Mechanical response of a capacitive microsensor under thermal load

A considerable fraction of commercial sensors are electrostatically actuated. Many sensor diaphragms are operated in different thermal environments that affect their performance. Because the interplay between the thermal and electrostatic loadings is of interest to designers, in this work we investigate such an interplay. We start with the coupled heat conduction equation and the Saint–Venant plate model. We use nondimensional analysis to show that the dissipation and the elastic coupling vary on a slow scale and hence they can be neglected. Consequently, the heat equation is uncoupled from the plate equation. We consider the case in which the temperature at the boundary is kept at a constant value above the ambient temperature. Substituting the resulting temperature distribution into the plate equation yields an equation with an equivalent compressive load and an electrostatic load due to a DC voltage. Then, a reduced-order model is used to investigate the influence of the dual loading on the plate deflection and their interplay.     

Holographic interferometry study of deformation of cement and concrete under mechanical and thermal loads

Compressive strain of concrete is accompanied by rotation of the rigid aggregate and by local shifts of the cement matrix, which by analogy with local deformation of metals is the cause of a decrease of the real strength of the material. It is shown that deformation of concrete with haydite and granite aggregates in the presence of a heat supply (within limits of positive operating temperatures) is distinguished by damping of deformations in the first case and by local deformation of the aggregate in the second.Presented at the Ninth International Conference on Mechanics of Composite Materials, Riga. October, 1995.Kharkov State Technical Academy of Railroad Transport, Ukraine. Kharkov State Technical Construction and Architecture University, Ukraine. Kharkov Fire Safety Institute Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 2, pp. 202–208, March–April, 1996.     

Optimization of vertical axisymmetric displacements of a thin circular plate under a nonstationary thermal load

We study the problem of optimal control of the distribution of vertical axisymmetric thermal displacements of a thin circular plate fixed along its edge. The displacements are caused by a nonstationary heat load on one of the end surfaces. The thermal action on the other end surface is chosen as the control function. Using the Hankel and Laplace transforms in the space of continuous functions, we construct the solution of the inverse problem of thermoelasticity to which the original control problem has been reduced.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 3, 1997, pp. 148–153.     

Simulation of 2D linear crack growth under constant load using GFVM and two-point displacement extrapolation method

A new approach to model two-dimensional linear crack propagation, based on the Galerkin Finite Volume Method (GFVM), is proposed. The displacement field is calculated using the GFVM method by solving two-dimensional equilibrium equations on an unstructured triangular mesh. An essential feature of this method is that it does not require matrix operations; hence, it obviously reduces computation time. The Two-Point Displacement Extrapolation (TPDE) technique is employed to calculate Stress Intensity Factors (SIFs). The accuracy of the structural solver that has been developed is evaluated using five test cases. In the first example, a Timoshenko cantilever beam, carrying an end point load, is analyzed. In the second and third examples, stress intensity factors are computed for edge and inner crack development in plates under transient loading. The GFVM results are then compared with their counterparts that resulted from the Explicit Finite Element Method (E-FEM). The comparison indicates that the FVM has an accuracy close to E-FEM, whereas the FVM drastically reduces the computational time. A case study is conducted to simulate the gradual propagation of crack. The results computed by the numerical simulation presented are in excellent agreement with the corresponding results from the analytical solution as well as experimental measurements.     

Simulation of constrained mechanical systems

Motion equations of constrained mechanical Multi Body Systems (MBS) are described by differential and algebraic equations (DAE). Various modeling methods are implemented, while the simulation is based on commercial DAE-solvers. A comparison study concerning the quality of their results is presented. Issues, such as the importance of DAE-index, finding a consistent set of initial conditions, the drift-off phenomenon as well as the application of projection and stabilization techniques are discussed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Wave propagation and transient response of a functionally graded material plate under a point impact load in thermal environments

In this paper, the wave propagation and transient response of an infinite functionally graded plate under a point impact load in thermal environments are studied. The thermal effects and temperature-dependent material properties are taken into account. The temperature field considered is assumed to be a uniform distribution over the plate surface and varies in the thickness direction only. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Considering the effects of transverse shear deformation and rotary inertia, the governing equations of the wave propagation in the functionally graded plate are derived from Hamilton’s principle. The analytic dispersion relation of the functionally graded plate is obtained by means of integral transforms and a complete discussion of dispersion for the functionally graded plate is given. Using the dispersion relation and integral transforms, exact integral solutions of the functionally graded plate under a point impact load in thermal environments are obtained. The influences of the volume fraction distributions and temperature field on the wave propagation and transient response of functionally graded plates are discussed in detail. The results carried out can be used in the ultrasonic inspection techniques and provide a theoretical basis for engineering applications.     

Vibration and buckling analyses of FGM plates with multiple internal defects using XIGA-PHT and FCM under thermal and mechanical loads

In this paper, the vibration and buckling analyses of the FGM (functionally graded material) plates with multiple internal cracks and cutouts under thermal and mechanical loads are numerically investigated using the combined XIGA-PHT (extended isogeometric analysis based on PHT-splines) and FCM (finite cell method). Material properties are graded only in the thickness direction. The effective material properties are estimated by using either the rule of mixture or the Mori-Tanaka homogenization technique. The plate displacement field is based on the HSDT (higher-order shear deformation plate theory) without any requirement of the SCF (shear correction factor). The HSDT model can exactly represent the shear stress distribution and improve the accuracy of solutions. The PHT-splines can naturally fulfill the C¹-continuous requirement of the HSDT model. The representation of internal defects is mesh-independent. The discontinuous and singular phenomena induced by the cracks are captured using the enrichment pattern in the XIGA, and the influence of cutouts is implemented by the FCM. The geometries of cutouts are captured by means of adaptive quadrature procedure based on a simple unfitted structural mesh, which avoids the need for multiple patches to describe the complex geometry and eliminates the enforcement of C¹-continuity patch-coupling across the patch boundaries. The initial mesh density around the cracks and cutouts can be controlled flexibly utilizing the local refinement property of the PHT-splines. After validating the results of the developed approach with those available in the literature, the effects of material gradient index, side to thickness ratio, boundary conditions, cutout size and crack length on the normalized frequency and the critical buckling parameter are investigated. Numerical results illustrate the effectiveness and accuracy of the present approach.     

Delamination of composite plates under tensile load

Conclusions Among the two configurations discussed, the beam has a rather theoretical importance, as an extension and generalization of the cracked beam problem. Unlike this, embedded delaminations can be found often in real constructions. The fact that the maximum value of SERR vs. fibre orientation angle curve for the circular embedded delamination is surpassed by that for the split beam only by three times and by that for the split beam under mode II loading approximately six times means that an embedded delamination can lead to difficulties when the plate is tensed (or compressed — even in an underbuckled state — within the linear approach the non-opening modes of stress concentration will just change their signs when the load changes its sign), especially under a cyclic loading. Of course, the shell model used is fairly rough and does not take in account several features or real delaminations extension and does not allow one to evaluate properly the stress field near the crack front; thus, more analytical and experimental studies would be needed, to establish the crack development process. The 3D analysis is necessary when initiating delaminations are studied, for the beam/plate assumptions can no longer be regarded as necessary since the delamination linear dimensions are comparable to or less than the thickness of the sublaminate.Published in Mekhanika Kompozitnykh Materialov, Vol. 31, No. 1, pp. 45–50, January–February, 1995.     

Assessing the mechanical responses for anisotropic multi-layered medium under harmonic moving load by Spectral Element Method (SEM)

The article is concerned with the mechanical responses of anisotropic multi-layered medium under harmonic moving load. An analytical solution for two-dimensional anisotropic multi-layered medium subjected to harmonic moving load is devoted via Spectral Element Method (SEM), while the anisotropic property is approximated as transverse isotropy. Starting with the constitutive equations of transversely isotropic body and the governing equations of motion based on the loading properties. The analytical spectral elements in the wavenumber domain are obtained according to the principle of wave superposition and Fourier transformation. Then, the spectral global stiffness matrix of the multi-layered medium is derived by assembling the nodded stiffness matrices of all layers depended on the different interlayer conditions between the adjacent layers, i.e. sliding and bonded. The corresponding analytical solutions are achieved by taking the Fourier series and Inverse Fast Fourier Transform (IFFT) algorithm. Finally, some examples are given to validate the accuracy of the proposed analytical solution, and to demonstrate the impact of both anisotropy, top layer thickness, interlayer conditions, and loading properties (velocity and natural frequency) on the mechanical response of the multi-layered medium.     

Simulation of hydrodynamics and thermal physics of reliefographic processes

The development of latent images on the free surface of thermoplastic thin films is modeled by the finite-difference method. The mixed boundary-value problem for the Navier—Stokes equations is solved by an algorithm which avoids the standard difficulties of integration of continuity equations. The efficiency of the implicit schemes is analyzed by comparing the numerical and analytical solutions in the isothermal case. The allowance for energy balance makes it possible to compute the hydrodynamic and thermophysical parameters in conditions close to reality.Academy of Sciences of the Ukrainian SSR. Kiev University. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 68, pp. 100–107, 1989.     

Active damping of forced resonance vibrations of an isotropic shallow viscoelastic cylindrical panel under the action of an unknown mechanical load

Using a new approach, we consider the problem of active damping of the forced resonance vibrations of a viscoelastic isotropic cylindrical panel with simply supported edge faces. The mechanical load is assumed to be unknown; it can be found from the experimental data of a sensor. The problem is solved by the Bubnov–Galerkin method. A relation was obtained for the potential difference that has to be supplied to an actuator for the damping of resonance vibrations of the panel. We also study the influence of sizes of sensors and actuators, the dissipative properties of materials, and temperature on the efficiency of active damping of the forced resonance vibrations of a cylindrical panel.     

Membranes of revolution under partially vanishing normal load

This paper investigates the existence and uniqueness of solutions of some boundary value problems modeling the deformation of a membrane of revolution under a partially vanishing normal load. The frame of the membrane models we deal with is the Reissner theory of thin shells of revolution, in which strain-displacement relations are nonlinear, although it assumes a linear stress-strain relation.     

Asymptotic independence of queues under randomized load balancing

Randomized load balancing greatly improves the sharing of resources while being simple to implement. In one such model, jobs arrive according to a rate-??N Poisson process, with ??<1, in a system of N rate-1 exponential server queues. In Vvedenskaya et al. (Probl. Inf. Transm. 32:15?C29, 1996), it was shown that when each arriving job is assigned to the shortest of D, D??2, randomly chosen queues, the equilibrium queue sizes decay doubly exponentially in the limit as N????. This is a substantial improvement over the case D=1, where queue sizes decay exponentially. The reasoning in Vvedenskaya et al. (Probl. Inf. Transm. 32:15?C29, 1996) does not easily generalize to jobs with nonexponential service time distributions. A?modularized program for treating randomized load balancing problems with general service time distributions was introduced in Bramson et al. (Proc. ACM SIGMETRICS, pp.?275?C286, 2010). The program relies on an ansatz that asserts that, for a randomized load balancing scheme in equilibrium, any fixed number of queues become independent of one another as N????. This allows computation of queue size distributions and other performance measures of interest. In this article, we demonstrate the ansatz in several settings. We consider the least loaded balancing problem, where an arriving job is assigned to the queue with the smallest workload. We also consider the more difficult problem, where an arriving job is assigned to the queue with the fewest jobs, and demonstrate the ansatz when the service discipline is FIFO and the service time distribution has a decreasing hazard rate. Last, we show the ansatz always holds for a sufficiently small arrival rate, as long as the service distribution has 2 moments.