Active Control of Free Paraboloidal Membrane Shells Using Photostrictive Actuators

The paraboloidal membrane shell with free boundary condition is actively controlled using photostrictive actuators which can provide contactless actuation under the illumination of ultraviolet light. The governing equations of the paraboloidal shell laminated with paired photostrictive actuators are established based on membrane approximation. The modal control actions of meridional/circumferential actuators are respectively formulated and evaluated by case studies. Constant light intensity related to the velocity of the shell is adopted, and then the governing equations are written in a closed-loop form which can be solved with Newmark-β method. Considering the multi-field coupling behavior of photostrictive actuators, time histories of transverse displacement and control light intensity are simulated and evaluated. The results show that photostrictive actuators can effectively control the vibration of the paraboloidal membrane shell, and the photostrictive actuators oriented along circumferential direction can give better control effect than photostrictive actuators placed along the meridional direction.

Theories and Analyses Thick Hyperbolic Paraboloidal Composite Shells

This paper presents the stress resultants of hyperbolic paraboloidal shells using higher order shear deformation theory recently developed by Zannon [1]-[3]. The equilibrium equations of motion use Hamilton’s minimum energy principle for a simply supported cross-ply structure by Zannon (TSDTZ) [2] [3]. The results are calculated for orthotropic, two-ply unsymmetrical [90/0] shells. The extensional, bending and coupling stiffness parameters are calculated using MATLAB algorithm for laminated composite hyperbolic paraboloidal shells. A comparison of the present study with other researchers in the literature is given, and is in good agreement.

Deployment dynamics for flexible deployable primary mirror of space telescope with paraboloidal and laminated structure by using absolute node coordinate method

A nonlinear dynamic modeling method for primary mirror of Flower-like Deployable Space Telescope(F-DST)undergoing large deployment motion is proposed in this paper.To ensure pointing accuracy and attitude stability of the paraboloidal primary mirror,the mirror is discretized into equal thickness shell elements by considering shell curvature.And the material nonlinear constitutive relation of flexible mirror is acquired using Absolute Nodal Coordinate Formulation(ANCF).Furthermore,the primary mirror of F-DST can be regarded as a clustered multi-body system,and its dynamic equations of elastic deformation and deployment motion are established by virtual work principle.Finally,the deployment motion of primary mirror by different driving conditions are simulated,the results show that the vibrations of mirrors that driven by elastic hinge device are more than that driven by servo motor.In addition,single sub-mirror deployment process will perturb the pointing accuracy of primary mirror,and the multiple sub-mirrors simultaneously deploying will seriously affect all the sub-mirrors surface accuracy because of the coupling effect.Thus,there are theoretical value and practical significance for the controlling surface accuracy and attitude accuracy of space telescope.

On the Axisymmetric Steady Incompressible Beltrami Flows

In this paper, Beltrami vector fields in several orthogonal coordinate systems are obtained analytically and numerically. Specifically, axisymmetric incompressible inviscid steady state Beltrami (Trkalian) fluid flows are obtained with the motivation to model flows that have been hypothesized to occur in tornadic flows. The studied coordinate systems include those that appear amenable to modeling such flows: the cylindrical, spherical, paraboloidal, and prolate and oblate spheroidal systems. The usual Euler equations are reformulated using the Bragg-Hawthorne equation for the stream function of the flow, which is solved analytically or numerically in each coordinate system under the assumption of separability of variables. Many of the obtained flows are visualized via contour plots of their stream functions in the rz-plane. Finally, the results are combined to provide a qualitative quasi-static model for a progression of tornado-like flows that develop as swirl increases. The results in this paper are equally applicable in electromagnetics, where the equivalent concept is that of a force-free magnetic field.

Assessment and Prediction of Thermodynamic Functions of Compounds in Sialon System

According to the quasi paraboloid rule, a computer program was developed and the Gibbs free energy functions of some compounds in Sialon system were assessed and predicted. It makes the theoretical design of the Sialon materials possible.

Effect of Porosity on the Wind Loads on a Hyperbolic Paraboloid Canopy Roof

A discussion is made of the wind force coefficients for designing the main wind force resisting systems of H.P. （Hyperbolic-Paraboid）-shaped porous canopy roofs on the basis of a wind tunnel experiment. Roof models with a number of small circular holes were made of nylon resin using laser lithography. The porosity was changed from 0 （solid） to 0.4. Besides the porosity, the geometric parameters of the models were the rise to span ratio and slope of the roof. The overall aerodynamic forces and moments acting on a model were measured by a six-component force balance in a turbulent boundary layer. The results indicate that the porosity significantly reduces the wind loads. The design wind force coefficients for porous canopy roofs can be provided by those for solid roofs with the same configuration multiplied by a reduction factor. The proposed wind force coefficients are verified by a comparison of the load effect predicted by the proposed wind force coefficients with the maximum load effect obtained from dynamic analyses using the time history of wind force and moment coefficients. The axial forces induced in the columns supporting the roof are regarded as the load effect for discussing the design wind loads.

Wind Loading on a Hyperbolic Paraboloid Free Roof

Wind loading on an H.P. （hyperbolic paraboloid） free roof has been investigated on the basis of a wind tunnel experiment. The roof models of 1 mm thickness were made of nylon resin using laser lithography. The parameters under consideration are the rise to span ratio and slope of the roof. The overall aerodynamic forces and moments were measured by a six-component force balance in a turbulent boundary layer. Based on a combination of the lift and moment coefficients, the design wind force coefficients, CNW^＊ and CNL^＊, on the windward and leeward halves of the roof are proposed. Focus is on the column axial forces induced by wind loading as the load effect for discussing the design wind loads, assuming that the roof is rigid and supported by four comer columns. Indeed, two pairs of CNW^＊ and CNL^＊, generating the maximum tension and compression in the columns, are provided for each of the two or three wind directions parallel to the roof＇s diagonal lines. The proposed values of the wind force coefficients are compared with the specified values in the Australia/New-Zealand Standard for a limited range of rise to span ratio.

Bioconvection Mangnetohydrodynamic Tangent Hyperbolic Nanofluid Flow with Quartic Chemical Reaction Past a Paraboloid Surface

In this numerical study,the effect of quartic autocatalysis type of chemical reaction,buoyancy force and thermal radiation phenomenon and magnetic effect on tangent hyperbolic nanofluid past an upper horizontal surface of a paraboloid has been studied.By considering the Buongiorno model approach,a diffusion of unequal coefficients in the presence of gyrotactic microorganism is discussed.Implementation of microorganism’s idea is used to stabilize the nanoparticles through bioconvection.The modeled PDEs of the problems are converted into nonlinear ODEs with the assistant of the similarity transformations.To tackle nonlinear ODEs,MATLAB package bvp4c is used.In addition,a hallmark of the Matlab code with the reported results in the literature is achieved by benchmarking.The variations in motion,concentration,temperature,and motile density due to sundry parameters have been analyzed in-depth via graphs.Our analysis shows that the density profile of motile of microorganism is hiked with an increment in the bioconvection Rayleigh number but decreases for higher thermal Grashof number.

Surface registration algorithm for rapid detection of surface thermal deformation of paraboloid antennas

In order to obtain and master the surface thermal deformation of paraboloid antennas,a fast iterative closest point( FICP) algorithm based on design coordinate guidance is proposed,which can satisfy the demands of rapid detection for surface thermal deformation. Firstly,the basic principle of the ICP algorithm for registration of a free surface is given,and the shortcomings of the ICP algorithm in the registration of surface are analysed,such as its complex computation,long calculation time,low efficiency,and relatively strict initial registration position. Then an improved FICP algorithm based on design coordinate guidance is proposed. Finally,the FICP algorithm is applied to the fast registration test for the surface thermal deformation of a paraboloid antenna. Results indicate that the approach offers better performance with regard to fast surface registration and the algorithm is more simple,efficient,and easily realized in practical engineering application.

Numerical and Experimental Investigation of an Elliptical Paraboloid Shell Model

For practical engineering purpose, a new flat shell element baptized （ACM_Q4SBE1） is presented in this paper. The formulated element can be used for the analysis of thin shell structures; no matter how the geometrical shape might be. Tests on standard problems have been examined. Since, the analysis of thin shell structures has generally been purely carried out on a theoretical basis; it is of importance to present some experimental results of an elliptical paraboloid under uniformly distributed load pressure. The results obtained from both numerical and experimental work are presented.

Linking Conditions for Models with Geometrical Basis

Usually it is demanded that the metric and its 1st derivatives have to match at the boundary of two adjacent regions which are solutions to Einstein’s field equation. We propose a new linking condition concerning gravitational models based on surfaces which could be embedded into a higher dimensional flat space. We probe this condition for the Schwarzschild interior and exterior solution.

A Yield Mapping Procedure Based on Robust Fitting Paraboloid Cones on Moving Elliptical Neighborhoods and the Determination of Their Size Using a Robust Variogram

The yield map is generated by fitting the yield surface shape of yield monitor data mainly using paraboloid cones on floating neighborhoods. Each yield map value is determined by the fit of such a cone on an elliptical neighborhood that is wider across the harvest tracks than it is along them. The coefficients of regression for modeling the paraboloid cones and the scale parameter are estimated using robust weighted M-estimators where the weights decrease quadratically from 1 in the middle to zero at the border of the selected neighborhood. The robust way of estimating the model parameters supersedes a procedure for detecting outliers. For a given neighborhood shape, this yield mapping method is implemented by the Fortran program paraboloidmapping.exe, which can be downloaded from the web. The size of the selected neighborhood is considered appropriate if the variance of the yield map values equals the variance of the true yields, which is the difference between the variance of the raw yield data and the error variance of the yield monitor. It is estimated using a robust variogram on data that have not had the trend removed.