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Showing papers on "Displacement field published in 1997"


Journal ArticleDOI
TL;DR: In this paper, a geometrically non-linear version of the EAS-approach is applied which is based on the enhancement of the Green-Lagrange strains instead of the displacement gradient as originally proposed by Simo and Armero.
Abstract: Well-known finite element concepts like the Assumed Natural Strain (ANS) and the Enhanced Assumed Strain (EAS) techniques are combined to derive efficient and reliable finite elements for continuum based shell formulations. In the present study two aspects are covered: The first aspect focuses on the classical 5-parameter shell formulation with Reissner–Mindlin kinematics. The above-mentioned combinations, already discussed by Andelfinger and Ramm for the linear case of a four-node shell element, are extended to geometrical non-linearities. In addition a nine-node quadrilateral variant is presented. A geometrically non-linear version of the EAS-approach is applied which is based on the enhancement of the Green–Lagrange strains instead of the displacement gradient as originally proposed by Simo and Armero. In the second part elements are derived in a similar way for a higher order, so-called 7-parameter non-linear shell formulation which includes the thickness stretch of the shell (Buchter and Ramm). In order to avoid artificial stiffening caused by the three dimensional displacement field and termed ‘thickness locking’, special provisions for the thickness stretch have to be introduced. © 1997 John Wiley & Sons, Ltd.

371 citations


Journal ArticleDOI
TL;DR: In this paper, the authors studied the initiation of an unstable antiplane elastodynamic shear process under slip-weakening friction and gave an analytical expression of the slip that they intrepret using an eigenvalue analysis.
Abstract: We study the initiation of an unstable antiplane elastodynamic shear process under slip-weakening friction. We give an analytical expression of the slip that we intrepret using an eigenvalue analysis. Considering only the part of the solution associated with positive eigenvalues, we define a “dominant part” characterized by an exponential growth with time. An explicit formula is given for the dominant part that controls the development of the instability after the application of an initial perturbation on the surface or inside the elastic body. It shows that in response to a small initial perturbation the instability will develop in a limited spectral domain. The limiting wavenumber (or reciprocal critical length) is a function of the parameters of the friction law and the elastic properties. The part of the solution associated with negative eigenvalues (the “wave part”) becomes rapidly negligible when the instability develops. We found that in the initiation phase the displacement field in the elastic body has a simple exponential dependence on the coordinate perpendicular to the fault. Using the expression of the dominant part, we estimate the duration of the initiation phase. We show the accuracy of the theoretical analysis by comparison with numerical tests computed with an independent technique. Finally, we show how the initiation phase determines the evolution toward the dynamic rupture propagation. We introduce the critical patch length in a natural way. The transition between the initiation and the propagation stages is characterized by an apparent supersonic velocity of the rupture front.

144 citations


Journal ArticleDOI
TL;DR: In this article, the effects of target size on displacements between the actual and remembered vanishing points of moving and stationary targets were examined, and it was shown that weight, rather than mass, influences displacement because the representational system incorporates subjective or experiential aspects of physical principles.
Abstract: Effects of target size on displacements between the actual and remembered vanishing points of moving and stationary targets were examined. For horizontally or vertically moving targets, target size influenced displacement only along the axis aligned with the direction of implied gravitational attraction; larger targets exhibited greater downward displacement when targets moved horizontally, greater forward displacement when targets descended, and smaller forward displacement when targets ascended. For stationary targets, target size did not influence displacement along the axis aligned with the direction of implied gravitational attraction. The data are consistent with the hypothesis that mental representation incorporates an analogue of weight. It is proposed that weight, rather than mass, influences displacement because the representational system incorporates subjective or experiential aspects of physical principles rather than physical principles per se. An observer who perceives a target that is moving in a consistent direction will usually remember that target as having traveled slightly further than it actually did; in other words, memory for the final orientation or location of a target will be slightly displaced in the direction of anticipated target motion (for a review, see Hubbard, 1995b).

106 citations


Journal ArticleDOI
01 Aug 1997-Pramana
TL;DR: In this article, a new class of exact solutions for FRW models was obtained by considering a time dependent displacement field for constant deceleration parameter models of the universe, which is based on Lyra's geometry.
Abstract: FRW models have been studied in the cosmological theory based on Lyra’s geometry. A new class of exact solutions has been obtained by considering a time dependent displacement field for constant deceleration parameter models of the universe.

97 citations


Journal ArticleDOI
TL;DR: In this paper, a B-spline Rayleigh-Ritz method is proposed for free vibration analysis of skew fiber-reinforced composite laminates which may have arbitrary lay-ups, admitting the possibility of coupling between in-plane and out-of-plane behaviour and general anisotropy.

87 citations


Journal ArticleDOI
TL;DR: In this paper, a geometrically nonlinear theory of anisotropic multilayered plates of general layups featuring interlayer slips is discussed, and the pertinent equations of motion and consistent boundary conditions are derived by means of the dynamic version of virtual work.
Abstract: The formulation of a geometrically nonlinear theory of anisotropic multilayered plates of general layups featuring interlayer slips is discussed. The theory rests on a displacement field, which accounts for an arbitrary distribution of the tangential displacements through the laminate thickness, fulfills a priori the static continuity conditions of tangential stresses at the layer interfaces, and allows for jumps in the tangential displacements so as to provide the possibility of incorporating effects of interfacial imperfection. For the interlayer displacement jump, a linear shear slip law is postulated. No a priori assumption is made on the type and order of the expansion in the thicknesswise direction of the tangential displacements. The pertinent equations of motion and consistent boundary conditions are derived by means of the dynamic version of the principle of virtual work. These are given in terms of force and moment stress resultants and in terms of generalized displacements. The generalization achieved by the proposed approach is shown by deriving, as particular cases, the recently proposed first-order and third-order models for laminated plates featuring interlayer slips

84 citations


Journal ArticleDOI
TL;DR: A survey of the existing and some other yet unpublished T-element formulations can be found in this paper, where it is shown that their choice can considerably influence the accuracy of the solution.

83 citations


Journal ArticleDOI
TL;DR: A new family of finite element methods for the Naghdi shell model, one method associated with each nonnegative integer k, based on a nonstandard mixed formulation, and the kth method employs triangular Lagrange finite elements of degree k+2 augmented by bubble functions ofdegree k + 3 for both the displacement and rotation variables.
Abstract: We propose a new family of finite element methods for the Naghdi shell model, one method associated with each nonnegative integer k. The methods are based on a nonstandard mixed formulation, and the kth method employs triangular Lagrange finite elements of degree k+2 augmented by bubble functions of degree k + 3 for both the displacement and rotation variables, and discontinuous piecewise polynomials of degree k for the shear and membrane stresses. This method can be implemented in terms of the displacement and rotation variables alone; as the minimization of an altered energy functional over the space mentioned. The alteration consists of the introduction of a weighted local projection into part, but not all, of the shear and membrane energy terms of the usual Naghdi energy. The relative error in the method, measured in a norm which combines the H I norm of the displacement and ro tation fields and an appropriate norm of the shear and membrane stress fields, converges to zero with order k+1 uniformly with respect to the shell thickness for smooth solutions, at least under the assumption that certain geometrical coefficients in the Nagdhi model are replaced by piecewise constants.

83 citations


Journal ArticleDOI
TL;DR: In this paper the strain variance is derived from the statistical properties of the displacement field to define a point signal-to-noise ratio for elastography (SNR0), which characterizes the noise properties, dynamic range, and sensitivity of strain images based on the spatial resolution requirements.
Abstract: Accurate displacement estimates are required to obtain high-quality strain estimates in elastography. In this paper the strain variance is derived from the statistical properties of the displacement field to define a point signal-to-noise ratio for elastography (SNR0). Displacements caused by compressional forces applied along the axis of the transducer beam are modeled by scaling and shifting the axial reflectivity profile of the tissue. The strain variance is given as a function of essential experimental parameters, such as the amount of tissue compression, echo waveform window length, and the amount of window overlap. SNR0 is defined in terms of applied compression and strain variance and normalized by the input signal-to-noise ratio (SNRi) for echo signals, to formulate the performance metric SNR0/SNRi. This quantity characterizes the noise properties, dynamic range, and sensitivity of strain images based on the spatial resolution requirements. The results indicate that low noise, high sensitivity, and limited dynamic range strain images are obtained for high-frequency bandpass signals when the applied strain is small. For large strains, however, one strategy for low-noise strain imaging employs base-band signals to obtain images with large dynamic range but limited peak sensitivity and noise figure. A better strategy includes companding, which eliminates the average strain in the echo signal before cross-correlation to reduce the dynamic range requirement and increase peak sensitivity for strain estimates.

74 citations


Journal ArticleDOI
TL;DR: In this article, a refined higher-order laminate theory is developed to analyze smart materials, surface bonded or embedded, in composite laminates, using a refined displacement field which accounts for transverse shear stresses through the thickness.
Abstract: A refined higher order laminate theory is developed to analyze smart materials, surface bonded or embedded, in composite laminates. The analysis uses a refined displacement field which accounts for transverse shear stresses through the thickness. All boundary conditions are satisfied at the free surfaces. Non-linearities are introduced through the strain dependent piezoelectric coupling coefficients and the assumed strain distribution through the thickness. The analysis is implemented using the finite element method. The procedure is computationally efficient and allows for a detailed investigation of both the local and global effects due to the presence of actuators. The finite element model is shown to agree well with published experimental results. Numerical examples are presented for composite laminates of various thicknesses and the results are compared with those obtained using classical laminate theory. The refined theory captures important higher order effects which are not modeled by the classical laminate theory, resulting in significant deviations.

71 citations


Journal ArticleDOI
TL;DR: In this article, two optical methods are presented for the mechanical characterization of thin films, namely real-time holographic interferometry and a fringe projection method called "contouring", which are coupled to the inter-ferometry by the phase measurements, thus allowing the displacement field to be measured at all points on the membrane.
Abstract: Two optical methods are presented for the mechanical characterization of thin films, namely real time holographic interferometry and a fringe projection method called “contouring.” These two methods are coupled to the interferometry by the phase measurements, thus allowing the displacement field to be measured at all points on the membrane. We discuss the solutions retained in terms of their precision and sensitivity. These methods are then applied to membrane bulging tests, a type of test that is widely used in micro-mechanical studies. The measurements are performed on silicon single crystal and the results are compared to the solutions calculated by finite element methods. In both cases, the good agreement between theory and experiments allows the experimental apparatus to be validated.

Journal ArticleDOI
Abstract: Planar digital image correlation has been extended to measure surface deformations of cylindrical specimens without physical contact for high-temperature situations. A single CCD camera acquires the surface image patterns of a section of a specimen in the undeformed and deformed states to determine two-dimensional displacements on a projection plane. Axial, circumferential and shear deformations are determined through curvature transformation on the two-dimensional projection displacement field. The resolution of this technique was determined for a cylinder of 22.23-mm diameter to be 3.5 μm for the axial displacement, 0.05 percent for the axial and shear strains and 0.08 percent for the circumferential strain when correlation computations are carried out over a field of 5 mm×5 mm.

Journal ArticleDOI
TL;DR: In this paper, the buckling and free vibration of stepped laminated composite beams were studied using simple higher-order theory (SHOT), which assumes a cubic distribution for the displacement field through the thickness.

Journal ArticleDOI
TL;DR: In this article, a general four-degrees-of-freedom beam theory (G4DOFBT) is proposed for the accurate stress analysis of either homogeneous or laminated composite beams subjected to arbitrary edge boundary conditions.

Journal ArticleDOI
TL;DR: The free energy and the profile of the displacement field in a stack of sterically interacting smectic multilayers bounded by surfaces under tension is investigated and it is shown that this tension can lead to a significant change in the multilayer free energy.

Journal ArticleDOI
TL;DR: In this paper, the effect of the debonding angle, the shear moduli ratios in the constituents and the fiber volume fractions on the composite shear modulation is evaluated through finite element analyses.

Patent
06 Jun 1997
TL;DR: In this article, a backstop or target particularly suited for use in athletic applications such as baseball or golf, and which includes a frame from which a flexible net is suspended at its corners and connected to a plurality of linear displacement sensors.
Abstract: A backstop or target particularly suited for use in athletic applications such as baseball or golf, and which includes a frame from which a flexible net is suspended at its corners and connected to a plurality of linear displacement sensors. As the net is displaced due to the impact of a projectile such as a ball, tension is applied to the cords which in turn move the axially-moveable components of each linear displacement sensor. In one embodiment, the linear displacement sensors utilize a light beam and photoelectric detector to plot the time intervals at which equally-spaced indices on the axially-moveable component pass a predetermined point. This data is used to determine position, velocity, or trajectory of the projectile relative to the initial plane of the net using direct geometric and trigonometric calculations.

Proceedings ArticleDOI
28 May 1997
TL;DR: In this paper, a finite element formulation of the vibrations of piezoelectric quartz resonators based on Mindlin plate theory is derived, and the vibration frequency and vibration mode shapes including the electric potential distribution are obtained.
Abstract: A finite element formulation of the vibrations of piezoelectric quartz resonators based on Mindlin plate theory is derived. The higher-order plate theory is employed for the development of a collection of successively higher-order plate elements which can be effective for a broad frequency range including the fundamental and overtone modes of thickness-shear vibrations. The presence of electrodes is also considered for its mechanical effects. The mechanical displacements and electric potential are combined into a generalized displacement field, and the subsequent derivations are carried out with all the generalized equations. Through standard finite element procedure, the vibration frequency and vibration mode shapes including the electric potential distribution are obtained. The frequency spectra is compared with some well-known experimental results with good agreement. Our previous experience with finite element analysis of high frequency quartz plate vibrations leads us to believe that memory and computing time will always remain as key issues despite the advances in computers. Hence, the use of sparse matrix techniques, efficient eigenvalue solvers, and other reduction procedures are explored.

Journal ArticleDOI
TL;DR: In this article, a refined shear deformation theory assuming a nonlinear variation for the displacement field is used to develop discrete models for the sensitivity analysis and optimization of thick and thin multilayered angle ply composite plate structures.

Journal ArticleDOI
TL;DR: In this article, a theoretical and numerical analysis of mixed-mode separation in fracture dynamics, based on new path independent integrals, is presented, where strain energy density is expressed as a function of the actual displacement field and of an auxiliary kinematically admissible field.
Abstract: This paper presents a theoretical and numerical analysis of mixed-mode separation in fracture dynamics, based on new path independent integrals. The M-integral method proposed by Chen and Shield is generalized for dynamic fracture applications. Strain energy density is expressed as a function of the actual displacement field and of an auxiliary kinematically admissible field. On the other hand, the concept of the GΘ-integral developed by Destuynder using the Rice J-integral is extended to dynamic problems. Introducing the same concept in the M-integral formulation leads to the new path-independent integral MΘ in elastodynamics. Numerical tests give us accurate results of separated mode.

Journal ArticleDOI
TL;DR: An analytical solution for the inelastic response of an arbitrarily layered concentric cylinder assemblage under axial shear loading of the type that produces homogeneous deformation in an equivalent homogenized medium is presented in this paper.

Journal ArticleDOI
TL;DR: In this article, a theory of laminated composite shells with higher-order transverse shear deformation is presented based on refined analysis, and the continuity conditions of displacements and in-plane stresses at layer interfaces are introduced to improve and simplify the displacement field.

Journal ArticleDOI
TL;DR: In this paper, a spectral method is employed to study the response to surface loads of a Maxwell earth including lateral viscosity variations, and the long-wavelength vertical displacement is not greatly affected by the presence of a lithospheric craton, while the tangential displacement is severely modified for the case of a homogeneous mantle.
Abstract: Accepted 1997 March 10. Received 1997 February 20; in original form 1996 June 10 S U M M A R Y A spectral method is employed to study the response to surface loads of a Maxwell earth including lateral viscosity variations. In particular, we focus on the effects of lithospheric cratons on the long-wavelength time-dependent displacement field for simple earth models. The viscosity contrast of the craton with respect to the surrounding mantle is kept fixed, whereas its thickness is allowed to vary. We show that the longwavelength vertical displacement is not greatly affected by the presence of a lithospheric craton, while the tangential displacement is severely modified for the case of a homogeneous mantle. With increasing harmonic degree and thickness of the craton, the load-deformation coefficients deviate from those pertaining to a homogeneous mantle with a viscosity of 10” Pa s. These deviations are particularly enhanced on timescales larger than a few hundred years. These findings indicate that the interpretation of the viscosity structure of the mantle inferred from postglacial rebound signatures based on radially stratified models is affected by the presence of lateral viscosity variations.

Journal ArticleDOI
TL;DR: In this paper, the effect of distinct fluid densities is investigated in the region of low to intermediate Reynolds numbers for equally viscous fluids and the efficiency of the displacement is analyzed for various flow situation.

Journal ArticleDOI
TL;DR: In this paper, the authors presented a simple approach to describe these resonances (called lateral resonances) in 1-3 piezoelectric composite materials which have a 2-D periodicity, based on the analysis of the propagation of transverse waves in a 2D periodic medium of infinite thickness.
Abstract: Materials with a periodic microstructure show resonances caused by the elastic wave Bragg diffraction. This paper presents a simple approach to describe these resonances (called lateral resonances) in 1-3 piezoelectric composite materials which have a 2-D periodicity. Our model is based on the analysis of the propagation of transverse waves in a 2-D periodic medium of infinite thickness and takes into account the periodic and interfacial boundary conditions. This model predicts the displacement field vectors and frequencies of lateral resonances from which the phase velocity of lateral waves is determined. The theoretical and experimental variations of this velocity versus the ceramic rod width to pitch ratio are compared. It is shown that the first lateral mode frequency is maximum when the ceramic volume fraction is around 0.65. Theoretical predictions of the mechanical displacement at the composite surface are compared with measurements obtained by an interferometric laser technique. A good agreement is observed, showing that lateral waves are mainly vertically polarized.

Journal ArticleDOI
TL;DR: In this article, a software package HRPACK is presented to simulate well-oriented defects visible in high-resolution electron microscopy (HREM) images, assuming an elastic planar deformation field.

Journal ArticleDOI
TL;DR: In this article, the singular stress field at the vertex of a bimaterial wedge under in-plane loading is derived using the continuity conditions along the interface and the traction-free conditions along free edges.
Abstract: This paper is concerned with the singular stress field at the vertex of a bimaterial wedge under in-plane loading. The boundary value problem is initially formulated in terms of the complex function method. The eigenequations are obtained using the continuity conditions along the interface and the traction-free conditions along the free edges, leading to the development of explicit expressions for the singular stress and displacement fields for a general bimaterial wedge. These expressions are then used to develop a new singular finite element. This element enables the determination of the singular stress field and the associated stress intensity factors reliably and efficiently. To establish the validity of the method, test cases are examined and compared with existing solutions. The method is then applied to evaluate the effect of the wedge geometry and the elastic mismatch upon the resulting stress intensity factors.

Journal ArticleDOI
TL;DR: In this article, a consistent continuous cracked bar vibration theory is developed, where the stress and displacement field about the crack was used to modify the displacement field throughout the bar, and reduction to one spatial dimension was achieved by integrating the stressed and displacement fields throughout the cross-sections so that the total displacement would be exact.

Journal ArticleDOI
TL;DR: In this paper, a three-dimensional theory is developed to model composite box beams with arbitrary wall thicknesses, which can accurately capture the transverse shear stresses through the thickness of each wall while satisfying stress-free boundary conditions on the inner and outer surfaces of the beam.
Abstract: A three-dimensional theory is developed to model composite box beams with arbitrary wall thicknesses. The theory, which is based on a refined displacement field, approximates the three-dimensional elasticity solution so that the beam cross-sectional properties are not reduced to one-dimensional beam parameters. Both in-plane and out-of-plane warping are included automatically in the formulation. The model can accurately capture the transverse shear stresses through the thickness of each wall while satisfying stress-free boundary conditions on the inner and outer surfaces of the beam. Numerical results are presented for beams with varying wall thicknesses and aspect ratios. The static results are correlated with available experimental data and show excellent agreement. Results presented for thick-walled box beams show the importance of including transverse shear in the formulation and the difficulty of defining a ‘beam’ twist for the entire cross-section.

01 Jan 1997
TL;DR: In this paper, the authors extend the domain of influence to cover the thermoelasticity of bodies with voids and prove that for a finite time, the displacement field, temperature, and volume fraction generate no disturbance outside a bounded domain.
Abstract: The domain of influence, proposed by Cowin and Nunziato, is extended to cover the thermoelasticity of bodies with voids. We prove that for a finite time $t>0$ the displacement field $u_{i}$, the temperature $\theta $ and the change in volume fraction $\sigma$ generate no disturbance outside a bounded domain $B_t$.