Improved hybrid elements for structural analysis

Hybrid elements, which are based on a two-field variational formulation with the displacements and stresses interpolated separately, are known to deliver very high accuracy, and to alleviate to a large extent problems of locking that plague standard displacement-based formulations. The choice of the stress interpolation functions is of course critical in ensuring the high accuracy and robustness of the method. Generally, an attempt is made to keep the stress interpolation to the minimum number of terms that will ensure that the stiffness matrix has no spurious zero-energy modes, since it is known that the stiffness increases with the increase in the number of terms. Although using such a strategy of keeping the number of interpolation terms to a minimum works very well in static problems, it results either in instabilities or fails to converge in transient problems. This is because choosing the stress interpolation functions merely on the basis of removing spurious energy modes can violate some basic principles that interpolation functions should obey. In this work, we address the issue of choosing the interpolation functions based on such basic principles of interpolation theory and mechanics. Although this procedure results in the use of more number of terms than the minimum (and hence in slightly increased stiffness) in many elements, we show that the performance continues to be far superior to displacement-based formulations, and, more importantly, that it also results in considerably increased robustness.

Psi-angle dependence of geminal proton–carbonyl-13C coupling constants in peptides. A theoretical investigation†

Theoretical calculations of the geminal carbonyl-13C- proton coupling constant, 2J(C′H), in α-amino acids have been carried out using Dirac Vector model and Penney-Dirac bond order formulations. The results indicate that the couplings are dependent on the backbone torsion angle psi (ψ) of the amino acid residues in peptides. The meagre available experimental data seem to support the theoretical findings.

A Smooth Finite Element Method Based on Reproducing Kernel DMS-Splines

The element-based piecewise smooth functional approximation in the conventional finite element method (FEM) results in discontinuous first and higher order derivatives across element boundaries Despite the significant advantages of the FEM in modelling complicated geometries, a motivation in developing mesh-free methods has been the ease with which higher order globally smooth shape functions can be derived via the reproduction of polynomials There is thus a case for combining these advantages in a so-called hybrid scheme or a `smooth FEM' that, whilst retaining the popular mesh-based discretization, obtains shape functions with uniform C-p (p >= 1) continuity One such recent attempt, a NURBS based parametric bridging method (Shaw et al 2008b), uses polynomial reproducing, tensor-product non-uniform rational B-splines (NURBS) over a typical FE mesh and relies upon a (possibly piecewise) bijective geometric map between the physical domain and a rectangular (cuboidal) parametric domain The present work aims at a significant extension and improvement of this concept by replacing NURBS with DMS-splines (say, of degree n > 0) that are defined over triangles and provide Cn-1 continuity across the triangle edges This relieves the need for a geometric map that could precipitate ill-conditioning of the discretized equations Delaunay triangulation is used to discretize the physical domain and shape functions are constructed via the polynomial reproduction condition, which quite remarkably relieves the solution of its sensitive dependence on the selected knotsets Derivatives of shape functions are also constructed based on the principle of reproduction of derivatives of polynomials (Shaw and Roy 2008a) Within the present scheme, the triangles also serve as background integration cells in weak formulations thereby overcoming non-conformability issues Numerical examples involving the evaluation of derivatives of targeted functions up to the fourth order and applications of the method to a few boundary value problems of general interest in solid mechanics over (non-simply connected) bounded domains in 2D are presented towards the end of the paper

A method for estimation of the radius of elastic-plastic boundary around cold-worked holes

The radius of an elastic-plastic boundary was measured by the strain gage method around the cold-worked region in L72-aluminum alloy. The relative radial expansion was varied from 2.5 to 6.5 percent during the cold-working process using mandrel and split sleeve. The existing theoretical studies in this area are reviewed. The experimental results are compared with existing experimental data of various investigators and with various theoretical formulations. A model is developed to predict the radius of elastic-plastic boundary, and the model is assessed by comparing with the present experiments.

Arene ruthenium complexes of N,N′- and N,O-donor schiff base ligands: an X-ray structure of [(η6-p-cymene) RuCl(C5,H4N-2-CH=NC6H4-p-Me)Cl·C6H6·H2O

Arene ruthenium(II) Schiff base complexes of formulations [(η -p-cymene)RuCl(C5H4N-2-CH=NC6H4-p-X)](ClO4) (1) and [(η6-p-cymene)RuCl(O-o-C6H4CH=NC6H4-p-X)] (2) (X = H, Me, OMe, NO2, Cl) were prepared by reacting [(η6-p-cymene)RuCl2]2 with corresponding pyridine-2-carboxaldimines and sodium salts of salicylaldimines in dry THF, respectively. Complex 1 is isolated as a perchlorate salt. The molecular structure of [(η6-p-cymene)RuCl(C5H4 N-2-CH=NC6H4-p-Me)]Cl·C6H6·H2O has been determined by X-ray crystallography. The complex contains an η6-p-cymene group, a chloride and a bidentate chelating Schiff base ligand.

Differential scanning calorimetry cure studies on the effect of addition of epoxy diluents of tetrafunctional epoxy resins

The effect of the addition of p-aminophenol and aniline-based epoxy diluents on the curing behavior of highly viscous tetraglycidyl diamino diphenyl methane resin with diamino diphenyl sulfone hardener have been investigated kinetically by differential scanning calorimetry. Dynamic scans were carried out over a temperature range 30–300°C for different resin formulations. Isothermal scans at four differnt temperatures have also been carried out for the evaluation of kinetic parameters. Heat flow measurements at different heating rates have indicated the evidence of autocatalytic behavior of curing reaction following a simple nth-order kinetics.

Chemical toughening of epoxies. II. Mechanical, thermal, and microscopic studies of epoxies toughened with hydroxyl-terminated poly(butadiene-co-acrylonitrile)

Diglycidyl ether–bisphenol-A-based epoxies toughened with various levels (0–12%) of chemically reacted liquid rubber, hydroxyl-terminated poly(butadiene-co-acrylonitrile) (HTBN) were studied for some of the mechanical and thermal properties. Although the ultimate tensile strength showed a continuous decrease with increasing rubber content, the toughness as measured by the area under the stress-vs.-strain curve and flexural strength reach a maximum around an optimum rubber concentration of 3% before decreasing. Tensile modulus was found to increase for concentrations below 6%. The glass transition temperature Tg as measured by DTA showed no variation for the toughened formulations. The TGA showed no variations in the pattern of decomposition. The weight losses for the toughened epoxies at elevated temperatures compare well with that of the neat epoxy. Scanning electron microscopy revealed the presence of a dual phase morphology with the spherical rubber particles precipitating out in the cured resin with diameter varying between 0.33 and 6.3 μm. In contrast, a physically blended rubber–epoxy showed much less effect towards toughening with the precipitated rubber particles of much bigger diameter (0.6–21.3 μm).

Dielectric friction and solvation dynamics: Novel results on relaxation in dipolar liquids

In this article we present a new, general but simple, microscopic expression for time-dependent solvation energy of an ion. This expression is surprisingly similar to the expression for the time-dependent dielectric friction on a moving ion. We show that both the Chandra-Bagchi and the Fried-Mukamel formulations of solvation dynamics can be easily derived from this expression. This expression leads to an almost perfect agreement of the theory with all the available computer simulation results. Second, we show here for the first time that the mobility of a light solute ion can significantly accelerate its own solvation, specially in the underdamped limit. The latter result is also in excellent agreement with the computer simulations.

Time-domain-finite-wave analysis of the engine exhaust system by means of the stationary-frame method of characteristics. Part I. Theory

Time-domain-finite-wave analysis of the engine exhaust system is usually done using the method of characteristics. This makes use of either the moving frame method, or the stationary frame method. The stationary frame method is more convenient than its counterpart inasmuch as it avoids the tedium of graphical computations. In this paper (part I), the stationary-frame computational scheme along with the boundary conditions has been implemented. The analysis of a uniform tube, cavity-pipe junction including the engine and the radiation ends, and also the simple area discontinuities has been presented. The analysis has been done accounting for wall friction and heat-transfer for a one-dimensional unsteady flow. In the process, a few inconsistencies in the formulations reported in the literature have been pointed out and corrected. In the accompanying paper (part II) results obtained from the simulation are shown to be in good agreement with the experimental observations.

Decoupled three-dimensional finite element computation of thermoelastic damping using Zener's approximation

We consider three dimensional finite element computations of thermoelastic damping ratios of arbitrary bodies using Zener's approach. In our small-damping formulation, unlike existing fully coupled formulations, the calculation is split into three smaller parts. Of these, the first sub-calculation involves routine undamped modal analysis using ANSYS. The second sub-calculation takes the mode shape, and solves on the same mesh a periodic heat conduction problem. Finally, the damping coefficient is a volume integral, evaluated elementwise. In the only other decoupled three dimensional computation of thermoelastic damping reported in the literature, the heat conduction problem is solved much less efficiently, using a modal expansion. We provide numerical examples using some beam-like geometries, for which Zener's and similar formulas are valid. Among these we examine tapered beams, including the limiting case of a sharp tip. The latter's higher-mode damping ratios dramatically exceed those of a comparable uniform beam.

Variable Sparsity Kernel Learning

This paper(1) presents novel algorithms and applications for a particular class of mixed-norm regularization based Multiple Kernel Learning (MKL) formulations. The formulations assume that the given kernels are grouped and employ l(1) norm regularization for promoting sparsity within RKHS norms of each group and l(s), s >= 2 norm regularization for promoting non-sparse combinations across groups. Various sparsity levels in combining the kernels can be achieved by varying the grouping of kernels-hence we name the formulations as Variable Sparsity Kernel Learning (VSKL) formulations. While previous attempts have a non-convex formulation, here we present a convex formulation which admits efficient Mirror-Descent (MD) based solving techniques. The proposed MD based algorithm optimizes over product of simplices and has a computational complexity of O (m(2)n(tot) log n(max)/epsilon(2)) where m is no. training data points, n(max), n(tot) are the maximum no. kernels in any group, total no. kernels respectively and epsilon is the error in approximating the objective. A detailed proof of convergence of the algorithm is also presented. Experimental results show that the VSKL formulations are well-suited for multi-modal learning tasks like object categorization. Results also show that the MD based algorithm outperforms state-of-the-art MKL solvers in terms of computational efficiency.

Novel geodesic splitting on paraboloid of revolution with applications to ray-theoretic analysis

Computer simulations have shown a novel geodesic splitting on the paraboloid of revolution leading to a multiplicity of surface ray paths. Such a phenomenon would have wide ramifications for wave propagation problems in general, besides applications in target-detection problems and the computational requirements of ray-theoretic formulations such as the UTD, in computing the antenna characteristics in the high-frequency domain.

The principle of microscopic reversibility in organic chemistry - a critique

The principle of microscopic reversibility is one of the few generalising principles used in organic chemistry which have their roots in the fundamental laws of thermodynamics. It has, therefore, been highly popular. However, although the principle has some important uses, its general application is not without pitfalls. The principle is easy to misunderstand and to misapply: indeed, some of its formulations are semantically dubious. The principle is most dangerous when used as a charm, for it is more subtle than some of its formulations suggest. But above all, the principle may not be used for deducing or disproving the mechanism of a reaction, except when the mechanism in the reverse direction is known independently. For, such use is, perhaps, the deadliest misapplication.

Synthesis and characterization of epoxy resins based on N,N'-aliphatic dicarboxyl bis(hydrazones)

A new class of epoxy resins having N-N bonds in their structure has been synthesized by reacting N,N'-aliphatic dicarboxyl bis(hydrazones) (the aldehyde/ketone derivatives of malonic, adipic, and sebacic dihydrazides) with epichlorohydrin. The reactivity of the[GRAPHICS] protons as a function of the substituent group and the number of methylene spacer groups present in the hydrazone has been examined. The resins obtained have been characterized by elemental and epoxy equivalent analyses and IR and NMR spectra. All these resins are found to have adequate viscosity and cure easily with amine curatives at elevated temperatures. Relevant properties for their use as binders in propellant formulations, such as thermal stability, heat of combustion, density, temperature dependence of viscosity, and mechanical strength of the composites, have been evaluated. (C) 1997 John Wiley & Sons, Inc.

Advantage of the ether linkage between the positive charge and the cholesteryl skeleton in cholesterol-based amphiphiles as vectors for gene delivery

Twelve novel cationic cholesterol derivatives with different linkage types between the cationic headgroup and the cholesteryl backbone have been developed. These have been tested for their efficacies as gene transfer agents as mixtures with dioleoyl phosphatidylethanolamine (DOPE). A pronounced improvement in transfection efficiency was observed when the cationic center was linked to the steroid backbone using an ether type bond. Among these, cholest-5-en-3b-oxyethane-N, N,N-trimethylammonium bromide (2a) and cholest-5-en-3b-oxyethane-N, N-dimethyl-N-2-hydroxyethylammonium bromide (3d) showed transfection efficiencies considerably greater than commercially available reagents such as Lipofectin or Lipofectamine. To achieve transfection, 3d did not require DOPE. Increasing hydration at the headgroup level for both ester- and ether-linked amphiphiles resulted in progressive loss of transfection efficiency. Transfection efficiency was also greatly reduced when a 'disorder'-inducing chain like an oleyl (cis-9-octadecenyl) segment was added to these cholesteryl amphiphiles. Importantly, the transfection ability of 2a with DOPE in the presence of serum was significantly greater than for a commercially available reagent, Lipofectamine. This suggests that these novel cholesterol-based amphiphiles might prove promising in applications involving liposome-mediated gene transfection. This investigation demonstrates the importance of structural features at the molecular level for the design of cholesterol-based gene delivery reagents that would aid the development of newer, more efficient formulations based on this class of molecules.