Principal Axis Method Research Articles

Stress analysis of functionally gradient beam using effective principal axes

The mechanical model is established for the functionally gradient material (FGM) beam with rectangular cross section. A new method of effective principal axes is put forth, based on which the normal stress formula is derived for the FGM beam. The method is verified to be correct by the retrogression of it to the centroidal principal axes method of the traditional beam made of homogeneous elastic material. For several different loading cases, the␣effects of the non-homogeneity parameter on the distribution of the normal stress and on the position of the neutral axis are discussed. It is indicated that, with the increase of the absolute value of the non-homogeneity parameter, the normal stress at the more rigid region in the cross section increases, the normal stress at the less rigid region decreases, and the neutral axis moves toward the more rigid region.

A novel approach to examining double-shearing type models for granular materials

A novel method, designated as the Rotation of Principal Axes Method (RPAM), capable of examining the double-shearing type kinematic models for granular materials is presented herein. A planar velocity field, which is proposed to represent a continuous rotation of principal strain rate axes, is applied to each model to analyse the rotation of principal stress axes. The proposed approach was proven to show main features of the double-shearing model, the double-sliding free-rotating model, and the revised double-shearing model, in a simple way interesting to geo-researchers. Furthermore, the RPAM was efficient in investigating the choice of a Cosserat rotation rate in kinematic theories and determining a key model parameter in the revised double-shearing model.

Vibrational symmetry classification and torsional tunneling splitting patterns in G6(EM), G12, and G36(EM) molecules

It is shown that the torsional splitting patterns in methanol-like molecules, with the excitation of small amplitude vibrational modes in the methyl group, are determined by mechanisms that can be formulated in an almost identical fashion to that for ethane-like molecules. This is achieved by treating ethane-like molecules by the internal axis method (IAM) and methanol-like molecules by the principal axis method (PAM) or rho-axis method (RAM). Using the extended molecular groups G6(EM) or C6v(M) for methanol and G36(EM) for ethane, vibrations perpendicular to the internal rotation axis are conveniently described by modes of higher degeneracy (E for methanol and Gs for ethane) in the absence of coupling of top and frame. Head–tail coupling operators, except the cos-type barrier terms, lower the degeneracy, causing vibrational splittings. Coupled vibrational pairs with torsional splitting patterns that we call ‘regular’ (pure A1, A2 pairs for methanol and pure E1d, E2d pairs for ethane) or ‘inverted’ (pure B1, B2 pairs for methanol and pure E1s, E2s pairs for ethane) can be formed as limit cases. Actual splitting patterns occur between the above limits, and are basically determined by torsional Coriolis coupling, which can tune more or less to resonance pairs of uncoupled basis levels linked by specific head-tail coupling operators. The inversion of torsional splitting patterns, observed in perpendicular vibrational modes of the methyl group of methanol, can be predicted by these theoretical considerations. Similar considerations apply to molecules of G12 symmetry.

The analysis of correlative error in principal axis method for five-axis machining of sculptured surfaces

Correlative error is a kind of error between the cutter locations. This text presents a detailed analysis about correlative error in the principal axis method (PAM) that is a strategy of tool positioning for five-axis machining. It points out all the strategies based on linear projection cannot avoid this interference and cannot be disregarded especially in the strategies with large stepover. Accurate calculating is made individually on linear and curve feed and formulae are developed. The author also gave the available application range of PAM and the algorithm for estimating correlative error.

A method of optimum transformation of 3D objects used as a measure of shape dissimilarity

In this work, we present a method which transforms an object into another. The computation of this transformation is used as a measure of shape-of-object dissimilarity. The considered objects are composed of voxels. Thus, the shape difference of two objects can be ascertained by counting how many voxels we have to move and how far to change one object into another. This work is based on the method presented in [Pattern Recognition 29 (1996) 1117], and our contributions to such a work are a method of optimum transformation of objects and a proposed method of principal axes, which is used to orientate objects. The proposed method is applied to global data. Finally, we present some results using objects of the real world.

Basis free relations for the conjugate stresses of the strains based on the right stretch tensor

In this paper, general relations between two different stress tensors T f and T g, respectively conjugate to strain measure tensors f( U) and g( U) are found. The strain class f( U) is based on the right stretch tensor U which includes the Seth–Hill strain tensors. The method is based on the definition of energy conjugacy and Hill’s principal axis method. The relations are derived for the cases of distinct as well as coalescent principal stretches. As a special case, conjugate stresses of the Seth–Hill strain measures are then more investigated in their general form. The relations are first obtained in the principal axes of the tensor U. Then they are used to obtain basis free tensorial equations between different conjugate stresses. These basis free equations between two conjugate stresses are obtained through the comparison of the relations between their components in the principal axes, with a possible tensor expansion relation between the stresses with unknown coefficients, the unknown coefficients to be obtained. In this regard, some relations are also obtained for T (0) which is the stress conjugate to the logarithmic strain tensor ln U.

Correlation between ciliary beat frequency and metachronal wave disorder using image analysis method.

Ciliary beating and metachronal waves are fundamental to effective mucociliary transport. The ciliary beat frequencies (CBFs) and metachronal wave directions of multiple cilia beating in culture media were measured simultaneously using digital microscopic images. The degree of synchronisation between ciliary beats was determined by the correlation between ciliary signals at two different locations. The wave propagation directions of cilia were determined from a two-dimensional correlation map by a principal axis method. The standard deviation of measured wave directions in a region of interest was defined as a measure of metachronal wave disorder (MWD). Considerable variation was found in the beat frequencies and metachronal wave directions of cilia beating on epithelium. The pooled mean of MWDs was 23.4 +/- 8.8 degrees, and the pooled mean of CBFs was 10.1 +/- 1.9 Hz on 120 cells from five healthy subjects. The means of the MWD and the CBF from subjects were highly correlated (correlation = -0.83). The higher the CBF, the lower the level of the MWD.

A principal axes method for comparing contingency tables: MFACT

A new methodology is introduced for comparing the structures of several contingency tables. The latter, built up from different samples or populations, present the same rows and different columns (or vice versa). This methodology combines some aspects of principal axes methods (global maximum dispersion axes), canonical correlation techniques (canonical dispersion axes) and Procrustes analysis (superimposed representations) but takes into account the particularities of contingency tables in order to extend correspondence analysis to multiple contingency tables. Two main problems arise: the differences between the margins of the common dimension and the need for balancing the influence of the different tables in global processing. A study of the four structures induced on Spanish regions by mortality causes (by gender) and by age distribution (by gender), in conjunction, will illustrate the methodology.

Systemic lupus erythematosus in three ethnic groups. X. Measuring cognitive impairment with the cognitive symptoms inventory.

To determine the factor structure of the Cognitive Symptoms Inventory (CSI) in patients with systemic lupus erythematosus (SLE) participating in a multiethnic longitudinal study of outcome, the Lupus in Minority populations, Nature versus nurture (LUMINA) study. LUMINA patients of Hispanic (n = 48), African American (n = 64), and Caucasian (n = 44) ethnicity who had a study visit (enrollment or followup) between January 1 and September 30, 2000 were included. Patients completed the CSI, a 21-item self-report measure of cognitive function. Sociodemographic, clinical, immunologic, psychosocial, and behavioral variables were ascertained per protocol and as previously described. Data were analyzed with SPSS. The factor structure of the CSI was determined using the principal axis method with oblique rotation as decided by Gorsuch. All factors having an Eigenvalue greater than 1 were considered. A 4-factor solution was derived that accounted for 42.6% of the common variance. The correlations between patient factor scale scores and variables from the demographic, clinical, psychosocial, and behavioral domains were then examined. The four factors and their respective variance are, Attention/Concentration (28.8%), Pattern Recognition/Activity Management (5.7%), Intermediate Memory (4.7%), and Initiation of Executive Functions (3.4%); each factor correlated with the total CSI score. Overall, patients' factor scale scores were positively and significantly correlated with other measures of cognitive dysfunction such as the Systemic Lupus Activity Measure (neuromotor domain) or the Systemic Lupus International Collaborating Clinics Damage Index (neurocognitive impairment), as well as with measures of fatigue, maladaptive coping skills, poor mental functioning, poor social support, and helplessness. They were, however, not correlated with sociodemographic or clinical variables. In addition to demonstrating that the CSI can be used to measure cognitive impairment in patients with SLE in the research setting, we have determined a 4-factor solution for the CSI that appears to have adequate metric properties. At present, the CSI may best be used as a screen for difficulties in daily activities involving intermediate memory, concentration, attention, and executive function. Nevertheless, further work with the CSI items and factor scales is necessary to establish internal and test-retest reliability of the factor scales; and provide additional evidence of the convergent and predictive validity of these scales in larger samples of patients from each ethnic subgroup.

Análise Fatorial de Uma Medida de Estratégias de Enfrentamento

O objetivo do estudo foi investigar a estrutura fatorial da Escala Modos de Enfrentamento de Problemas - EMEP, na versão adaptada para a população brasileira por Gimenes e Queiroz (1997), para mensurar estratégias de enfrentamento em relação a estressores específicos. A amostra foi composta por 409 adultos de ambos os sexos, onde 252 consideraram como estressor um problema atual que estivesse ocasionando estresse, enquanto 157 foram pessoas portadoras de enfermidades crônicas, que responderam à escala com base no problema de saúde que estavam apresentando. Foram extraídos quatro fatores pelo método dos eixos principais, rotação ortogonal: estratégias de enfrentamento focalizadas no problema, estratégias de enfrentamento focalizadas na emoção, práticas religiosas/pensamento fantasioso e busca de suporte social. A análise dos achados nas duas sub-amostras, diferenciadas quanto aos estressores dominantes, sugere possibilidades positivas de aplicação em contextos de pesquisa e de intervenção profissional, em especial a atuação clínica voltada para manejo do estresse junto a diferentes clientelas.

Comparison of 5-Axis and 3-Axis Finish Machining of Hydroforming Die Inserts

The recent growth in hydroforming technology has sparked interest in alternative methods to the current conventional die manufacturing techniques. Hydroforming dies typically have shallow forming channels and open, low curvature surfaces, making them ideally suited for 5-axis machining. To fully appreciate the benefits and to properly demonstrate the capabilities of 5-axis machining for hydroforming dies, a comparison of 5-axis and 3-axis finish machining was done. Two hydroforming die insert sets were machined on a 5-axis machine with a tilt/rotary table. The tool paths for 5-axis machining were generated using custom software based on a modified form of a tool positioning strategy called the principal axis method. The quality of generated 3-axis toolpaths was verified against the machining times of a third set of die inserts, similar to those machined in 5-axis, by an independent industrial mould and die manufacturer using a 3-axis highspeed machine. A comparison of the generated 3-axis paths versus the 5-axis paths for one of the die inserts was made using total finish machining tool path lengths to eliminate differences in machines. The results show that the generated 3-axis tool paths are longer than the 5-axis paths by at least 247%. The paper discusses the different tool-path generation methods along with the geometry of cusp formation and the effect of tool selection. Methods to improve the 3-axis results are also presented.

Effect of inapplicable items in the factor structure of the Spanish version of the Ways of Coping Questionnaire.

The aim of this work was to examine how the presence of inapplicable items might change the factor structure of the 1984 Ways of Coping Questionnaire by Lazarus and Folkman. The Spanish version of the Ways of Coping Questionnaire was administered to 156 subjects with university degrees. The 95 women and 61 men whose ages were from 18 and 45 years (M = 27.8, SD = 12.1) were of middle socioeconomic status. All were residents of Buenos Aires. To study whether relevant items modify the factor structure of the Ways of Coping Questionnaire, two factor analyses were carried out, one with items rated as not relevant (Item Mean) and the other with the same items rated as not chosen. In both factor analyses, principal axes method and oblimin rotation were performed, and five factors were considered. Congruence indexes were performed. Analysis showed that not choosing an item because it does not coincide with one's behavior or ideas is not the same as not selecting that item because it does not apply to the current threatening situation. Lack of discrimination between situations when analyzing data leads to a distorted interpretation of the way in which the subject actually behaves or copes with the situation.

Conjugate stresses of the Seth–Hill strain tensors

In this paper, conjugate stresses of the Seth–Hill strain measures are treated by means of the definition of energy conjugacy and Hill’s principal axis method. This approach results in relations between components of two different conjugate stress tensors. The results are valid for distinct as well as coalescent principal stretches. Illustrative examples are solved to demonstrate the simplicity and usefulness of the derived relations between conjugate stress tensors.

Comparison between multi-point and other 5-axis tool positioning strategies

A method of generating sculptured surfaces at multiple points of contact between the tool and the workpiece was developed and proven viable by the current authors in previous work. They denoted this finish machining method, “Multi Point Machining”, or simply MPM. This paper compares MPM with two other 5-axis tool positioning strategies; namely: the inclined tool, and the principal axis method. It is also compared with 3-axis ball nose machining. Comparisons are conducted using computer simulations and experimental cutting tests. Results obtained show that MPM produced scallop heights that are much smaller than those produced by the other tool positioning strategies.

The Millimeter‐ and Submillimeter‐wave Spectrum of Methyl Formate (HCOOCH3)

Methyl formate (HCOOCH3), a threefold internal rotor, is a well-known interstellar molecule located in hot cores of giant molecular clouds. Over a decade ago, we published separate analyses of the rotational-torsional spectra of methyl formate in its A and E ground torsional substates. The analysis of the A substate was undertaken with a standard asymmetric top Hamiltonian, while that of the E substate was undertaken with a principal axis method (PAM), which was less than entirely satisfactory. In the interim, we have measured many new lines of the rotational-torsional spectrum of both the ground A and E torsional substates of this species through the rotational quantum number J = 50 using two spectrometers: our standard klystron-based system and a new fast scan spectrometer (FASSST). The newly measured lines have been combined with previous data to form a data set consisting of over 2000 lines that has been fitted to the accuracy of our experiments using a modification of the internal axis method (IAM) we have previously applied to methanol. The spectral constants obtained from the fit have allowed us to predict the frequencies of many additional lines up to 700 GHz in frequency and up to J = 50 in rotational quantum number.

Finite deformation plasticity in principal axes: from a manifold to the euclidean setting

This contribution presents a link between early developments in finite deformation plasticity, where the notion of a covariant formulation is introduced and employed, and more recent developments, where rediscovery of a fundamental work of Hill on the method of principal axes led to a very efficient implementation scheme. More precisely, we demonstrate how to develop a covariant theory of finite deformation plasticity in an invariant form, by making use of the elastic principal stretches. We also show how to implement principal axis formulation in the framework of manifold, to carry out all the necessary manipulations by exploiting the Lie derivative formalism and eventually to simplify the final result to the Euclidean setting. Much of our work on numerical implementation reflects the fruitful cross-fertilization of ideas with those from theoretical formulation. In particular, we show how the operator split method, which is typically used to simplify the plastic flow computation, can also be used to reduce the computational cost related to the special finite element interpolation schemes based on incompatible modes. The latter proves to be an indispensable ingredient for accommodating the near-incompressibility constraint arising in the finite deformation deviatoric plasticity. An important advantage of the proposed formulation as opposed to alternative remedies (e.g. B-bar method) is that the basic structure of the governing equations need not be modified.

Prediction of Stress Distribution in a Two-Dimensional Bunker Using the Fixed Principal Axes Method

The fixed principal axes method proposed by Wittmer et al. (Nature 1996, 392, 337) for the analysis of the stress distribution in a sandpile has been used to predict the stress distribution in a two-dimensional bunker. The results are compared with those predicted by Janssen's method and are found to be considerably greater than his results for the active case, but not quite as large as his prediction for the passive case.

Robust rotation angle estimator

The conventional method of estimating the rotation angle of a pattern using the principal axes is not suitable for circular symmetric patterns since their eigenvalues are similar in both directions. In the paper, a robust method of estimating a rotation angle using the phase information of Zernike moments is presented. The experimental results show that the proposed method estimates the rotation angle of the circular symmetric patterns more accurately than the principal axes method, even in the presence of noise.

Microwave spectrum of 3-methyl-2H-azirine

The microwave spectrum of 3-methyl-2H-azirine produced by pyrolyzing N-chloro-2-methylaziridine was observed. This new, unstable molecule was identified based on a comparison of observed molecular constants and those determined by an ab initio MO calculation. The rotational constants are A = 22338.04(4), B = 6618.622(9), and C = 5464.442(7) MHz. The dipole moments obtained are μ a = 1.90(5) and μ b = 1.86(5) D from the analysis of the Stark effect. The potential barrier to internal rotation of the methyl group was determined by the principal axis method (PAM) to be V 3 = 1315(10) cal mol −1.

Tool path planning for five-axis machining using the principal axis method

A study of the effect of feed direction on five-axis tool paths generated using local surface properties for tool orientation and positioning is presented in this paper. The principal axis method for five-axis machining defines the placement of the cutting tool at a single point on the workpiece surface and assumes that a preferred feed direction will be maintained. This preferred direction may not represent a practical choice for tool path planning. In this work, numerical simulations are used to evaluate tool paths with different feed directions. Numerical simulations are then verified experimentally by machining two example surfaces. The results show that both gouging and the effective cutter profile will dictate the optimal choice of feed direction.