Thermal buckling analysis of temperature-dependent FG-CNTRC quadrilateral plates

The main objective of the present study is to analyze the thermal buckling of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) quadrilateral plates. Functionally graded patterns are introduced for the distribution of the carbon nanotubes (CNTs) through the thickness direction of the plate. The effective material properties of nanocomposite plate reinforced by CNTs are considered to be temperature-dependent (TD) and estimated using the micromechanical model. By the use of minimum total potential energy principle and based on the first-order shear deformation theory of plates, the stability equations are obtained. In order to use the generalized differential quadrature (GDQ) method and solve the stability equations, the irregular domain of quadrilateral plate is transformed into regular computational domain employing the mapping technique. The efficiency and accuracy of the proposed approach are first validated. Then, a comprehensive parametric study is presented to examine the effects of model parameters on the thermal buckling of FG-CNTRC quadrilateral plates. The results indicate that considering temperature dependency of the material properties plays an important role in the stability of the FG-CNTRC quadrilateral plates subjected to thermal loading.     

Lateral buckling analysis of beams by the fem

Two new finite element formulations for the calculation of the lateral buckling load for elastic straight prismatic thin-walled open beams under conservative static loads, are presented. The stability criterion used is based on the positive definiteness of the second variation of the total potential energy. One formulation is suitable for sections where the initial bending is about a dominant major axis. The other finite element formulation takes account of initial bending curvature and essentially takes the form of a quadratic eigenvalue problem. Both formulations are tested with problems that have classical solutions or experimentally determined results and are shown to be accurate.     

Lateral buckling of tee beams under moment gradient

This paper investigates the elastic lateral buckling of simply supported tee beams under moment gradient. Solutions are obtained via the energy approach, assuming a general Fourier sine series for the buckled shapes. It is found that buckling capacity of tee beams is greatly influenced by the inability of the web to resist compressive bending stresses. Although uniform moment is the most severe loading condition for inverted tee beams, this is not true in the case of tee beams. This study shows that a high moment gradient is generally a more critical form of loading for tee beams. Formula for the buckling moment modification factor for doubly symmetric I-beams found in design specifications and standard texts could be unsafe when applied to tee beams.     

Some notes on finite element buckling formulations for beams

Based on a formulation for the elastic distortional buckling of tapered I-beams, some observations have been developed that are germane to the finite element modelling of the lateral buckling of beams. In particular, it is shown that a commonly cited formulation omits a boundary term, and can in some cases lead to erroneous results. A new set of degrees of freedom for distortional buckling are proposed, and these may be modified easily to account for lateral buckling in the simplified case.     

Lateral buckling of locally buckled beams using finite element techniques

This paper deals with lateral-torsional buckling of beams which have already buckled locally before the occurrence of overall buckling. Due to the weakening effects of local buckling, the stiffness of the beam is reduced. As a result, overall lateral buckling takes place at a lower load than the member would carry in the absence of local buckling. The effective width concept is used in this investigation to account for the post-buckling strength in the buckled compression plate elements of the beam section. A finite element formulation in conjunction with effective width concept is presented. Due to the nonlinearity involved because of local buckling, an iterative procedure is necessary. Search techniques are used to find the load factor. The method combined with an analysis on nonlinear bending moment distribution can be used to analyze the lateral stability problem of locally buckled continuous structure. In this case, both elastic stiffness matrix and geometric stiffness matrix must be revised at each load level. A computer program has been prepared for an IBM 370/165 computer.     

Inelastic interactive distorsional buckling of W-shape steel beams

A modified flow theory based on the concept of discontinuous stress-strain yielding for structural steel has been used to study the problem of interactive (local-lateral) buckling of beams in the plastic range. Finite element formulations have been established to conduct numerical experiments for a parametric study of the interactive buckling problem. Limits are suggested for the maximum laterally unsupported length for class (1) sections in Limit States Design. It was also concluded that proportioning the cross-section to allow interactive buckling modes to develop improves the overall plastic rotational capacity of the structure.     

On the design optimization of built-up stiffened steel beams with buckling and frequency constraints

The literature on the structural design optimization of steel-plate girders indicates a need for more refined research studies to obtain optimal designs by formulating and solving the design problem that combines structural sizing and shape parameters in one unified, constrained problem. For this purpose, the structural optimization design problem of stiffened steel-plate girders is formulated with specified loading conditions and constraints on strength and serviceability considerations including limits on fundamental frequency and buckling modes. The finite-element method-based model is used to define the objective function and the structural/geometric response functions, while the geometric domain elements are used to systematically perturb the structural shape during the search for an optimal shape of the structure. The mathematical statement of the gradient-based-design problem is solved for an optimal structural size and shape with buckling and frequency constraints in addition to the traditional strength constraints. The numerical results obtained are compared with results obtained from a less formal ad hoc design procedure, and some conclusions are drawn to emphasize the design benefits obtained from solving the design problem for optimal structural size and shape.     

A simple method to determine the critical buckling loads for axially inhomogeneous beams with elastic restraint

In this paper, a new and simple approach is presented to exactly calculate the critical buckling loads of beams with arbitrarily axial inhomogeneity. For various end boundary conditions, we transform the governing equation with varying coefficients to linear algebraic equations; then a characteristic equation in critical buckling loads will be obtained. Several examples of estimating buckling loads under typical end supports are discussed. By comparing our numerical results with the exact and existing results for homogeneous and nonhomogeneous beams, it can be found that our method has fast convergence and the obtained numerical results have high accuracy. Moreover, the buckling behavior of a functionally graded beam composed of aluminum and zirconia as two constituent phases is investigated for axially varying material properties. The effects of gradient parameters on the critical buckling loads are elucidated. Finally, we give an example to illustrate the enhancement of the load-carrying capacity of tapered beams for admissible shape profiles with constant volume or weight. The proposed method is of benefit to optimum design of beams against buckling in engineering applications.     

Optimization of bracing and internal support locations for beams against lateral buckling

Presented herein is a simple numerical method for determining the optimal location of internal restraints, such as braces and internal supports in beams so that their elastic lateraltorsional buckling capacities are maximized. The method consists of a direct search optimization technique and an automated Rayleigh-Ritz method for the buckling analysis. Some examples of braced and internally supportedI-beams are considered and their optimal restraint positions determined. The method can be used to solve similar problems of restraint locations optimization for any structural member against bending, buckling or vibration.     

Application of general variational methods with discontinuous fields to bending,buckling, and vibration of beams

The effectiveness of consistent variational statements for discontinuous fields is illustrated for bending, buckling, and vibration of elastic beams. General variational statements are developed, from which finite-element formulations with piece-wise constant and piece-wise linear trial functions, are obtained. Results are illustrated by means of numerical examples.     

Sectorial properties of straight thin-walled beams

The sectorial method of analysis for thin-walled beams subjected to torsional loading offers many advantages. In particular it enables warping restraint effects due to non-uniform torsion to be incorporated into a general beam theory covering all solid, thick-walled and thin-walled beams of non-deformable cross-section. The distribution of warping restraint stresses around the section is defined in a similar way as for bending by a system of sectorial co-ordinates and several additional geometrical terms. A wider understanding and acceptance of this useful method of analysis is only hindered by difficulties in calculating the various sectorial functions. Solutions are readily available for open sections and regular single cell closed sections. For more complex sections, particularly asymmetric or multicellular sections or those with tapering walls, pierced walls or bracing, these calculations are often tedious. A general computer program is described which analyses any cross-section with open or closed parts. Examples are given of its application to the analysis of several straight thin-walled beams.     

高性能多晶硅压力传感器的研制

本文介绍的高性能多晶硅压力传感器,以重掺杂的LPCVD多晶硅薄膜作应变敏感电阻,用二氧化硅层隔离单晶硅衬底,使其工作温度高达200℃以上,若用恒流源供应惠斯登电桥,即使在没有外电路补偿情况下,灵敏度系数(TDS)也仅1.32×10~(-6)FS/℃,可实现近乎理想的灵敏度温度补偿.     

应力集中式多晶硅薄膜压力传感器

介绍一种以多晶硅薄膜为敏感材料的压力传感器。该传感器利用了双岛结构膜片的应力集中效应，灵敏度得到提高，且具有良好的线性度和过载能力。     

Free and forced vibration analysis of viscoelastic damped FG-CNT reinforced micro composite beams

In this paper, free and forced vibration analysis of viscoelastic microcomposite beam reinforced by functionally graded single-walled carbon nanotubes (FG-SWCNTs) is studied using the modified couple stress theory (MCST). The material properties of micro composite beam by generalized rule of mixtures carbon nanotubes are estimated. In addition, these properties are stated as uniform, and functionally graded (FG) distributions in the thickness direction. Energy method and Hamilton’s principle are employed to establish the governing equations of motion for the vibration of viscoelastic damped micro composite beam reinforced by SWCNTs based on the Kelvin–Voigt model. The influences of material length scale parameter, structural damping coefficient and different distributions of SWCNTs on non-dimensional complex natural frequency and amplitude vibration of the viscoelastic micro composite beam are investigated. The results reveal that the lowest vibration amplitude of FG microcomposite beam by the FG-X and the highest occurs by FG-◊. Moreover, in the presence of external periodic load and the absence of structural damping coefficient, the vibration amplitude increases and FG microcomposite beam becomes unstable, even though the amplitude of vibration decreases with increasing structural damping coefficient. It is shown that the natural frequency of SWCNT reinforced composite is more than the frequency of multi-walled carbon nanotubes because SWCNT have more stiffness. In addition, the results illustrate that the experimental data by Lei et al. agree well with those predicted by the MCST in the present work.

     

First-order,buckling and post-buckling behaviour of GFRP pultruded beams. Part 1: Experimental study

Although fibre reinforced polymers exhibit several advantages over traditional materials, their widespread acceptance is being delayed by the lack of appropriate design codes. In fact, additional and comprehensive experimental data are needed to assess the accuracy of recently developed analytical and numerical design tools. This work reports an experimental study on the first-order, buckling and post-buckling behaviours of I-section beams made of GFRP pultruded profiles. Tests were first carried out on small-scale (coupon) specimens, in order to determine the most relevant material mechanical properties. Full-scale tests were then conducted on (i) simply supported beams with spans varying from 1.0 m to 4.0 m under 3-point bending and (ii) cantilevers with spans ranging from 2.0 m to 4.0 m subjected to a tip point load applied at the end cross-section centroid or top/bottom flange mid-point. While the first series is aimed at investigating the flexural behaviour under service and failure conditions (including the local buckling of the top flange), the objective of the second series is to study the collapse behaviour stemming from lateral-torsional buckling. The results obtained confirm that, due to the GFRP low Young’s modulus and high strength, the beam structural integrity is often governed by excessive deformation and/or local and global buckling phenomena, rather than by material strength limitations. Moreover, the low shear-to-Young’s modulus ratio implies that the role played by the shear deformation is quite relevant, particularly in stocky beams. The experimental data presented here is used to validate and assess the accuracy of numerical simulations reported in a companion paper (Part 2).     

Piezoelectric thin films formed by MOD on cantilever beams for micro sensors and actuators

Novel piezoelectric cantilever beams for micro sensors and actuators based on PZT thin films have been batch fabricated by surface micromachining. Lead zirconate titanate (PZT) thin film is formed by metalorganic deposition (MOD) on Pt/Ti/SiO₂/Si (1 0 0) substrates and Pt/Ti/LTO/Si₃N₄ cantilever beams and then annealed at 700 °C in air. The PZT thin film is 0.5 m thick and has dielectric permittivity of 1698, remanent polarization of 13.66 C/cm², and coercive field of 44.5 kV/cm. The influence of deposition temperatures on PZT thin film stress has been investigated. When continuously controlling the deposition temperatures, the stress of the thin film is reduced from 0.313 × 10⁸ to 0.269 × 10⁸ N/m, that is 16.4% decrease. With the total 120 designed devices on 4-inch wafers, the number of functional devices is increased from 82 to 97, that is 12.47%.Tianhong Cui joined the faculty of Institute for Micromanufacturing at Louisisana Tech University in 1999. He received his B.S. from Nanjing University of Aeronautics & Astronautics in 1991, and his Ph.D. from Chinese Academy of Sciences in 1995. He has conducted research and development work for the realization of microsensors and microactuators since 1992. Prior to joining the IfM in 1999, he was at the National Laboratory of Metrology in Japan as a Research Fellow under STA fellowship, and previous to that, served as a Postdoctoral Research Associate at the University of Minnesota. His current research interests include MEMS, polymer micro/nanoelectronics, and nanotechnology.     

First-order,buckling and post-buckling behaviour of GFRP pultruded beams. Part 2: Numerical simulation

This work deals with the numerical evaluation of the structural response of simply supported (transversally loaded at mid-span) and cantilever (subjected to tip point loads) beams built from a commercial pultruded I-section GFRP profile. In particular, the paper addresses the beam (i) geometrically linear behaviour in service conditions, (ii) local and lateral-torsional buckling behaviour, and (iii) lateral-torsional post-buckling behaviour, including the effect of the load point of application location. The numerical results are obtained by means of (i) novel Generalised Beam Theory (GBT) beam finite element formulations, able to capture the influence of the load point of application, and (ii) shell finite element analyses carried out in the code Abaqus. These numerical results are compared with (i) the experimental values reported and discussed in the companion paper (Part 1) and (ii) values provided by analytical formulae available in the literature.     

Real-time worst-case temperature analysis with temperature-dependent parameters

With the evolution of today’s semiconductor technology, chip temperature increases rapidly mainly due to the growth in power density. Therefore, for modern embedded real-time systems it is crucial to estimate maximal temperatures early in the design in order to avoid burnout and to guarantee that the system can meet its real-time constraints. This paper provides answers to a fundamental question: What is the worst-case peak temperature of a real-time embedded system under all feasible scenarios of task arrivals? A novel thermal-aware analytic framework is proposed that combines a general event/resource model based on network and real-time calculus with system thermal equations. This analysis framework has the capability to handle a broad range of uncertainties in terms of task execution times, task invocation periods, jitter in task arrivals, and resource availability. The considered model takes both dynamic and leakage power as well as thermal dependent conductivity into consideration. Thorough simulation experiments validate the theoretical results.     

Mechanical properties of glass frit bonded micro packages

Frit glass bonding is a widely used technology for encapsulation of surface micro-machined structures like inertial sensors or gyroscopes on wafer level. Since for sensors in automotive applications, a lifetime of 15–20 years has to be guaranteed for, a reliable lifetime prediction is necessary. Different material parameters have to be known for a lifetime estimation based on stress corrosion cracking, which determines the long-term strength behaviour of most bonded interfaces of microsystems. Parameters needed for lifetime prediction have to describe the material’s resistance against crack propagation (fracture toughness K _IC), the stress situation in a micro package and the long-term strength behaviour. Results for fracture toughness investigations presented in this paper were determined by the micro chevron test. The stress situation in a micro package was calculated by a thermo-mechanical Finite Element Analysis. Furthermore the residual stress in the glass layer and the linear thermal expansion coefficient were determined by a crack width measurement in an environmental scanning electron microscope.