Cellular Plates Research Articles

A simplified analysis of circular cellular plates

This paper presents a general analytical method for circular cellular plates with arbitrarily positioned large voids, in which the bending and the transverse shear deformations along with the frame deformation are considered. The frame deformation is defined as the flexural deformation of the frame, composed of the top and bottom platelets and of partitions in the cellular plate. The discontinuous variation of the bending and transverse shear stiffnesses due to the voids is expressed continuously by the use of a specific function, defined to exist continuously in a prescribed region. The bending stiffness is given by the actual bending stiffness at each point. The transverse shear stiffness per each void is given by an equivalent transverse shear stiffness, which is calculated from the stiffness of a frame and partitions like shear wall surrounding each void, and depends on the shape of each void. The governing equations are formulated by translating a theory for rectangular cellular plates into circular cellular plates. Static and dynamic solutions are obtained by the Galerkin method. The approximate solution for dynamic plates is proposed. The numerical results obtained from the proposed theory for simply-supported and clamped circular cellular plates show good agreement with results obtained from the finite element method. The theory proposed here includes the Mindlin and Reissner theories.

A simplified analysis of rectangular cellular plates

This paper presents a general analytical method for rectangular cellular plates with arbitrarily-positioned large voids, in which the bending and the transverse shear deformations along with the frame deformation are considered. The frame deformation is defined as the flexural deformation of frame composed of the top and bottom platelets and of partitions in the cellular plate. The discontinuous variation of the bending and transverse shear stiffnesses due to the voids is expressed continuously by the use of a specific function, defined to exist continuously in a prescribed region. The bending stiffness is given by the actual bending stiffness at each point. The transverse shear stiffness per void is given by an equivalent transverse shear stiffness, which is calculated from the stiffness of a frame and partitions, like shear walls surrounding each void, and depends on the shape of each void. The governing equations are formulated by means of Hamilton's principle. Neglecting the effect of voids, the proposed governing equations reduce to the Mindlin theory. Static and dynamic solutions are obtained by the Galerkin method. The approximate solution for dynamic plates is proposed. The numerical results obtained from the proposed theory for simply-supported and clamped cellular plates show good agreement with results obtained from the finite element method. The theory proposed here includes the Mindlin and Reissner theories, and Takabatake's theory [Takabatake, H. (1991). Static analyses of elastic plates with voids. Int. J. Solids Structures28, 179–196] based on the Kirchhoff-Love hypothesis.

Minimum cost design of laterally loaded welded rectangular cellular plates

Material and fabrication costs are included in the cost function. The fabrication cost is calculated by three formulae relating to the preparation, welding and additional costs. The design constraints are related to bending stresses, the local buckling of ribs due to bending and shear and to the limitation of the plate thicknesses. The local buckling of the compressed face plate elements is considered by an effective width calculation. In the numerical examples, the variables are the plate dimensions and the numbers of ribs in two directions. The optimization is carried out for steel Fe 360 and Fe 510 and for various values of the fabrication cost factor. The computations are performed by using the backtrack discrete combinatorial method, Rosenbrock's Hillclimb method and the FSQP method developed by Zhou and Tits (1992), and the results are compared with each other.

The role of cyclic AMP in the control of elasmobranch ocular tapetum lucidum pigment granule migration

We have studied the effect of adding cAMP to dogfish ocular tapetum lucidum tissue maintained in vitro. Normally, under conditions of dark-adaptation, tapetal pigment granules attain an aggregated state, exposing highly reflective cellular plates (which contain crystalline guanine) to incident illumination. The reflected light from these plates is believed to function in the visual process by increasing photoreceptor photon capture under low light conditions. Upon illumination, the pigment granules attain a dispersed state, occluding the reflective surfaces. We found that this occlusion may be mimicked in dark-adapted tissue in vitro by adding cAMP, or by the use of agents believed to increase intracellular cAMP concentrations such as forskolin and IBMX. Additionally, aggregation of pigment in light-adapted tissue transferred to darkness is inhibited by such agents. The results of this and previously published studies indicate that the processes of pigment aggregation and dispersal in vivo are under the control of the neural retina through the probable mediation of either hormonal or direct neural communication.

Accurate force evaluation with a simple, bi-linear, plate bending element

A great deal of attention has been given to the development of simple C ° continuous plate and shell elements based on the shear flexible theories for application to thick plates, sandwich or cellular plates and transversely isotropic or laminated plates. After considerable experimentation using unconventional approaches such as reduced integration, selective integration, mixed methods using discontinuous force fields, etc., it has been possible to develop simple displacement-type elements which can be reliably used. The stress recovery at nodes from such elements is often unreliable as the nodes are usually the points where strains or stresses are least accurate in the element domain. Further, nodal values can reflect severe oscillations at some difficult corner or edge conditions. In this paper, we focus attention on the optimal stress recovery from such an element. This is done after an interpretation of the displacement method as a procedure that obtains strains over the finite-element domain in a least-squares accurate fashion. If a shear flexible element is field-consistent, there are optimal locations at which bending moments and shear forces are accurate in a least-squares sense. These points are identified for the present element and used to study stresses in typical plate problems. Another difficulty faced is the rapid variation of twisting moments at free edges and corners of shear flexible plates and its influence on the shear forces at that edge. A related source of difficulty is the distinction made in Kirchhoff theory between shear forces and the effective shear reactions of that theory. The present study is seen to give accurate enough shear force and twisting moment predictions to allow one to draw the severe conclusion that the use of the Kirchhoff shear reaction at edges in classical plate theory is an ambiguous and unnecessary one and can be avoided. The findings confirm a recent suggestion that it may be more appropriate to have three (as introduced originally by Poisson) instead of the two boundary conditions (as modified by Kirchhoff) usually applied on the edge of a thin plate, especially if that edge is unsupported.

The cellular reaction in dilute copper-titanium alloys

A review is made of the various mechanistic models for the initiation of the cellular reaction. Observations of the production of theβ phase in dilute copper-titanium alloys are reported, and it is noted that the Widmanstatten product and small, recently nucleated intermediate cellular plates adhere strictly not only to the (111)α//(010)β [ 110]α //[001]β orientation relationship, but also to the favorable (111)α//(010)β habit plane. The plates in cellular colonies developed at lower transformation temperatures (and thus higher supercoolings) show appreciable deviations from the latter interface plane, though the orientation relationship is still obeyed. Three different initiation mechanisms for cellular precipitate are observed. The ‘pucker’ and the ‘conventional’ routes are found to operate, and in addition a mechanism relying on the preexistence of Widmanstatten plates has been identified. The intermediate level of crystallographic specificity displayed by the coppertitanium system is suggested, therefore, to give rise to a high.probability of cellular precipitation. It is shown that the reaction can proceed under the action of very low driving forces.

Some Microstructural Observations Of Transformations In A Copper‐Titanium Alloy

SUMMARYThis paper describes the microstructures observed when a dilute copper‐titanium alloy (Cu‐4wt%Ti) is isothermally transformed. The β phase which forms on transformation is observed in both Widmanstätten and cellular morphologies. It is shown, using light and electron microscopy, that some Widmanstätten plates become the nuclei of cellular plates and that there is often an association between cellular plates of the β phase and more than one twin variant of the matrix α. Dislocation arrays on the α/β interfaces have been resolved and a continuity of this structure between the migrating transformation interface and dislocation arrays on the habit plane has been found.