Finite element estimation of elastic interlaminar stresses in laminates

Low interlaminar strength and the consequent possibility of interlaminar failures in composite laminates demand an examination of interlaminar stresses and/or strains to ensure their satisfactory performance. As a first approximation, these stresses can be obtained from thickness-wise integration of ply equilibrium equations using in-plane stresses from the classical laminated plate theory. Implementation of this approach in the finite element form requires evaluation of third and fourth order derivatives of the displacement functions in an element. Hence, a high precision element developed by Jayachandrabose and Kirkhope (1985) is used here and the required derivatives are obtained in two ways. (i) from direct differentiation of element shape functions; and (ii) by adapting a finite difference technique applied to the nodal strains and curvatures obtained from the finite element analysis. Numerical results obtained for a three-layered symmetric and a two-layered asymmetric laminate show that the second scheme is quite effective compared to the first scheme particularly for the case of asymmetric laminates.

Method of Analysis if Uniaxial Deformation Data

A comprehensive scheme for analysing uniaxial deformation data, taking into account the finite stiffness of the testing machine is presented. Equations relevant to tension and stress relaxation tests carried out under cross head speed control, and to creep testing under constant load, are described. For the first two cases, the implications of not using gauge length extensometry but relying upon cross head displacement for inferring specimen extension, and the role of uncertainty in machine stiffness are also examined. The final section touches upon the extension of the present scheme to account for specimen anelasticity.

A monolithic strategy for fluid-structure interaction problems

In this work, we present a new monolithic strategy for solving fluid-structure interaction problems involving incompressible fluids, within the context of the finite element method. This strategy, similar to the continuum dynamics, conserves certain properties, and thus provides a rational basis for the design of the time-stepping strategy; detailed proofs of the conservation of these properties are provided. The proposed algorithm works with displacement and velocity variables for the structure and fluid, respectively, and introduces no new variables to enforce velocity or traction continuity. Any existing structural dynamics algorithm can be used without change in the proposed method. Use of the exact tangent stiffness matrix ensures that the algorithm converges quadratically within each time step. An analytical solution is presented for one of the benchmark problems used in the literature, namely, the piston problem. A number of benchmark problems including problems involving free surfaces such as sloshing and the breaking dam problem are used to demonstrate the good performance of the proposed method. Copyright (C) 2010 John Wiley & Sons, Ltd.

Squeezed states, photon-number distributions, and U(l) invariance

We study the photon-number distribution in squeezed states of a single-mode radiation field. A U(l)-invariant squeezing criterion is compared and contrasted with a more restrictive criterion, with the help of suggestive geometric representations. The U(l) invariance of the photon-number distribution in a squeezed coherent state, with arbitrary complex squeeze and displacement parameters, is explicitly demonstrated. The behavior of the photon-number distribution for a representative value of the displacement and various values of the squeeze parameter is numerically investigated. A new kind of giant oscillation riding as an envelope over more rapid oscillations in this distribution is demonstrated.

Influence of crack tip constraint on void growth in ductile FCC single crystals

Effect of constraint (stress triaxiality) on void growth near a notch tip in a FCC single crystal is investigated. Finite element simulations within the modified boundary layer framework are conducted using crystal plasticity constitutive equations and neglecting elastic anisotropy. Displacement boundary conditions based on model, elastic, two term K-T field are applied on the outer boundary of a large circular domain. A pre-nucleated void is considered ahead of a stationary notch tip. The interaction between the notch tip and the void is studied under different constraints (T-stress levels) and crystal orientations. It is found that negative T-stress retards the mechanisms of ductile fracture. However, the extent of retardation depends on the crystal orientation. Further, it is found that there exists a particular orientation which delays the ductile fracture processes and hence can potentially improve ductility. This optimal orientation depends on the constraint level. (C) 2010 Published by Elsevier B.V.

Paleoseismological evidence of surface faulting along the northeastern Himalayan front, India: Timing, size, and spatial extent of great earthquakes

The similar to 2500 km long Himalayan arc has experienced three large to great earthquakes of M-w 7.8 to 8.4 during the past century, but none produced surface rupture. Paleoseismic studies have been conducted during the last decade to begin understanding the timing, size, rupture extent, return period, and mechanics of the faulting associated with the occurrence of large surface rupturing earthquakes along the similar to 2500 km long Himalayan Frontal Thrust (HFT) system of India and Nepal. The previous studies have been limited to about nine sites along the western two-thirds of the HFT extending through northwest India and along the southern border of Nepal. We present here the results of paleoseismic investigations at three additional sites further to the northeast along the HFT within the Indian states of West Bengal and Assam. The three sites reside between the meizoseismal areas of the 1934 Bihar-Nepal and 1950 Assam earthquakes. The two westernmost of the sites, near the village of Chalsa and near the Nameri Tiger Preserve, show that offsets during the last surface rupture event were at minimum of about 14 m and 12 m, respectively. Limits on the ages of surface rupture at Chalsa (site A) and Nameri (site B), though broad, allow the possibility that the two sites record the same great historical rupture reported in Nepal around A.D. 1100. The correlation between the two sites is supported by the observation that the large displacements as recorded at Chalsa and Nameri would most likely be associated with rupture lengths of hundreds of kilometers or more and are on the same order as reported for a surface rupture earthquake reported in Nepal around A.D. 1100. Assuming the offsets observed at Chalsa and Nameri occurred synchronously with reported offsets in Nepal, the rupture length of the event would approach 700 to 800 km. The easternmost site is located within Harmutty Tea Estate (site C) at the edges of the 1950 Assam earthquake meizoseismal area. Here the most recent event offset is relatively much smaller (<2.5 m), and radiocarbon dating shows it to have occurred after A.D. 1100 (after about A.D. 1270). The location of the site near the edge of the meizoseismal region of the 1950 Assam earthquake and the relatively lesser offset allows speculation that the displacement records the 1950 M-w 8.4 Assam earthquake. Scatter in radiocarbon ages on detrital charcoal has not resulted in a firm bracket on the timing of events observed in the trenches. Nonetheless, the observations collected here, when taken together, suggest that the largest of thrust earthquakes along the Himalayan arc have rupture lengths and displacements of similar scale to the largest that have occurred historically along the world's subduction zones.

Fracture Properties of Concrete-Concrete Interfaces Using Digital Image Correlation

The mode I and mode II fracture toughness and the critical strain energy release rate for different concrete-concrete jointed interfaces are experimentally determined using the Digital Image Correlation technique. Concrete beams having different compressive strength materials on either side of a centrally placed vertical interface are prepared and tested under three-point bending in a closed loop servo-controlled testing machine under crack mouth opening displacement control. Digital images are captured before loading (undeformed state) and at different instances of loading. These images are analyzed using correlation techniques to compute the surface displacements, strain components, crack opening and sliding displacements, load-point displacement, crack length and crack tip location. It is seen that the CMOD and vertical load-point displacement computed using DIC analysis matches well with those measured experimentally.

A general procedure for modified crack closure integral in 3D problems with cracks

In linear elastic fracture mechanics (LEFM), Irwin's crack closure integral (CCI) is one of the signficant concepts for the estimation of strain energy release rates (SERR) G, in individual as well as mixed-mode configurations. For effective utilization of this concept in conjunction with the finite element method (FEM), Rybicki and Kanninen [Engng Fracture Mech. 9, 931 938 (1977)] have proposed simple and direct estimations of the CCI in terms of nodal forces and displacements in the elements forming the crack tip from a single finite element analysis instead of the conventional two configuration analyses. These modified CCI (MCCI) expressions are basically element dependent. A systematic derivation of these expressions using element stress and displacement distributions is required. In the present work, a general procedure is given for the derivation of MCCI expressions in 3D problems with cracks. Further, a concept of sub-area integration is proposed which facilitates evaluation of SERR at a large number of points along the crack front without refining the finite element mesh. Numerical data are presented for two standard problems, a thick centre-cracked tension specimen and a semi-elliptical surface crack in a thick slab. Estimates for the stress intensity factor based on MCCI expressions corresponding to eight-noded brick elements are obtained and compared with available results in the literature.

An experimental study on acoustic emission energy as a quantitative measure of size independent specific fracture energy of concrete beams

Notched three point bend specimens (TPB) were tested under crack mouth opening displacement (CMOD) control at a rate of 0.0004 mm/s and during the fracture process acoustic emissions (AE) were simultaneously monitored. It was observed that AE energy could be related to fracture energy. An experimental study was done to understand the behavior of AE energy with parameters of concrete like its strength and size. In this study, AE energy was used as a quantitative measure of size independent specific fracture energy of concrete beams and the concepts of boundary effect and local fracture energy were used to obtain size independent AE energy from which size independent fracture energy was obtained. (C) 2010 Elsevier Ltd. All rights reserved.

Dynamic analysis of three point bend specimens under impact

A simple one dimensional inertial model is presented for transient response analysis of notched beams under impact, and extracting dynamic initiation toughness values. The model includes the effects of striker mass interactions, and contact deformations of the beam. Displacement time history of the striker mass is applied to the model as forcing function. The model is validated by comparison with the experimental investigation on ductile aluminium 6061 alloy and brittle polymer, PMMA.

Modified Crack Closure Integral (MCCI) For 3-D Problems Using 20-Noded Brick Elements

The Modified Crack Closure Integral (MCCI) technique based on Irwin's crack closure integral concept is very effective for estimation of strain energy release rates G in individual as well as mixed-mode configurations in linear elastic fracture mechanics problems. In a finite element approach, MCCI can be evaluated in the post-processing stage in terms of nodal forces and displacements near the crack tip. The MCCI expressions are however, element dependent and require a systematic derivation using stress and displacement distributions in the crack tip elements. Earlier a general procedure was proposed by the present authors for the derivation of MCCI expressions for 3-dimensional (3-d) crack problems modelled with 8-noded brick elements. A concept of sub-area integration was proposed to estimate strain energy release rates at a large number of points along the crack front. In the present paper a similar procedure is adopted for the derivation of MCCI expressions for 3-d cracks modelled with 20-noded brick elements. Numerical results are presented for centre crack tension and edge crack shear specimens in thick slabs, showing a comparison between present results and those available in the literature.

Identification of Local Conformational Similarity in Structurally Variable Regions of Homologous Proteins Using Protein Blocks

Structure comparison tools can be used to align related protein structures to identify structurally conserved and variable regions and to infer functional and evolutionary relationships. While the conserved regions often superimpose well, the variable regions appear non superimposable. Differences in homologous protein structures are thought to be due to evolutionary plasticity to accommodate diverged sequences during evolution. One of the kinds of differences between 3-D structures of homologous proteins is rigid body displacement. A glaring example is not well superimposed equivalent regions of homologous proteins corresponding to a-helical conformation with different spatial orientations. In a rigid body superimposition, these regions would appear variable although they may contain local similarity. Also, due to high spatial deviation in the variable region, one-to-one correspondence at the residue level cannot be determined accurately. Another kind of difference is conformational variability and the most common example is topologically equivalent loops of two homologues but with different conformations. In the current study, we present a refined view of the ``structurally variable'' regions which may contain local similarity obscured in global alignment of homologous protein structures. As structural alphabet is able to describe local structures of proteins precisely through Protein Blocks approach, conformational similarity has been identified in a substantial number of `variable' regions in a large data set of protein structural alignments; optimal residue-residue equivalences could be achieved on the basis of Protein Blocks which led to improved local alignments. Also, through an example, we have demonstrated how the additional information on local backbone structures through protein blocks can aid in comparative modeling of a loop region. In addition, understanding on sequence-structure relationships can be enhanced through our approach. This has been illustrated through examples where the equivalent regions in homologous protein structures share sequence similarity to varied extent but do not preserve local structure.

Modified crack closure integral (MCCI) for 3-d problems using 20 noded brick elememnts

The Modified Crack Closure Integral (MCCI) technique based on Irwin's crack closure integral concept is very effective for estimation of strain energy release rates G in individual as well as mixed-mode configurations in linear elastic fracture mechanics problems. In a finite element approach, MCCI can be evaluated in the post-processing stage in terms of nodal forces and displacements near the crack tip. The MCCI expressions are however, element dependent and require a systematic derivation using stress and displacement distributions in the crack tip elements. Earlier a general procedure was proposed by the present authors for the derivation of MCCI expressions for 3-dimensional (3-d) crack problems modelled with 8-noded brick elements. A concept of sub-area integration was proposed to estimate strain energy release rates at a large number of points along the crack front. In the present paper a similar procedure is adopted for the derivation of MCCI expressions for 3-d cracks modelled with 20-noded brick elements. Numerical results are presented for centre crack tension and edge crack shear specimens in thick slabs, showing a comparison between present results and those available in the literature.

3-D Warping in Four-Bar Laminated Linkages

This paper deals with the evaluation of the component-laminate load-carrying capacity, i.e., to calculate the loads that cause the failure of the individual layers and the component-laminate as a whole in four-bar mechanism. The component-laminate load-carrying capacity is evaluated using the Tsai-Wu-Hahn failure criterion for various layups. The reserve factor of each ply in the component-laminate is calculated by using the maximum resultant force and the maximum resultant moment occurring at different time steps at the joints of the mechanism. Here, all component bars of the mechanism are made of fiber reinforced laminates and have thin rectangular cross-sections. They could, in general, be pre-twisted and/or possess initial curvature, either by design or by defect. They are linked to each other by means of revolute joints. We restrict ourselves to linear materials with small strains within each elastic body (beam). Each component of the mechanism is modeled as a beam based on geometrically nonlinear 3-D elasticity theory. The component problems are thus split into 2-D analyses of reference beam cross-sections and nonlinear 1-D analyses along the three beam reference curves. For the thin rectangular cross-sections considered here, the 2-D cross-sectional nonlinearity is also overwhelming. This can be perceived from the fact that such sections constitute a limiting case between thin-walled open and closed sections, thus inviting the nonlinear phenomena observed in both. The strong elastic couplings of anisotropic composite laminates complicate the model further. However, a powerful mathematical tool called the Variational Asymptotic Method (VAM) not only enables such a dimensional reduction, but also provides asymptotically correct analytical solutions to the nonlinear cross-sectional analysis. Such closed-form solutions are used here in conjunction with numerical techniques for the rest of the problem to predict more quickly and accurately than would otherwise be possible. Local 3-D stress, strain and displacement fields for representative sections in the component-bars are recovered, based on the stress resultants from the 1-D global beam analysis. A numerical example is presented which illustrates the failure of each component-laminate and the mechanism as a whole.

Analysis of a long thick orthotropic circular cylindrical shell panel

An exact three-dimensional elasticity solution has been obtained for an infinitely long, thick transversely isotropic circular cylindrical shell panel, simply supported along the longitudinal edges and subjected to a radial patch load. Using a set of three displacement functions, the boundary value problem is reduced to Bessel's differential equation. Numerical results are presented for different thickness to mean radius ratios and semicentral angles of the shell panel. Classical and first-order shear deformation orthotropic shell theories have been examined in comparison with the present elasticity solution.