Finite Prism Research Articles

Three-dimensional hierarchical finite element free vibration analysis of annular sector plates

An annular sector solid hierarchical finite element is presented and applied to three-dimensional free vibration analysis of annular sector plates. The element's displacements are expressed in terms of a fixed number of linear polynomial shape functions plus a variable number of shape functions which are forms of the shifted Legendre orthogonal polynomial. The linear polynomial shape functions are used to describe the element's nodal displacements and the higher order shape functions are used to provide additional freedom to the edges, faces, and interior of the element. Results of frequency calculations are found for annular sector plates with two straight edges simply supported like a diaphragm condition and comparisons are made with those obtained by the finite prism method. The manner of convergence of the solution as a function of the numbers of hierarchical modes is also investigated. Furthermore, contributions to original three-dimensional frequencies are made for annular sector plates with other boundary conditions along the two straight edges.

Finite strip method: 30 years A bibliography (1968‐1998)

This bibliography contains references to papers, conference proceedings, theses and books dealing with finite strip, finite prism and finite layer analysis of structures, materially and/or geometrically linear or non‐linear.

Stress Analysis of Cylindrical Webbed Spur Gears: Parametric Study

In this paper, a numerical computer software based on the Finite Prism Method, is proposed in order to design external cylindrical spur gears with a web. It enables computing load sharing, pressure distribution, meshing stiffness and 3D tooth fillet stresses. The software is generally used during the detailed design for optimizing gear meshing. The software is also used to quantify the influences of web design parameters. The process is based on a statistical method: experimental design, that permits studying the influence of parameters. Thus, a simple formula was found in order to estimate the maximum principal stress in the tooth root. The results of the formula were compared with those found in the bibliography. The formula can be useful during the preliminary design for predimensioning webbed spur gears in design department.

Magnetization reversal in finite and infinite square prisms

We present first 3D micromagnetic calculations on finite as well as infinite square prisms. We have studied the magnetization reversal mechanisms taking place in these systems as a function of the prism width. We observe strong differences between reversal mechanisms in infinite prisms and nucleation/reversal processes in finite prisms. For infinite prisms buckling and curling are the modes that have been obtained in the whole width range studied. Substantial differences have been observed between magnetization reversal in finite prisms and inifinite prisms. While for small widths the magnetization reversal takes place following a buckling-like deformation strongly influenced by the extremities, for large widths, domain nucleation and wall propagation has been found to be the ad hoc reversal mechanism after a curling like nucleation. From stability arguments we have determined the critical domain (or activation volume) in low anisotropy systems. Both the switching fields and the activation volume obtained from simulations compare favorably with measurements on Ni electrodeposited nanowires.

鋼・硬質ウレタン複合部材の局部振動特性

When the composite member of I-section steel member and rigid urethane vibrates, the independent modes of the rigid urethane are generated at high-frequency region and the such modes are supposed to give the vibration reduction effect. In this paper, natural vibration analyses on local vibration of the composite members are carried out and the characteristics of the independent modes of rigid urethane are clarified. The discrete model which is the combination of finite strip method and finite prism method is applied and the parametric analyses of dimensions and material values of the rigid urethane are carried out. Based on these results, the boundary frequencies which generate the independent modes of the rigid urethane are obtained.

Vortex response to the ac field in anisotropic high- Tc superconductors

The ac response of anisotropic high- T c superconductors in the mixed states is theoretically analyzed. The physical picture proposed by Geshkenbein, Vinokur and Fehrenbacher together with the theory of thermally assisted flux flow is generalized to include the material anisotropy. The results show that the transition in the real part and the peak in the imaginary part of magnetic ac permeability are due to skin effect and, additionally, related to the sample dimensions. For an isotropic superconductor, the infinite slab geometry exhibits a maximum peak absorption, while a minimum dissipation peak is obtained in the case of a square rod. The peak frequency in the infinite slab is, however, the lowest as compared with other finite prisms. In the very anisotropic superconductors, the thin edges lower the dissipation peak and raise the peak frequency as well. Dependence of the irreversibility line in the mixed state on the geometric factor is therefore suggested.

Two‐dimensional inversion filters in magnetic prospecting: Application to the exploration for buried antiquities

The magnetic total field anomaly is considered as the convolution of two analytically determined functions. One of them is chosen such that it modifies the amplitude of the anomaly while the other controls the anomaly pattern. Using the anomaly of vertical‐sided finite prisms, the inverse of the shape function is computed in the Wiener mode. This is an optimum filter operator, in the least‐square sense, to be convolved with the data. The majority of the structures which are the targets of exploration at archaeological sites can be represented as assemblages of vertical‐sided prisms. This fact motivates the selection of the basic model. On that basis the filtering scheme results in anomalies centered at the epicenter of the disturbing bodies, delineates their lateral extent fairly well, and gives a measure of their magnetization. Applications of synthetic and actual data clarify the merits and disadvantages of the technique.

Vibration of thick annular sector plates using semi-analytical methods

This paper deals with the vibration of thick annular sector plates with simply supported straight edges. The finite strip method based on the Mindlin plate theory and the finite prism method based on the three-dimensional elastic theory, which are known as semi-analytical methods, are used. To demonstrate the accuracy of the semi-analytical methods, results are compared with those obtained by other analytical and numerical methods. Comparison of the results of the two methods is discussed in order to analyze the thick annular plates with different thickness ratios, sector angles and boundary conditions. It is seen that the results of the two methods show good agreement, while some discrepancies between them are shown in the cases of larger thickness ratios, of higher modes and of plates with free edges.

A hybrid model for prismatic solids

AbstractA finite prism approach for the approximate analysis of three‐dimensional solids is proposed. The approach is based on a semi‐algebraic assumed stress hybrid model, according to Pian's scheme. Prismatic solids with various end conditions can be analysed with a traditional matrix‐displacement procedure, thus enlarging the possibilities offered by analogous compatible models.

Analytical, numerical and experimental investigations of architectural sandwich panels

Architectural sandwich panels with thin-walled cold-formed steel facings and rigid foamed insulating core are becoming more and more popular as enclosures for system buildings. In this paper, the structural behavior, including flexural stresses/deflections, flexural wrinkling, axial stability, thermal stresses and vibration, is presented, summarizing more than a decade of research. Methods used are analytical (boundaryvalued approaches), numerical (finite-strip, finite-layer, finite prism approaches) and experimental (full-scale testings). Key equations are formulated, and results by different methods are compared.

A Relation between Semi-Inverse and Saint-Venant Solutions for Prisms

It is shown that in an infinite prism the linearization at a natural state of a family of Ericksen’s semi-inverse solutions is a combination of elementary St.-Venant solutions, namely, extension bending and torsion. Moreover, the span of these St. Venant solutions is precisely the linear manifold of solutions having locally uniformly bounded strain energy. This implies that any solution of a linearized problem in a finite prism continuable to a solution in the infinite prism in a manner that its energy on any portion of fixed length remains bounded, is an elementary St.-Venant solution.

Finite prism analysis of plates and shells

AbstractThe finite prism technique introduced by Zienkiewicz and Too4 is extended to include 12‐node prism elements and, more importantly, a novel offset beam element. The use of 12‐node prism elements enables parabolic strain distributions to be simulated, this being useful for structures which have strongly tapered cross‐sections. The offset beam element is used to simulate flexure and torsion of a beam whose centroid is offset from the main structure. The element is specified completely at the nodes of adjacent prism elements and so is not really an ‘element’ in the usual sense.The analysis is applied to thin and thick plates and to shells, with and without edge beams. It is shown to be more versatile than the finite strip method and it requires smaller computer resources than the finite element method. Experimental verification of the analysis is obtained by comparison with measurements for a double‐T bridge deck tested by Loo14.

Evanescent Intensity Of A Focused Gaussian Light Beam Undergoing Total Internal Reflection In A Prism

We calculate the evanescent electric field and intensity profile of a circular Gaussian light beam when it is focused by a lens, enters a spatially finite prism, and is totally internally reflected at a planar interface of the prism and a dielectric substance. The electric field and intensity at the interface depend on the indices of refraction of the prism, the 1 /e 2 width, wavelength, and polarization of the incident beam, the focal length and exit pupil of the focusing lens, the distance from lens to prism, the shape and size of the prism, and the beam's angle of incidence. Our calculations show the evanescent intensity profile to be well approximated by a Gaussian shape for many practical realizations of the lens and prism optical apparatus. The 1/e 2 width of the profile appears to depend primarily on the beam's 1 /e 2 width, the ratio of the focal length of the lens to this width, and the incidence angle. The polarization of the evanescent electric field is approximately perpendicular to the incident plane of the beam center for an incident beam polarized in this direction. It is within the incidence plane, but rotates with time and position along the inter­ face, for an incident beam polarized in the incidence plane of the beam center. The penetration depth (into the dielectric) does not have a strong dependence on position within the illuminated area. Experimental measurement of the intensity profile in one optical geometry agrees well with our theoretical predictions.

On the three dimensional analysis of thick laminated plates

Several finite element models and finite prism models based on the elasticity theory formulation are compared. The basis of comparison is the accuracy in predicting natural frequencies of simply supported plates, and the suitability to model delamination of composite laminates. The emphasis of this work is on the finite prism method. It was found that the classical approach of using beam functions as part of assumed displacement functions is no longer suitable when the finite prism models are used to analyze antisymmetric angle-ply composite laminates.

Free vibration of formed sandwich panel

In this paper, the free vibration of prefabricated architectural sandwich panels is studied. The core of the sandwich panel is approximated by finite prisms and the thin faces are modelled by finite strips. The finite prism-strip method is simple to program and saves considerable computing effort when compared with the finite element method. In this paper, only the dynamic characteristics of flat faced homogeneous sandwich panels are compared with results obtained by other methods, and also with the analytical solutions. Several examples are also presented for the free vibration of prefabricated architectural sandwich panels.

Thermal behavior of formed sandwich plate by finite-prism-strip method

In this paper, the thermal analysis for prefabricated architectural sandwich panels is carried out. The core of the sandwich panel is approximated by the finite prism, and the thin faces are handled by the finite strip. The finite-prism-strip method is simple to program and saves considerable computing effort compared with the finite element method. The results are compared with the Chong's approximate solution.

Space- and Angle-Dependent Steady-State Thermal-Neutron Spectra Inside Finite Prisms of Graphite

We report here our calculated results of steady-state space- and angle-dependent thermal-neutron spectra inside an infinite slab as well as inside finite prisms of graphite with transverse dimensions varying from 100 × 100 cm2 to 30 × 30 cm2 and different longitudinal dimensions (ranging from 100 to 180 cm). We find that in the forward direction, due to streaming, cold neutrons pile up with distance. Neutron spectra in backward directions are depleted in sub-Bragg neutrons. At all distances from the source plane, the proportion of cold neutrons in the energy spectrum in the forward direction increases with decrease in transverse dimensions.The question of the existence of asymptotic conditions in these assemblies has been discussed in detail. We show that in the forward direction a true discrete mode does not exist even in an infinite slab 150 cm thick. However, pseudo-asymptotic conditions should exist beyond 30 cm in a prism of transverse dimensions nearly 100 × 100 cm2. The critical transverse dimensions for the existence of a pseudo-asymptotic mode lie somewhere between 100 × 100 cm2 and 70 × 70 cm2, in conformity with the observed results of DeJuren and Swanson and theoretical predictions of Ahmed et al.

A finite prism element for stability analysis of bulb flat stiffeners

For the purpose of analysing the effect of the bulb on the torsional buckling stress of panels with bulb flat stiffeners, an element in the form of a triangular prism has been developed. The bulb was divided up into a mesh of such prisms, whilst the web was treated according to classical thin plate theory. The elastic and geometric stiffness matrices of a typical prism are presented in explicit form, and the procedure for enforcing compatibility between the bulb and web plate, in order to connect them together, is explained.

Comments on the relationship between magnetic anomalies, crustal spreading and continental drift

The desirability of accurate delineation of areas of active crustal spreading is the motive for presentation of arguments against unrestricted application of the crustal spreading hypothesis to analyses of all linear magnetic anomalies associated with mid-oceanic rises. It is suggested that no clear delineation will result if spreading rate changes are invoked to force a fit of local observation to hypothetical geomagnetic polarity changes; if major crustal tectonic histories are proposed by the absence rather than the presence of the classic magnetic anomaly patterns; if minor characteristics of magnetic anomalies and available local submarine geological data are ignored; and if for the period prior to 4 m.y. ago a geomagnetic polarity time scale which is either hypothetical or insufficiently well defined is utilized. A summary is made of relevant rock properties and igneous thermal and structural histories before examining a published magnetic traverse and other data from the mid-Atlantic ridge at 22.5° North. It is concluded that a series of flat finite prisms of alternating polarity, as required by the simple crustal spreading model, is inconsistent with the observations.