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.

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.

Integral treatment for the representation of thermodynamic properties in multicomponent systems using interaction parameters

The partial thermodynamic functions of the solvent component of a ternary system have been deduced in terms of the interaction parameters by integration of several series which emerge from the Maclaurin infinite series based on the integral property of the system and subjected to appropriate boundary conditions. The series integration shows that the resulting partial functions are suitable for interpreting the thermodynamic properties of the system and are independent of compositional paths. In the present analysis, the higher order terms of these series are found to make insignificant contributions.

Transmembrane domains participate in functions of integral membrane proteins

Integral membrane proteins have one or more transmembrane a-helical domains and carry out a variety of functions such as enzyme catalysis, transport across membranes, transducing signals as receptors of hormones and growth factors, and energy transfer in ATP synthesis. These transmembrane domains are not mere structural units anchoring the protein to the lipid bilayer but seem to-contribute in the overall activity. Recent findings in support of this are described using some typical examples-LDL receptor, growth factor receptor tyrosine kinase, HMG-CoA reductase, F-0-ATPase and adrenergic receptors. The trends in research indicate that these transmembrane domains participate in a variety of ways such as a linker, a transducer or an exchanger in the overall functions of these proteins in transfer of materials, energy and signals.

Relation between integral and partial properties of ternary solutions along different composition trajectories

The relations between partial and integral properties of ternary solutions along composition trajectories suggested by Kohler, Colinet and Jacob, and along an arbitrary path are derived. The chemical potentials of the components are related to the slope of integral free energy by expressions involving the binary compositions generated by the intersections of the composition trajectory with the sides of the ternary triangle. Only along the Kohler composition trajectory it is possible to derive the integral free energy from the variation of the chemical potential of a single component with composition or vice versa. Along all other paths the differential of the integral free energy is related to two chemical potentials. The Gibbs-Duhem integration proposed by Darken for the ternary system uses the Kohler isogram. The relative merits of different limits for integration are discussed.

Solution of a hypersingular integral equation of the second kind

A straightforward analysis involving the complex function-theoretic method is employed to determine the closed-form solution of a special hypersingular integral equation of the second kind, and its known solution is recovered.

Freezing of classical fluids in a quenched random potential

The phase diagram of a hard-sphere fluid in the presence of a random pinning potential is studied analytically and numerically. In the analytic work, replicas are introduced for averaging over the quenched disorder, and the hypernetted chain approximation is used to calculate density correlations in the replicated liquid. The freezing transition of the liquid into a nearly crystalline state is studied using a density-functional approach, and the liquid to glass transition is studied using a phenomenological replica symmetry breaking approach. In the numerical work, local minima of a discretized version of the Ramakrishnan-Yussouff free-energy functional are located and the phase diagram in the density-disorder plane is obtained from an analysis of the relative stability of these minima. Both approaches lead to similar results for the phase diagram. The first-order liquid to crystalline solid transition is found to change to a continuous liquid to glass transition as the strength of the disorder is increased above a threshold value.

Describing Hand Postures: Inspirations from Classical Mudras

The objective of this work is to develop a systematic methodology for describing hand postures and grasps which is independent of the kinematics and geometry of the hand model which in turn can be used for developing a universal referencing scheme. It is therefore necessary that the scheme be general enough to describe the continuum of hand poses. Indian traditional classical dance form, “Bharathanatyam”, uses 28 single handed gestures, called “mudras”. A Mudra can be perceived as a hand posture with a specific pattern of finger configurations. Using modifiers, complex mudras could be constructed from relatively simple mudras. An adjacency matrix is constructed to describe the relationship among mudras. Various mudra transitions can be obtained from the graph associated with this matrix. Using this matrix, a hierarchy of the mudras is formed. A set of base mudras and modifiers are used for describing how one simple posture of hand can be transformed into another relatively complex one. A canonical set of predefined hand postures and modifiers can be used in digital human modeling to develop standard hand posture libraries.

Classical screw theory: A fresh look using dual eigenvalue approach

This paper presents a novel algebraic formulation of the central problem of screw theory, namely the determination of the principal screws of a given system. Using the algebra of dual numbers, it shows that the principal screws can be determined via the solution of a generalised eigenproblem of two real, symmetric matrices. This approach allows the study of the principal screws of the general screw systems associated with a manipulator of arbitrary geometry in terms of closed-form expressions of its architecture and configuration parameters. The formulation is illustrated with examples of practical manipulators.