Deformation Quantities Research Articles

A Characteristic Analysis of the Dynamic Evolution of Preseismic‐Coseismic‐Postseismic Interferometric Deformation Fields Associated with the M 7.9 Earthquake of Mani, Tibet in 1997

Abstract: By using the D‐InSAR technique, we have acquired the temporal‐spatial evolution images of preseismic‐cosesimci‐postseismic interferometric deformation fields associated with the M 7.9 earthquake of Mani, Tibet on 8 November 1997. The analysis of these images reveals the relationships between the temporal‐spatial evolution features of the interferometric deformation fields and locking, rupturing, and elastic restoring of the source rupture plane, which represent the processes of strain accumulation, strain release, and postseismic restoration. The result shows that 10 months prior to the Mani event, a left‐lateral shear trend appeared in the seismic area, which was in accordance with the earthquake fault in nature. The quantity of local deformation on the north wall was slightly larger than that on the south wall, and the deformation distribution area of the north wall was relatively large. With the event impending, the deformation of the south wall varied increasingly, and the deformation center shifted eastward. Two and half monthd before the event, the west side of the fault was still locked while the east side began to slide, implying that the whole fault would rupture at any moment. These features can be regarded as short‐term precursors to this earthquake. Within the period from 16 April 1996 to two and half months before the earthquake, the most remarkable deformation zones appeared in the north and south walls, which were parallel to and about 40 km apart from the fault, with accumulated local displacements of 344 mm and 251 mm on the north and south walls, respectively. The south wall was the active one with larger displacements. Five months after the earthquake, the distribution feature of interferometric fringes was just opposite to that prior to the event, expressing evident right‐lateral shear. The recovered displacements are ∼179 mm on the north wall and ∼79 mm on the south wall, close to the east side of the fault. However, in the area of the south wall far from the fault there still existed a trend of sinistral motion. The deformation of the north wall was small but recovered fast in a larger area, while the active south wall began to recover from the east section of the fault toward the WSW.

Analysis of dynamic deformation processes with adaptive KALMAN-filtering

The analysis of dynamic deformation processes is an important task in civil and in mechanical engineering. One main emphasis is set on the derivation of the objects transmission function, represented by systems of ordinary or partial differential equations (“white box”-models). The parametric identification of the initial and boundary conditions and relevant material parameters is one of the new challenges in the application of least-square algorithms. Embedding the investigation of the deformation process in a combination of a theoretical and an experimental system analysis suitable methods are provided with adaptive KALMAN-filtering as central identification tool. In this paper the approach of a full system analysis is shown quantifying a dynamic “white-box”-model for the calculation of thermal deformations of bar-shaped machine elements. The task was motivied from mechanical engineering searching new methods for the precise prediction and computational compensation of thermal influences in the heating and cooling phases of machine tools (i.e. robot arms, etc.). The quantification of thermal deformations under variable dynamic loads requires the modelling of the non-stationary spatial temperature distribution inside the object. Based upon FOURIERS law of heat flow the high-grade non-linear temperature gradient is represented by a system of partial differential equations within the framework of a dynamic Finite Element topology. It is shown that adaptive KALMAN-filtering is suitable to quantify relevant disturbance influences and to identify thermal parameters (i.e. thermal diffusivity) with a deviation of only 0,2%. As result an identified (and verified) parametric model for the realistic prediction respectively simu-lation of dynamic temperature processes is presented. Classifying the thermal bend as the main deformation quantity of bar-shaped machine tools, the temperature model is extended to a temperature deformation model. In lab tests with an aluminium column control measurements show that the identified model can be used to predict the columns bend with a mean deviation smaller than 10 mgon. Consequently the deformation model is a precise predictor and suitable for realistic simulations of thermal deformations under variable dynamic loads. In future our activities will be primarily focussed on applications in industrial manufacturing. 1. Parametric identification of dynamic deformation processes The creation of a realistic parametric dynamic deformation model is directly associated with the task to combine systems of differential equations (theoretical physical model) with empirical measurements. Consequently basic principles of system theory can be adapted to the geodetic deformation analysis. The parametric identification of a dynamic “white box”-model 3rd IAG / 12th FIG Symposium, Baden, May 22-24, 2006

A unified exact analysis for the Poynting effects of cylindrical tubes made of Hill’s class of Hookean compressible elastic materials at finite strain

A direct, natural extension of Hooke’s law to finite strain was achieved by R. Hill in 1978, employing the notion of work-conjugate measures of stress and strain. With Seth-Hill (Doyle-Ericksen) class of finite strain measures, this extension actually defines a broad class of compressible hyperelastic materials at finite strain, each of which retains the simple linear structure of Hooke’s law as stress–strain relationship. Several known simple elasticity models at finite strain are included as its particular examples. With a novel idea of utilizing a suitable parametric variable, here we present a unified study of the free-end torsion problem (Poynting effects) of thin-walled cylindrical tubes made of the foregoing Hill’s class of Hookean type hyperelastic materials. We show that it is possible to derive a unified exact solution to the nonlinear coupling equations relating the torque (the shear stress) and the controlling deformation quantities including, in particular, the axial length change. Discussions and comparisons concerning various Hookean type elasticity models are made based on the exact solution obtained.

Effect of Hot Deformation on Formation and Growth of Thermal Fatigue Crack in Chromium Wear Resistant Cast Iron

The formation and growth of thermal fatigue crack in chromium wear resistant cast iron was investigated, and the effect of hot deformation on the crack was analyzed by means of optical microscope and scanning electron microscope and high frequency induction thermal fatigue tester. The results show that eutectic carbide is the main location and passage for initiation and extension of thermal fatigue cracks, hot deformation can improve the eutectic carbide’s morphology and distribution, inhibit the generation and propagation of thermal fatigue cracks. In the experiment, the propagation rate of thermal fatigue crack reduces with the quantity of hot deformation increasing, which was analyzed in the point view of the activation energy of crack propagation.

An observation on the physical essence of elastoplastic deformations

AbstractOn account of the basic physical feature of elastoplastic deformations, namely, the occurrence of internal self‐equilibrated stress field upon removal of external loadings, a process of destressing an elastoplastic body with non‐uniform stress field would inevitably lead to loss of the line element concept in the resultant incompatible unstressed configuration. This would mean the loss of the kinematic ground or prerequisite for defining kinematic quantities in usual material continua. Then, an additional variable labelled as “elastic” or “plastic” via destressing could not be endowed with the necessary kinematic and physical content characterising a deformation quantity and, accordingly, might actually be a formal variable in mathematical sense. Thus follows an observation that the elastoplastic deformation would be an inherently inseparable physical entity. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The link between discrete and continuous modeling of liquid foam at the level of a single bubble

In order to test the adaptability of a homogenization scheme originally developed for dry granular media, a micromechanical constitutive law for three-dimensional monodisperse wet foam is developed. The advantage of the homogenization scheme is that it provides a link between the discrete bubble-scale microstructure and the continuum quantities of stress and deformation. Furthermore, the resulting constitutive law is in terms of physical material properties (e.g., fluid viscosity, surface tension, and bubble radius) rather than the more phenomenological parameters, such as power-law indices, etc. Hence, predictions of the continuum model can be, and are, compared directly to experiments and simulations. Many of the general features of foam behavior are reproduced, including small-strain elasticity, dependence on gas fraction, and Bingham plastic type deformation rate dependency. However, the current micromechanical continuum model substantially overestimates the static shear modulus and yield stress of foams in comparison to simulations and experiments. This discrepancy is due to the adoption of a mean-field assumption for the deformation in the current model. It is then argued that future micromechanical continuum models for foams cannot neglect the nonaffine motions associated with bubble rearrangements. Finally, for both foams and granular materials, our study indicates that the uniform deformation assumption is only valid near the critical packing of monodisperse spherical particles.

PERCEPTUALLY ADAPTIVE VIDEO WATERMARKING USING MOTION ESTIMATION

Video watermarks must maintain picture quality and withstand image processing, and resolving the tradeoff between these conflicting requirements has been one of the central problems in research on video watermarking. This paper shows that watermarks are less perceptible where picture contents are moving and proposes a new criterion for measuring watermark imperceptibility from motion vectors and deformation quantities. It also proposes a watermarking method that uses this criterion to allocate watermarks to picture areas adaptively. Experimental evaluation showed that the proposed method reduces degradation in picture quality and that, for the same picture quality after MPEG encoding and decoding, between 30% and 40% more watermarks can be embedded, improving detection reliability after MPEG processing by an average of 9.5%. The proposed method would be most effective when used with MPEG encoders because they already have the necessary motion estimation functions.

Buckling of short beams with warping effect included

A beam theory for the stability analysis of short beam that includes shear deformation and warping of the cross-section is developed. The warping of the cross-section is taken to be an independent kinematics quantity and corresponding force resultants are defined. For the beam subjected to the external loading only at the ends of the beam, equilibrium equations have been obtained by the principle of virtual work. The variations of lateral displacement, rotational angle of the cross-section and the multiplier of the warping shape along the beam axis are solved in closed form and expressed in terms of deformation quantities at the ends of the beam. Based on this beam theory, the lateral stiffness of the beam sustained an axial compression force and a lateral shear force at one end is explicitly derived, from which the equation of the buckling load is established and the buckling load can be solved. When the effect of cross-section warping is neglected, the derived lateral stiffness and buckling load converge to the solutions of the Haringx theory.

An evaluation of simplified finite element models for spot-welded joints

Spot-welded joints are widely used in automobile structures. Since a typical vehicle contains several thousands of spot welds, it is often not practical in a vehicle structural analysis to model each and every spot-welded joint in detail. As such, simplified structural models have been proposed in the literature for spot-welded joints in large-scale structural computations. To be adequate, a simplified joint model must be able to produce relevant loading, stress or deformation quantities around a joint that are sufficiently accurate when compared to the results of a more refined model. To this end, the current paper describes the findings of a careful study in which several types of simplified finite element structural models for spot-welded joints are implemented with several mesh refinements and their performance is evaluated against converged three-dimensional finite element models. Various loading conditions and joint parameters are considered. The evaluation is carried out based on comparisons of the structural stiffness of the joint. A detailed error analysis is provided. It is found that most of the simplified joint models and mesh refinements have good accuracy when a joint is subjected to tension, torsion, and out-of-plane bending. However, under in-plane bending and torsion conditions, large errors are introduced even when fine meshes are used.

Effects of mechanical constraints on angular distortion of welding joints

During the manufacture of steel structures, welding deformations have undesirable effects on the accuracy of assembly, external appearance, buckling strength, fatigue strength, etc. In particular, in such large steel structures as ships, welding deformations produced during assembly lead to variations in dimensions which require considerable time and expense for repair, resulting in a decrease in productivity. In the present work a new method is presented to derive the constraint coefficient from the degree of angular deformation caused by welding, as measured experimentally by varying the shape of welded joints and the magnitude of constraints and from analysis results obtained via the elastic finite element method. The equivalent load was then calculated using this constraint coefficient. The validity of the numerical analysis involved in this new method was confirmed by its agreement with the experimental results. Regarding the effects of the constraints in relation to the shape of the welded joints, when the constraint coefficients are not considered for butt welding, the quantity of deformation predicted by analysis is greater than that produced in experiments and consequently butt welding is strongly affected by the constraints. However, for fillet welding, the quantity of deformation is hardly affected regardless of constraint coefficient considerations.

2510 折り紙構造物の圧潰特性の最適化

From the viewpoint of the pedestrian protection and the light collision in the car, it is effective to make deformation quantity large under the small load. In order to increase deformation quantity of axis crash problems, it is important how to make beautifully folded patterns. Therefore, in this research, on the basis of the principle of the origami engineering, several kinds of completely foldable structures were proposed. In addition, the characteristic of the proposed structures were analyzed by using finite element method simulation and optimized by the method of response curved surface method.

Three-dimensional GSMAC-FEM simulations of the deformation process and the flow structure in the floating zone method

This paper presents an improved level set method (LSM) for the analysis of a free surface deformed in an alternating current magnetic field. Three-dimensional numerical simulations are carried out based on the generalized simplified marker and cell—finite element method (GSMAC-FEM) algorithm to investigate the deformation processes of a silicon liquid bridge similar to the floating zone (FZ) configuration with the coil position, width, and the magnitude of surface tension changed under microgravity. The A- ϕ method is adopted to calculate the physical quantities of the magnetic field, and it is solved by the hybrid finite element method–boundary element method (FEM–BEM). The liquid part at the coil position becomes largely squeezed by the Lorentz force if the magnitude of surface tension is small, and the radius of a liquid bridge varies when a coil moves from the upper position in height to the middle one. However, the deformation becomes greatly suppressed if the magnitude of surface tension is large because the outward force in proportion to the magnitude of curvature increases. From these results, it is expected that the deformation quantity of a liquid bridge will be rather small in the real FZ process because of large surface tension and a high frequency which causes the skin effect.

Anwendung eines CAS-Systems in der Arthroskopischen Kreuzbandchirurgie - Adaption und Applikation in der klinischen Praxis

The anterior cruciate ligament (ACL) is of great importance for the knee joint function. In the case of a complete ligament injury there is hardly any chance for complete recovery. The clear advantages of an operative reconstruction by replacing the ACL has been shown in many trails. The accurate placement of the graft's insertions has a significant effect on the mid- and probably long-term outcome of this procedure. Reviewing the literature, there are poor long-term results of ACL replacement in 5 to 52% of all cases, depending on the score system. One of the main reasons for unacceptable results is graft misplacement. This led to the construction of a CAS system for ACL replacement. The system assists this surgical procedure by navigating the exact position of the drilling holes. The Potential deformation quantity of the transplant can be controlled by this system in real time. 40 computer-assisted ACL replacements have been performed under active use of the CAS system. The short-term results are encouraging, no special complications have been seen so far. Prospective long-term follow-up studies are ongoing. ACL reconstruction by manual devices has many sources of error. The CAS system is able to give the surgeon reasonable views that are unachieveable by conventional surgery. He is therefore able to control a source of error and to optimise the results. The feasibility of this device in clinical routine use has been proven.

Inverse stiffness design of shear-flexural building models including soil–structure interaction

A new efficient seismic stiffness design procedure is developed for a shear-flexural building–pile–soil system. A set of design earthquakes is defined at the bedrock (beneath surface soil layers) to take into account the effects of surface soil layers on the design of building super-structures. It is shown that a closed-form solution to a hybrid inverse eigenmode problem can be utilized in developing the efficient seismic stiffness design procedure by regarding the fundamental natural period of the total system and the lowest-mode deformation quantities as the principal parameters for adjustment of the story deformations. Physical interpretation of the governing equations enables one to transform a set of formally nonlinear equations into a set of simultaneous linear equations. A model twenty-story building supported by a pile–soil system with ten sublayers is presented to demonstrate the usefulness of this design procedure.

Growth behavior of internal delaminations in composite beam/plates under compression: effect of the end conditions

The effect of the end conditions, i.e. clamped-clamped vs. simply-supported ends on the initial postbuckling and growth behavior of delaminations in plates in studied. The study does not impose any restrictive assumptions regarding the delamination thickness and plate length. First, a closed form solution for the mode mixity, energy release rate and deformation quantities is derived for the case of a clamped-clamped delaminated plate, which complements the already existing solution for a delaminated simply-supported plate. A perturbation procedure is followed, which is based on an asymptotic expansion of the load and deformation quantities in terms of the distortion parameter of the delaminated layer, the latter being considered a compressive elastica. The additional complication in the clamped-clamped case arises because now the amplitude at the clamped end needs to be expanded in terms of the distortion parameter of the delaminated part, in addition to the amplitude at the common section and the distortion parameter of the base plate. The effects of the end conditions on the growth behavior are found to depend on the relative location of the delamination through the thickness. For the same plate length and thickness and the same delamination length and applied strain, delaminations located closer to the surface exhibit nearly the same energy release rate and mode mixity either in a clamped-clamped or a simply supported configuration. However, in delaminations located further away from the surface, for the same applied strain, the energy release rate is larger and there is also a higher mode II component in the simply-supported case. Moreover, the mid-point transverse displacement of the delaminated layer as well as that of the substrate part, is larger in the simply supported case. The same major trend that has been observed in the simply supported case, i.e. the increased growth resistance of the delaminations located near the surface relative to the ones located further inside the plate, is also observed in the clamped-clamped case.

Hybrid Inverse Mode Problems for FEM-Shear Models

A class of hybrid inverse eigenmode problems is formulated such that a set of stiffnesses of a structure supported by a prescribed shear-type foundation system at an interface is determined for a specified lowest eigenvalue and a specified set of lowest-mode deformation-quantity ratios in the structure. The key point of the hybrid inverse eigenmode formulation is to take full advantage of the dynamic equilibrium of the whole superstructure, including the interface, and to express the lowest-mode interstory-drift components in the foundation system in terms of the specified lowest eigenvalue and the specified lowest-mode deformation quantities in the superstructure. A property on signs of the lowest-mode components is clarified for a general finite-element model supported by a shear-type foundation system. A systematic procedure for determining the stiffnesses of the superstructure is devised. The condition for uniqueness of the stiffnesses is then disclosed. Finally an example of application of this formulation is presented for a finite-element beam model supported by a shear-type foundation system.

The stability of delamination growth in compressively loaded composite plates

The stability of growth of internal delaminations in composite plates subjected to compressive loading is investigated. Due to the compressive loading, these structures can undergo buckling of the delaminated layer and subsequently growth of the delamination. The study does not impose any restrictive assumptions regarding the delamination thickness and plate length (as opposed to the usual thin film assumptions). The growth characteristics of the delamination under monotonic compressive loading are obtained on the basis of a combined delamination buckling/postbuckling and fracture mechanics model. The postbuckling solution is derived through a perturbation procedure, which is based on an asymptotic expansion of the load and deformation quantities in terms of the distortion parameter of the delaminated layer, the latter being considered a compressive elastica. The closed form solutions for the energy release rate at the delamination tip versus applied compressive strain during the initial postbuckling phase are used to define the combinations of delamination length and applied strain that lead to unstable growth. This would practically cause either contained “jump” growth or complete (catastrophic) growth of the delamination. Estimates for the lower and upper bounds of the jump distance (unstable growth) are provided. Moreover, a study of the influence of the mode dependence of interface toughness on the conditions of initiation and extent of delamination growth is performed.

Computer Simulation of the Deformation of Weft-Knitted Fabrics for Composite Materials

A new method for predicting the deformation behaviour and the related mechanical properties of weft-knitted fabrics is presented. A two-dimensional hexagonal mechanical model is derived, which is based on the geometrical structure of plain-stitch fabric. An analytical method of converting the experimental data of the knitted fabric into the parameters of the model is proved to be effective. By using the model-knitted fabric, the elongation deformation is simulated, and the calculated results are compared with the experimental data in order to verify the validity of the model. Moreover, the slippage effect experienced with knitted fabrics is introduced into the model to simulate the greater deformation which occurs with improved accuracy. The model can also predict deformation and related mechanical quantities in the case of three-dimensional deformations.

The Initial Post-buckling and Growth Behavior of Internal Delaminations in Composite Plates

The initial post-buckling and growth behavior of delaminations in plates is studied by a perturbation procedure. In this work, no restrictive assumptions regarding the delamination thickness and plate length are made, i.e., the usual thin film assumptions are relaxed. The perturbation procedure is based on an asymptotic expansion of the load and deformation quantities in terms of the distortion parameter of the delaminated layer, the latter being considered a compressive elastica. Closed-form solutions for the load and midpoint delamination deflection versus applied compressive displacement during the initial post-buckling phase are derived. Moreover, closed-form expressions for the energy release rate and the mixity ratio (i.e., Mode II versus Mode I) at the delamination tip are produced. A higher Mode I component is found to be present during the initial post-buckling phase for delaminations of increasing ratio of delamination thickness over plate thickness, h/T (i.e., delaminations further away from the surface). Moreover, the-energy release rate corresponding to the same applied strain is larger for a higher h/T ratio. The reduced growth resistance of these configurations is verified by experimental results on unidirectional composite specimens with internal delaminations.

Modeling Procedures for the Stress Analysis of Flexible Pipe Cross Sections

Thick tube theory is incorporated into an existing analytical model for the three-dimensional analysis of bonded flexible pipe cross sections under offshore loading conditions. The original model considers material layers as isotropic/orthotopic thin tubes, and layers of helically wound reinforcing cables are modeled separately. The improvement in the results obtained with the incorporation of the new thick tube layer is demonstrated for a flexible pipe with D/t = 10. The finite element technique has also been used to model this type of pipe structure. Pipe sections are discretized using axisymmetric elements for the tube-type layers and special discrete reinforcement elements for the helical cables. A particular example of a three-layer doubly reinforced pipe section under internal pressure is studied. Good agreement is found between analytical model and finite element results for all the main deformation and stress quantities including cable stresses.