The application of micro-plate dynamics on monitoring cell property

The paper presents a novel biosensing method of monitoring cell properties using the information derived from the dynamics of micro-scale plates. Micro cantilevers have been widely applied as mechanical biosensors. In dynamic sense, cantilever is considered as 1 dimensional whereas plate is a 2 dimensional structure. In this paper we provide the first analytical solution to the dynamics of distributed mass loaded microplate in submerged fluid. In a further step, we propose to derive the dynamical infomation of the micro plate and use it to infer the spatial information of the cells when monitoring the cell growth on the plate

Dynamic analysis of submerged microscale plates: the effects of acoustic radiation and viscous dissipation

The aim of this paper is to study the dynamic characteristics of micromechanical rectangular plates used as sensing elements in a viscous compressible fluid. A novel modelling procedure for the plate–fluid interaction problem is developed on the basis of linearized Navier–Stokes equations and no-slip conditions. Analytical expression for the fluid-loading impedance is obtained using a double Fourier transform approach. This modelling work provides us an analytical means to study the effects of inertial loading, acoustic radiation and viscous dissipation of the fluid acting on the vibration of microplates. The numerical simulation is conducted on microplates with different boundary conditions and fluids with different viscosities. The simulation results reveal that the acoustic radiation dominates the damping mechanism of the submerged microplates. It is also proved that microplates offer better sensitivities (Q-factors) than the conventional beam type microcantilevers being mass sensing platforms in a viscous fluid environment. The frequency response features of microplates under highly viscous fluid loading are studied using the present model. The dynamics of the microplates with all edges clamped are less influenced by the highly viscous dissipation of the fluid than the microplates with other types of boundary conditions

Analysis and design for the moderately deep postbuckling behavior of composite plates

It is widely acknowledged that tracking the postbuckling response of structures made from thin plates can be problematical. Such difficulty is associated with highly nonlinear effects, including mode jumping, imperfection sensitivity, and their combined interactions. Two widely used techniques that are currently used involve path following and asymptotic expansion. The former is often implemented in commercial finite element codes but can prove unreliable at representing branch switching. The latter is a relatively quick technique due to its recursive linear nature but is only reliable in the vicinity of bifurcations. Due to the overall complex nonlinearity, analytical closed-form solutions do not exist for path following and exist rarely for quadratic asymptotic expansions where simple forms have been adopted. This paper presents an analytical-based approach that enables the efficient optimal design of “moderately deep” nonlinear postbuckling behavior of laminated composite plates under uniaxial or biaxial loading. It provides a closed-form solution that more reliably reflects a deeper postbuckling response than the state of the art. Subsequently, highly efficient postbuckling optimization is attributed to the newly derived closed-form solution and a recent two-level optimization framework

A comparison of variational, differential quadrature, and approximate closed-form solution methods for buckling of highly flexurally anisotropic laminates

The buckling response of symmetric laminates that possess strong exural-twist coupling are studied using different methodologies. Such plates are dfficult to analyse due to localised gradients in the mode shape. Initially, the energy method (Rayleigh-Ritz) using Legendre polynomials is employed and the difficulty of achieving reliable solutions for some extreme cases is discussed. To overcome the convergence problems, the concept of Lagrangian multiplier is introduced into the Rayleigh-Ritz formulation. The Lagrangian multiplier approach is able to provide the upper and lower bounds of critical buckling load results. In addition, mixed variational principles are used to gain a better understanding of the mechanics behind the strong exural-twist anisotropy effect on buckling solutions. Specifically, the Hellinger-Reissner variational principle is used to study the effect of exural-twist coupling on buckling and also to explore the potential for developing closed form solutions for these problems. Finally, solutions using the differential quadrature method are obtained. Numerical results of buckling coefficients for highly anisotropic plates with different boundary conditions are studied using the proposed approaches and compared with finite element results. The advantages of both Lagrangian multiplier theory and variational principle in evaluating buckling loads are discussed. In addition, a new simple closed form solution is shown for the case of a exurally anisotropic plate with three sides simply supported and one long edge free

Buckling analysis of variable angle tow composite plates using differential quadrature

Variable Angle Tow (VAT) placement allows the designer to tailor the composite structure to enhance the structural response under prescribed loading conditions. VAT technology allows curvilinear placement of tows within the plane of a structure and gives freedom for altering pointwise in-plane, coupling and flexural stiffnesses of a plate. This stiffness tailoring improves the buckling performance of VAT plates by allowing re-distribution of loads from the critical regions of the plate. In the present work, the Differential Quadrature Method (DQM) is investigated for performing buckling analysis of VAT panels. The governing differential equations are derived for the in-plane and buckling analysis of symmetric VAT plate structure based on classical laminated plate theory. DQM was applied to solve the buckling problem of simply supported VAT plates subjected to uniform edge compression. To show the accuracy and robustness of DQM, the results obtained using DQM are compared with finite element analysis. In this work, Non-Uniform Rational B-Splines (NURBS) curves are used to model the fibre path and the fibre orientation can be designed by modifying the control points within the domain of the plate. The NURBS representation allows general fibre angle variation of tow resulting in wider design space of VAT panels. Also, the number of design variables for VAT panels are reduced by using NURBS curves and the fibre manufacturing constraints can be handled easily. Genetic Algorithm (GA) has been coupled with DQM to determine the optimal tow path for improving the buckling performance

Postbuckling analysis of variable angle tow (VAT) composite plates

Variable angle tow (VAT) placement techniques provide the designer with the ability to tailor the point-wise stiffness properties of composite laminates according to structural design requirements. Whilst VAT laminates exhibiting substantial gains in buckling performance have been shown previously, beneficial ways of using VAT techniques to improve structural performance of composite laminates in the postbuckling regime remain unclear. In the present study, a semi-analytical formulation based on a variational approach is developed and the Rayleigh-Ritz method is subsequently applied to solve the postbuckling problem of VAT plates. The generality of the proposed formulation allows effective modelling of the pure or mixed stress boundary conditions and also provides a computationally effcient means to determine the postbuckling strength of VAT plates. The proposed methodology is applied to the postbuckling problem of simply supported VAT plates under uni-form edge displacement compression. To show the accuracy and robustness of the proposed approach, results are validated using finite element analysis. The postbuckling characteristics of VAT plates subject to different in-plane boundary conditions are analysed by studying their nonlinear load-end shortening and transverse deflection responses. Furthermore, a parametric study on the postbuckling response of VAT plates with linear variation of fibre angle is performed and the stiffness values of VAT plates in both pre- and postbuckling ranges are compared with the results of straight-fibre laminates

Optimal postbuckling design of variable angle tow composite plates

Perturbation-based approximation methods are widely used in preliminary design studies of thin-walled structures. In this paper, postbuckling analysis of a variable-angle-tow composite plate is performed using the perturbation-based asymptotic numerical method, which transforms the nonlinear problem into a set of well-posed recursive linear problems. These linear problems are solved using a novel generalized differential-integral quadrature method, and the postbuckling solutions are sought over a finite load step size around the critical buckling point using asymptotic expansions. The accuracy of the asymptotic numerical method in evaluating the initial postbuckling of variable-angle-tow plates under compression is investigated. Subsequently, a novel postbuckling optimization approach based on asymptotic numerical method results is proposed for the design of variable-angle tow laminates. The postbuckling features obtained from asymptotic numerical method are used in an efficient two level optimization framework for the design of variable-angle-tow plates. At the first level, a globally convergent method of moving asymptotes is adopted to determine the optimal lamination parameter distributions that maximize the postbuckling performance of the variable-angle-tow plate. At the second level, a genetic algorithm is used to convert the optimal lamination parameter distributions into realistic variable-angle-tow layups. The optimization studies are performed for square variable-angle-tow plates for axial/biaxial compression under different in-plane boundary conditions

Buckling analysis of stiffened variable angle tow panels

Variable angle tow (VAT) laminates have previously shown enhanced buckling performance compared to conventional straight fibre laminates. In this study, an analytical method is developed for the buckling analysis of a novel blade stiffened VAT panel to allow this potential to be more fully exploited. The prebuckling and buckling analysis, performed on a representative section of a blade stiffened VAT panel, are based on a generalised Rayleigh–Ritz procedure. The buckling analysis includes a first order shear deformation theory by introducing additional shape functions for transverse shear and is therefore applicable to structures with thick skins relative to characteristic length. Modelling of the stiffener is achieved with two approaches; idealisation as a beam attached to the skin’s midplane and as a rigidly attached plate. Comparing results with finite element analysis (Abaqus) for selected case studies, local buckling errors for the beam model and plate model were found to be less than 3% and 2% respectively, whilst the beam model error for global buckling was between 3% and 10%. The analytical model provides an accurate alternative to the computationally expensive finite element analysis and is therefore suitable for future work on the design and optimisation of stiffened VAT panels

Postbuckling optimisation of variable angle tow composite plates

The potential for enhanced postbuckling performance of flat plates using variable angle tow (VAT), in comparison with conventional laminated composites, has been shown previously. This paper presents an optimization strategy for the design of postbuckling behaviour of VAT composite laminates under axial compression. The postbuckling performance of composite laminated plates for a given compression loading is assessed by studying both the maximum transverse displacement and the end-shortening strain. For the postbuckling analysis of VAT composite plates, an efficient tool based on the variational principle and the Rayleigh-Ritz method is developed. In the optimization study, a mathematical definition based on Lagrangian polynomials, which requires few design parameters, is used to define a general fibre angle distribution of the VAT plate. A generic algorithm is subsequently used to determine the optimal VAT configuration for maximum postbuckling performance. The optimization of square VAT laminates under compression loading for different in-plane boundary conditions is studied and compared with straight fibre designs