, and geodetic data spanning 100 years. In the present work we assume the same fault and block geometry, and we use only the continuous GPS data. Compared to the previous study, the motions of the major blocks are a bit larger: 107 ± 8 mm/yr for the Pacific plate, 47 ± 2 mm/yr for the Philippine Sea plate, and 24 ± 2 mm/yr for the Izu block, all relative to the Amurian plate. The estimated slip directions on active inland faults are now more consistent with geological estimates. Slip deficit rates exceed 10 mm/yr along the Itoigawa-Shizuoka Tectonic Line, Shinanogawa Seismic Zone, Atotsugawa fault, Hanaori fault, Arima-Takatsuki Tectonic Line, Rokko faults, Median Tectonic Line, and southern boundary of the Beppu-Shimabara graben. Some interplate faults along the Japan and Kurile trenches have slip deficit rates larger than 100 mm/yr, although postseismic deformation from the 1994 Far Off Sanriku earthquake may contaminate these estimates. An interplate fault off Kyushu has a negative slip deficit, possibly due to post-seismic movements from the 1996 events in Hyuganada.

A nonlinear generalization of the Koiter–Sanders–Budiansky bending strain measure

A physically motivated kinematical property to be demanded of a bending strain measure, beyond the ones that are conventionally agreed upon, is proposed. Guided by the criterion, a bending strain measure is proposed for a first-order, nonlinear, elastic shell theory that has the property of vanishing in rigid and pure-stretch deformations of the shell. The measure is motivated by the Koiter–Sanders–Budiansky (KSB) bending measure of the first-order, linear shell theory, and is shown to linearize to the KSB measure about the undeformed shell. On retaining the standard measure for membrane straining, work-conjugate stress and stress-couple resultants to the membrane and bending strains are derived, as is the expression for the internal virtual work in terms of the proposed strains, stress and stress-couple resultants. The bending strain is calculated for some simple deformations and compared with other generalizations of the KSB measure of the linear theory.

Finite deformation plasticity and viscoplasticity laws exhibiting nonlinear hardening rules

This paper deals with plasticity and viscoplasticity laws exhibiting nonlinear kinematic hardening as well as nonlinear isotropic hardening rules. In Tsakmakis (1996a, b) a constitutive theory has been formulated within the framework of finite deformations, which is based on the concept of so-called dual variables and associated time derivatives. Within two families of dual variables, two different formulations have been proposed for kinematic hardening, referred to as Models 1 and 2. In particular, rigid plastic deformations without isotropic hardening have been considered. In the present paper, the constitutive theory of Tsakmakis (1996a, b) is appropriately extended to take into account isotropic hardening as well as elastic deformations. Care is taken that the evolution equations governing the hardening response fulfill the intrinsic dissipation inequality in every admissible process. For the case of small elastic strains combined with a simplification concerning kinematic hardening, to be explained in the paper, an efficient, implicit time-integration algorithm is presented. The algorithm is developed with a view to implementation in the ABAQUS Finite Element code. Also, explicit formulas for the consistent tangent modulus are derived.

On objectivity and material symmetry for simple elastic solids

Restrictions imposed on stress response functions by objectivity and material symmetry are usually obtained by appeal to both a reference configuration and a response function common to all observers. Here these restrictions are obtained by regarding the reference configuration to be observer-dependent in a natural manner, and without the need to assume the existence of a common response function. Remarks are made on the distinction which should be drawn between the notions of observer transformation and rigid deformation, the consequences of this distinction for the correct interpretation of ‘invariance under superposed rigid motions’, and on the domains of response functions.

Periphery deformations and tunneling at correlated quantum Hall edges

We argue that, at any filling factor $\ensuremath{\nu},$ correlated quantum Hall systems possess a set of chiral boson excitations that are generated by electronically rigid deformations of the system's periphery. We submit that tunneling electrons can be accommodated, at low energies, in these systems only by periphery-deformation excitations. This property would explain the recent observation of a tunneling density of states at the edge that does not exhibit a strong dependence on the occurrence or absence of the quantum Hall effect and has a power-law dependence on energy with exponent ${\ensuremath{\nu}}^{\ensuremath{-}1}\ensuremath{-}1.$

Seismic response of shear‐core with sliding support to bi‐directional ground excitation

To study the effectiveness of a sliding support for the isolation of structures from damaging ground motion, the model of a shear-core supported on a sliding foundation and subjected to random ground motion in two orthogonal directions is considered here. A fictitious spring model is adopted to deal with the discontinuous nature of the sliding structural system. The rigid friction force deformation characteristics of the sliding support are modelled as elasto-plastic with high elastic stiffness. The sliding support is assumed to remain in the elastic state during non-sliding and is treated as plastic during the sliding state. An incremental numerical scheme for the solution of a multi-degree-of-freedom system is used for solving the time history responses. The responses (the absolute value of the acceleration of the top of the wall, and the bending moment at the base of the wall), are calculated under various important parametric variations. The result presented here are of interest in the area of the vibration isolation of important structural systems. Copyright © 1999 John Wiley & Sons, Ltd.

Seismic response of shear-core with sliding support to bi-directional ground excitation

To study the effectiveness of a sliding support for the isolation of structures from damaging ground motion, the model of a shear-core supported on a sliding foundation and subjected to random ground motion in two orthogonal directions is considered here. A fictitious spring model is adopted to deal with the discontinuous nature of the sliding structural system. The rigid friction force deformation characteristics of the sliding support are modelled as elasto-plastic with high elastic stiffness. The sliding support is assumed to remain in the elastic state during non-sliding and is treated as plastic during the sliding state. An incremental numerical scheme for the solution of a multi-degree-of-freedom system is used for solving the time history responses. The responses (the absolute value of the acceleration of the top of the wall, and the bending moment at the base of the wall), are calculated under various important parametric variations. The result presented here are of interest in the area of the vibration isolation of important structural systems. Copyright © 1999 John Wiley & Sons, Ltd.

The problem of the stability of quasilinear flows with respect to perturbations of the hardening function

A formulation of the linearized boundary-value problem of the stability of a deformation process with respect to small perturbations of the hardening function (of the scalar constitutive relation of the material) is presented. The characteristic vector relations of the medium are assumed to be linear. The occurrence of rigid zones in the domain of the solid and the change in their boundaries in the perturbed motion are taken into account. A perfect rigid plastic deformation and the flow of a Newtonian fluid are considered explicitly as the basic flow. In the latter case, the equation of the asymptotic boundary of the rigid zone, which appears when there is a small variation in the yield stress and a transition to a viscoplastic material, is derived.

Elastic Plates in Multibody Systems: A Treatment Using Existing Rigid Body Codes

In the present paper, it is shown how one can employ existing rigid body codes to handle systems containing elastic plates by using a Rayleigh–Ritz discretization procedure. The equations of motion are formulated for a rectangular plate undergoing large rigid body motions but small elastic deformations. Geometric nonlinearities in the elastic coordinates are taken into account to include the effect of dynamic stiffening. As an example, a spin-up maneuver for a simply-supported plate is treated.

Efficient Collision Detection of Complex Deformable Models using AABB Trees

We present a scheme for exact collision detection between complex models undergoing rigid motion and deformation. The scheme relies on a hierarchical model representation using axis-aligned bounding boxes (AABBs). Recent work has shown that AABB trees are slower than oriented bounding box (OBB) trees for performing overlap tests. In this paper, we describe a way to speed up overlap tests between AABBs, such that for collision detection of rigid models, the difference in performance between the two representations is greatly reduced. Furthermore, we show how to update an AABB tree quickly as a model is deformed. We thus find AABB trees to be the method of choice for collision detection of complex models undergoing deformation. In fact, because they are not much slower to test, are faster to build, and use less storage than OBB trees, AABB trees might be a reasonable choice for rigid models as well.