Out Of Plane Displacement Research Articles

Crack-tip stress fields for dynamic fracture in functionally gradient materials

An asymptotic expansion of the stress field around a crack propagating at constant velocity in a Functionally Gradient Material (FGM) is developed. All the three modes of crack propagation are analyzed for FGMs having two different types of property variations in the direction of crack propagation. The assumed property variations are (1) exponential variation of shear modulus and mass density and (2) linear variation of the shear modulus with constant mass density. The Poisson's ratio is assumed to be constant throughout the analysis. The analysis reveals that the crack-tip stress fields retains the inverse square root singularity and only the higher order terms in the expansion are influenced by the material nonhomogeneity. Expression for stresses and strains in the form of a series, in powers of the radial distance from the crack tip, is obtained for the tearing mode of fracture. For the opening and shear modes of fracture, an expression for the first stress invariant under plane stress conditions is obtained in a series form in which the coefficient of the first term is proportional to the dynamic stress intensity factor. Contours of constant out of plane displacement, which is of interest in experimental techniques such as the coherent gradient sensing, are also given for different levels of nonhomogeneity. The stress fields are developed for large scale property variation where transient effects can be neglected.

A new approach to triaxial residual stress evaluation by the hole drilling method

AbstractA new analysis technique is introduced to resolve the triaxial residual stress profiles from measurements using the conventional strain gauges for the hole drilling or ring core method extended with a displacement transducer to measure the out of plane displacement. The new technique uses an inverse formulation with wavelets.

Predictions of Static Displacements in 1-3 Piezocomposites

Piezocomposites have demonstrated higher sensitivity and lower mechanical losses than single phase piezoelectric materials. As with any composite material, the properties and behavior of piezocomposites are highly dependent on the properties of the constituent materials and the interface between them. In this paper, the micromechanical behavior of 1-3 piezocomposites is investigated. An analytical model is developed for predicting the static displacement behavior of a single piezoelectric rod embedded in a matrix. In the model, the ceramic rod is treated as transversely isotropic since it has different piezoelectric coefficients in the longitudinal and transverse directions. It is proposed that presence of a thin interlayer or polymer coating around the ceramic rods can influence the longitudinal displacement of the rods and change the overall sensitivity. A composite cylinder model is adopted to incorporate the presence of an interlayer with varying properties. Theoretical predictions indicate that the introduction of a compliant interlayer greatly increases the outof-plane displacement of the rod and the sensitivity of the composite.

Analysis of plates and shells with a simplified three node triangular element

We present a 3 node triangular shell element with only three translational degrees of freedom per node, in which the out of plane displacement is the only d.o.f. considered for bending. The bending stiffness matrix of the element is derived by assuming constant curvature normal to the boundary with adjacent elements. The method is illustrated for a plate element and then for a triangular shell element. Results are presented for a variety of linear and non-linear problems to illustrate its accuracy compared with three other well-known triangular shell elements we have also implemented.

Kinetics and thermodynamics of oxygen and carbon monoxide binding to the T-state hemoglobin of Urechis caupo

The tetrameric hemoglobin from Urechis caupo is nearly ideal for studying ligation to the T-state. Our previous EXAFS study had shown that the Fe is displaced 0.35 A from the mean plane of the porphyrin in the HbCO derivative. We have carried out detailed kinetic studies of oxygen and CO ligation as a function of temperature in order to characterize both the kinetics and thermodynamics of ligation in this hemoglobin. The entropy change associated with ligation essentially corresponds to simple immobilization of the ligand and is virtually the same as that we have determined for leghemoglobin, an extreme R-state-type hemoglobin. The low ligand affinities thus derive from small enthalpies of ligation, which can be correlated with the large out of plane displacement of the Fe. Only oxygen pulse measurements revealed kinetic evidence for cooperative oxygen binding, but a direct measurement of oxygen binding gave a Hill number of 1.3. An allosteric analysis gave L = 2.6 and c = 0.048 (oxygen) and c = 0.77 (CO). The higher affinity state in this weakly cooperative hemoglobin is denoted T*, and it is for this state that thermodynamic quantities have been determined. The small differences between T and T* in CO binding were nevertheless sufficient to allow us to measure by flash photolysis the rate of the T*----T conformational change in terms of an allosteric model. The half-time for this transition was calculated to be 8-14 ms at 20 degrees C.

Probing protein structure and dynamics with resonance Raman spectroscopy: cytochrome c peroxidase and hemoglobin

Because vibrational frequencies are sensitive to structure, RR spectroscopy can provide structural information about kinetic steps in protein transformations when carried out in a time-resolved mode. UVRR spectroscopy has shown that the aromatic groups of the HbCO photoproduct respond with a delay of 20 microseconds and has provided direct structural evidence that the 20-microseconds kinetic step is the R-T quaternary re-arrangement of the subunits. RR bands of the porphyrin ring show that the core relaxes via a 0.1-microsecond protein motion, which probably allows the Fe atom to attain its full out-of plane displacement. The Fe-His stretching frequency has an elevated value immediately after CO photolysis, in part, perhaps, because of the protein constraint on the Fe displacement. It relaxes on both the 0.1- and 1-microsecond time scales to its value in R-state Hb and then decreases further to its T-state value. These changes may be connected with reorientation of the proximal His side chain. At very early times after a photolysis pulse, heating effects may be an important aspect of the protein dynamics, but further experiments are needed to understand the RR response.

ChemInform Abstract: THE INFRARED SPECTRA AND STRUCTURE OF ACETAMIDE AND ACRYLAMIDE

Abstract The far-IR vapour phase spectra of acetamide and acrylamide are reported and several transitions in the amido “inversion” vibration are identified. The potential energy curves governing the vibration are deduced from the experimental data and are found to have a single broad minimum for both molecules, implying that the amido hydrogens are copianar with the N-CO atoms, but that the resistance to their out of plane displacement is small. The band contours found in the mid-IR spectrum of acrylamide suggest that the cis orientation of the two double bonds about the C-C single bond is favoured over the trans orientation; indeed no evidence of the latter has been found.

The infrared spectra and structure of acetamide and acrylamide

The far-IR vapour phase spectra of acetamide and acrylamide are reported and several transitions in the amido “inversion” vibration are identified. The potential energy curves governing the vibration are deduced from the experimental data and are found to have a single broad minimum for both molecules, implying that the amido hydrogens are copianar with the N-CO atoms, but that the resistance to their out of plane displacement is small. The band contours found in the mid-IR spectrum of acrylamide suggest that the cis orientation of the two double bonds about the C-C single bond is favoured over the trans orientation; indeed no evidence of the latter has been found.

Electron paramagnetic resonance study of carp methemoglobin.

The g anisotropy of the EPR spectra of carp azidomethemoglobin is found to be pH-dependent, whereas, the spectra of human azidomethemoglobin are not. The two hemoglobins have the same g values at alkaline pH values. Crystal field analysis yielded values of 2.25 and 3.31, respectively, for the rhombic distortion, V/lambda, and the tetragonal distortion, delta/lambda. The spin orbit coupling constant is lambda. At pH 4.0 the values of V/lambda and delta/lambda for carp azidomethemoglobin became 1.95 and 4.76, respectively, whereas those for the human hemoglobin are virtually unchanged. The results are interpreted to mean an increase of out-ofplane displacement of the iron atom and stabilization of the T form of carp azidomethemoglobin by high proton concentration. At pH 6.0 and lower, the EPR spectra of carp azidomethemoglobin showed the presence of about 1.5% of high spin species, the amount is not affected by excess of either inositol hexaphosphate or sodium azide. The EPR spectra of aquo- and fluoroderivatives of carp methemoglobin were not affected by pH changes.

Some Two‐Field Variational Principles for Nonlinear Deformation Analysis of Shells

AbstractSome two‐field variational principles for nonlinear deflection analysis are formulated. Based on a specific mixed variational principle, a rectangular finite element model has been developed. The variables employed are the out of plane displacement and a stress function. The former satisfies out of plane compatibility requirements of the element, while the latter ensures the equilibrium of the in‐plane stresses. The efficiency of this method is illustrated on two examples.