Boundary effects on the vibration statistics of a random plate

This paper considers the estimation of statistics of displacement of a vibrating rectangular plate with random wave scatterers. The influence of uncertainty is investigated using point impedance theory. Coherent boundary effects are seen, which decrease when the number of scatterers increases. The boundary effect is investigated using images and the first side and corner reflections are found to be a minimum requirement to estimate the spatial correlation. Statistics for point driven response are investigated under the assumption that the statistics of the natural frequencies follow those of the Gaussian Orthogonal Ensemble (GOE). The estimates are compared with Monte Carlo simulation results, and they show good agreement. © 2012 Elsevier Ltd. All rights reserved.

Phase equilibria and plate-fluid interfacial tensions for associating hard sphere fluids confined in slit pores

The excess Helmholtz free energy functional for associating hard sphere fluid is formulated by using a modified fundamental measure theory [Y. X. Yu and J. Z. Wu, J. Chem. Phys. 117, 10156 (2002)]. Within the framework of density functional theory, the thermodynamic properties including phase equilibria for both molecules and monomers, equilibrium plate-fluid interfacial tensions and isotherms of excess adsorption, average molecule density, average monomer density, and plate-fluid interfacial tension for four-site associating hard sphere fluids confined in slit pores are investigated. The phase equilibria inside the hard slit pores and attractive slit pores are determined according to the requirement that temperature, chemical potential, and grand potential in coexistence phases should be equal and the plate-fluid interfacial tensions at equilibrium states are predicted consequently. The influences of association energy, fluid-solid interaction, and pore width on phase equilibria and equilibrium plate-fluid interfacial tensions are discussed.

Sole plate fixing details for modern methods of timber construction.

In order to resist lateral loads, modern methods of timber construction are reliant on the in-plane shear strength of the walls orientated parallel to the applied action. In closed panel systems, the shear stresses are transferred to the foundations by the sole plate through the sheathing board, which is usually mechanically jointed to the timber frame. Since closed panels are delivered to site as single units, access to the internal bottom rail is rather restricted and novel, efficient solutions to secure the panel to the substrate are required. Sole plate fixing components for open and closed panel systems were tested in isolation and combination in order to validate a simplistic version of the weakest link theory. As a result, findings were embedded into a software database with a direct link to a previously developed sole plate and racking design application. This integrated process facilitates the structural optimization of the sole plate detail.

Design of concrete platforms offshore using the three-layer shell theory

The concrete offshore platforms, which are subjected a several loading combinations and, thus, requires an analysis more generic possible, can be designed using the concepts adopted to shell elements, but the resistance must be verify in particular cross-sections to shear forces. This work about design of shell elements will be make using the three-layer shell theory. The elements are subject to combined loading of membrane and plate, totalizing eight components of internal forces, which are three membrane forces, three moments (two out-of-plane bending moments and one in-plane, or torsion, moment) and two shear forces. The design method adopted, utilizing the iterative process proposed by Lourenco & Figueiras (1993) obtained from equations of equilibrium developed by Gupta (1896) , will be compared to results of experimentally tested shell elements found in the literature using the program DIANA.

Linear analysis of building floor structures by a BEM formulation based on Reissner's theory

In this work, the plate bending formulation of the boundary element method (BEM) based on the Reissner's hypothesis is extended to the analysis of zoned plates in order to model a building floor structure. In the proposed formulation each sub-region defines a beam or a slab and depending on the way the sub-regions are represented, one can have two different types of analysis. In the simple bending problem all sub-regions are defined by their middle surface. on the other hand, for the coupled stretching-bending problem all sub-regions are referred to a chosen reference surface, therefore eccentricity effects are taken into account. Equilibrium and compatibility conditions are automatically imposed by the integral equations, which treat this composed structure as a single body. The bending and stretching values defined on the interfaces are approximated along the beam width, reducing therefore the number of degrees of freedom. Then, in the proposed model the set of equations is written in terms of the problem values on the beam axis and on the external boundary without beams. Finally some numerical examples are presented to show the accuracy of the proposed model.

A BEM formulation based on Reissner's theory to perform simple bending analysis of plates reinforced by rectangular beams

In this work, the plate bending formulation of the boundary element method (BEM), based on the Reissner's hypothesis, is extended to the analysis of plates reinforced by rectangular beams. This composed structure is modelled by a zoned plate, being the beams represented by narrow sub-regions with larger thickness. The integral equations are derived by applying the weighted residual method to each sub-region, and summing them to get the equation for the whole plate. Equilibrium and compatibility conditions are automatically imposed by the integral equations, which treat this composed structure as a single body. In order to decrease the number of degrees of freedom, some approximations are considered for both displacements and tractions along the beam width. The accuracy of the proposed model is illustrated by simple examples whose exact solution are known as well as by more complex examples whose numerical results are compared with a well-known finite element code.

Mathematical modeling and analysis of the particle interactions in the direct filtration using the colloidal theory

This work used the colloidal theory to describe forces and energy interactions of colloidal complexes in the water and those formed during filtration run in direct filtration. Many interactions of particle energy profiles between colloidal surfaces for three geometries are presented here in: spherical, plate and cylindrical; and four surface interactions arrangements: two cylinders, two spheres, two plates and a sphere and a plate. Two different situations were analyzed, before and after electrostatic destabilization by action of the alum sulfate as coagulant in water studies samples prepared with kaolin. In the case were used mathematical modeling by extended DLVO theory (from the names: Derjarguin-Landau-Verwey-Overbeek) or XDLVO, which include traditional approach of the electric double layer (EDL), surfaces attraction forces or London-van der Waals (LvdW), esteric forces and hydrophobic forces, additionally considering another forces in colloidal system, like molecular repulsion or Born Repulsion and Acid-Base (AB) chemical function forces from Lewis.

Designing piezoresistive plate-based sensors with distribution of piezoresistive material using topology optimization

Piezoresistive sensors are commonly made of a piezoresistive membrane attached to a flexible substrate, a plate. They have been widely studied and used in several applications. It has been found that the size, position and geometry of the piezoresistive membrane may affect the performance of the sensors. Based on this remark, in this work, a topology optimization methodology for the design of piezoresistive plate-based sensors, for which both the piezoresistive membrane and the flexible substrate disposition can be optimized, is evaluated. Perfect coupling conditions between the substrate and the membrane based on the `layerwise' theory for laminated plates, and a material model for the piezoresistive membrane based on the solid isotropic material with penalization model, are employed. The design goal is to obtain the configuration of material that maximizes the sensor sensitivity to external loading, as well as the stiffness of the sensor to particular loads, which depend on the case (application) studied. The proposed approach is evaluated by studying two distinct examples: the optimization of an atomic force microscope probe and a pressure sensor. The results suggest that the performance of the sensors can be improved by using the proposed approach.

A survey on folded plate structures

A compact formulation of the linear theory of folded plate structures utilizing matrix methods is given. Different usual approximations and comparison between them are also shown

A plastic analysis of nonprismatic folded plate structures

A computer method for the plastic analysis of folded plate structures is presented. The method considers the specific characteristics of the folded plate structural model using a simplified one-dimensional theory. and it can be applied to the analysis of any type of folded pIates, either prismatic or nonprismatic, with arbitrary cross-section. A simple example is analyzed in order to show the possibilities of the procedure and some results of interest are presented

The folded plate model in structural analysis. Elastic, plastic and dynamic formulations for nonprismatic structures

A specific numerical procedure for the analysis of arbitrary nonprismatic folded plate structures is presented. An elastic model is studied and compared with a harmonic solution for a prismatic structure. An extension to the plastic analysis is developed, and the influence of the structural geometry and loading pattern is analyzed. Nonprismatic practical cases, with arbitrary geometry and loading are shown, as well in the elastic range as in the plastic one. Finally, a dynamic formulation is outlined

The elasticity and failure of fluid-filled cellular solids: Theory and experiment

We extend and apply theories of filled foam elasticity and failure to recently available data on foods. The predictions of elastic modulus and failure mode dependence on internal pressure and on wall integrity are borne out by photographic evidence of distortion and failure under compressive loading and under the localized stress applied by a knife blade, and by mechanical data on vegetables differing only in their turgor pressure. We calculate the dry modulus of plate-like cellular solids and the cross over between dry-like and fully fluid-filled elastic response. The bulk elastic properties of limp and aging cellular solids are calculated for model systems and compared with our mechanical data, which also show two regimes of response. The mechanics of an aged, limp beam is calculated, thus offering a practical procedure for comparing experiment and theory. This investigation also thereby offers explanations of the connection between turgor pressure and crispness and limpness of cellular materials.

Kinetic study of the hypersonic flow past the leading edge of a flat plate.

Vita.

Phytologia; or, The philosophy of agriculture and gardening. With the theory of draining morasses and with an improved construction of the drill plough.

Each plate accompanied by leaf with descriptive letterpress.

Elements of Galvanism, in theory and practice : with a comprehensive view of its history, from the first experiments of Galvani to the present time : containing also, practical directions for constructing the Galvanic apparatus, and plain systematic instructions for performing all the various experiments ... /

Includes index.