One-dimensional Stresses Research Articles

Automated Fluid Model Generation and Numerical Analysis of Dielectric Barrier Discharges Using Comsol

MCPlas is introduced as a powerful tool for automated fluid model generation with application to the analysis of dielectric barrier discharges operating in different regimes. MCPlas consists of a number of MATLAB\textsuperscript{\textregistered} scripts and uses the COMSOL Multiphysics\textsuperscript{\textregistered} module LiveLink\textsuperscript{\texttrademark} for MATLAB\textsuperscript{\textregistered} to build up equation-based COMSOL Multiphysics\textsuperscript{\textregistered} models from scratch. The present contribution highlights how MCPlas is used to implement time-dependent models for non-thermal plasmas in spatially one-dimensional and axisymmetric two-dimensional geometries and stresses out the benefit of automation of the modelling procedure. The modelling codes generated by MCPlas are used to study diffuse and filamentary dielectric barrier discharges in argon at sub-atmospheric and atmospheric pressure, respectively. The seamless transition between different levels of model complexity with respect to the considered model geometry is demonstrated. The presented investigation of a single-filament dielectric barrier discharge interacting with a dielectric surface shows that complex phenomena of high technological relevance can be tackled by using plasma models implemented in COMSOL Multiphysics\textsuperscript{\textregistered} via MCPlas.

Electronically tunable auxetic behavior of shunted piezoelectric elements

This work demonstrates auxetic behavior in a solid polycrystalline shunted piezoelectric cube. Piezoelectric elements are commonly bonded to structures to reduce vibrations by tuning an attached shunt circuit to resonate at the same frequency as the mechanical vibrations in the structure. Literature has provided an extensive analysis of vibration suppression in passively shunted piezoelectric systems, but in practice, the three-dimensional constitutive equations are almost always reduced to one-dimensional stresses and strains within the piezoelectric. In this work, resistive–inductive shunt circuits are applied to the electrical terminals of a harmonically forced piezoelectric cube, and the directional displacements are determined in all three dimensions when it is loaded parallel and perpendicular to the poling direction, as well as dilatationally. By comparing these directional displacements, the effect of the shunt circuit on Poisson’s ratio can be measured. It is demonstrated that an inductive shunt leads to a complex Poisson’s ratio with a real part approaching positive and negative infinity over a discrete band of frequencies, implying that a polycrystalline piezoelectric cube can become auxetic through the application of a properly engineered shunt circuit. The auxetic behavior is explored through finite element modeling, and the derivation of analytical expressions for Poisson’s ratio in shunted piezoelectric elements.

A novel approach to thermal and mechanical stresses in a FGM cylinder with exponentially-varying properties

A novel approach is employed to a general solution for one-dimensional steady-state thermal and mechanical stresses in a hollow thick cylinder made of a functionally graded material (FGM). The temperature distribution is assumed to be a function of radius, with general thermal and mechanical boundary conditions on the inside and outside surfaces of the cylin- der. The material properties, except Poisson’s ratio, are assumed to be exponentially-varying through the thickness. Forcing functions applied to the inner boundary are internal pressures which may be in form of steps. These conditions result in governing differential equations with variable coefficients. Analytical solutions to such equations cannot be obtained except for certain simple grading functions and pressures. Numerical approaches must be adopted to solve the problem in hand. The novelty of the present study lies in the fact that the Complementary Functions Method (CFM) is employed in the analysis. The Complementary Functions method (CFM) will be infused into the analysis to convert the problem into an initial-value problem which can be solved accurately. Benchmark solutions available in the literature are used to validate the results and to observe the convergence of the numerical solutions. The solution procedure is well-structured, simple and efficient and it can be re- adily applied to cylinders. It is also well suited for problems in which mechanical properties are graded.

Airfield Pavement Response Caused by Heavy Aircraft Takeoff

The effect of wheel configuration on critical airfield pavement responses during takeoff was calculated, and variables, usually omitted in conventional pavement analysis, were considered. The numerical analysis matrix consisted of two takeoff speeds, two inflation pressures, two pavement structures, and four wheel configurations. One of the pavement structures was built at the National Airport Pavement Test Facility and had been previously described in the literature. The method used in this study advanced current knowledge in two respects. First, the study examined not only the tensile strains at the bottom of the asphalt concrete (AC) layer (fatigue cracking) and vertical strain on top of the subgrade (rutting) but also the transverse surface strain (surface cracking) and vertical shear strains (near-surface cracking and rutting). Second, several assumptions about existing methods were advanced. These assumptions included (a) nonuniform three-dimensional contact stresses instead of uniform one-dimensional vertical stresses over a circular contact area, (b) viscoelastic and nonlinear material characterization for AC and granular material under high stress levels in lieu of a linear elastic model, and (c) load variation with time to reflect takeoff. Transverse surface strain and vertical shear strain in the subgrade were most affected by wheel configuration. In addition, the variables had varying influence on pavement responses and wheel interaction. For instance, takeoff speed affected vertical strain on top of the subgrade but did not affect transverse surface strain. Tire inflation pressure modified wheel interaction for shear strain in the AC but not in the subgrade.

A two-director Cosserat rod model using unconstrained quaternions

Abstract Starting from a constrained three-dimensional analysis, we propose a new model for an initially curved Cosserat rod with two independent directors, in which the cross-section can inflate and ovalize. The usage of unconstrained quaternions gets rid of the non-linear constraints and singularities in the parametrization of objective strains, related to the orthonormality of rotation matrices. Furthermore, the classic definitions of curvatures and twist have been modified and tuned for a linear constitutive law (i.e. a linear relationship between one-dimensional stresses and strains). The capabilities and the limitations of the model in describing the non-linear effects of cross-section deformation on bending and torsion, and usually handled with bi- and three-dimensional theories, are then discussed.

Deformation and Stresses Analysis in FG Rotating Hollow Disk and Cylinder Subjected to Thermal and Mechanical Load

In this paper, a new solution is presented for one-dimensional steady-state mechanical and thermal stresses in a FG rotating hollow disk and cylinder. The material properties for FG are expressed as nonlinear exponential functions through the radius and Poisson’s ratio is taken to be constant. The temperature distribution is derived from first law of thermodynamics by solving energy equation, with a general thermal and mechanical boundary conditions on the inside and outside surfaces. Heat conduction and Navier equations are solved analytically by choosing elliptic cylinder coordinates system and the results are shown for displacement and stress components along the radial direction.

Mechanical and Thermal Stresses in a FGPM Hollow Cylinder due to Radially Symmetric Loads

The general solution of steady-state on one-dimensional Axisymmetric mechanical and thermal stresses for a hollow thick made of cylinder Functionally Graded porous material is developed. Temperature, as functions of the radial direction with general thermal and mechanical boundary-conditions on the inside and outside surfaces. A standard method is used to solve a nonhomogenous system of partial differential Navier equations with nonconstant coefficients, using complex Fourier series, rather power functions method and solve the heat conduction. The material properties, except poisson's ratio, are assumed to depend on the variable , and they are expressed as power functions of .

Analytical and numerical analysis for the FGM thick sphere under combined pressure and temperature loading

Thermo-mechanical analysis of functionally graded hollow sphere subjected to mechanical loads and one-dimensional steady-state thermal stresses is carried out in this study. The material properties are assumed to vary non-linearly in the radial direction, and the Poisson’s ratio is assumed constant. The temperature distribution is assumed to be a function of radius, with general thermal and mechanical boundary conditions on the inside and outside surfaces of the sphere. In the analysis presented here, the effect of non-homogeneity in FGM thick sphere was implemented by choosing a dimensionless parameter, named βi (i = 1, . . . , 3), which could be assigned an arbitrary value affecting the stresses in the sphere. It is observed that the solution process for βi(i = 3) = −1 are different from those obtained for other values of βi (i = 1, . . . , 3). Cases of pressure, temperature, and combined loadings were considered separately. It is concluded that by changing the value of βi (i = 1 . . . 3), the properties of FGM can be so modified that the lowest stress levels are reached. The present results agree well with existing results. Using FEM simulations, the analytical findings for FGM spheres under the influence of internal pressure and temperature gradient were compared to finite element results.

Magnetothermoelastic analysis of functionally graded hollow spherical structures under thermal and mechanical loads

The exact solution for the one-dimensional steady-state magnetothermoelastic stresses and perturbation of magnetic field vector in a FGM (functionally graded material) hollow sphere is presented. The material properties are assumed to depend on the variable r and they are expressed as power functions of r. The values used in this study are arbitrary chosen to demonstrate the effect of inhomogeneity on magnetothermoelastic stresses and perturbation of magnetic field vector distributions of the FGM hollow sphere. The direct method is used to solve the heat conduction and Navier equations. The results carried out may be used as a reference to solve other magnetothermoelastic problems in FGM hollow spherical structures and to design optimum FGM hollow spherical structures.

One-Dimensional Moving Heat Source in a Hollow FGM Cylinder

This paper presents the analytical solution of one-dimensional mechanical and thermal stresses for a hollow cylinder made of functionally graded material. The material properties vary continuously across the thickness, according to the power functions of radial direction. Temperature distribution is symmetric and transient. The thermal boundary conditions may include conduction, flux, and convection for inside or outside of a hollow cylinder. The thermoelasticity equation is transient, including the moving heat source. The heat conduction and Navier equations are solved analytically, using the generalized Bessel function. A direct method of solution of Navier equation is presented.

Single shot Hugoniot of cyclohexane using a spatially resolved laser driven shock wave

To develop a more efficient method of determining pressure dependent material response to shock loading, we used the spatial energy distribution of a shock generating laser beam to create a range of nearly one-dimensional stresses in a single laser shot. Ultrafast dynamic ellipsometry was used to measure the Hugoniot and shocked refractive index of cyclohexane subject to this shock loading.

A magnetoelasticity instrument for testing the mechanical properties of ferromagnetic materials

Magnetoelasticity noise is the electromagnetic energy and sound energy released at the surface of ferromagnetic materials due to the movement of the magnetic domain walls inside the material when the material is magnetized by an alternating magnetic field. The electromagnetic energy and sound energy are released simultaneously and interact with each other. These energies carry many characteristics of the material, such as the electromagnetic character, the mechanical character, the material character, etc., and thus can be used to test these characteristics of the material. Based on this theory, an instrument for testing the stresses in ferromagnetic materials is developed in this article. The theory and the structure of the instrument are introduced. The experiment for testing the one-dimensional and two-dimensional stresses in ferromagnetic materials and the analysis of the fatigue damages are carried out. It is a portable instrument and can be used on the field. The outcomes of the test fit quite well with those obtained by the x-ray method.

The propagation of thermal stresses in an infinite elastic slab

In this paper, the one-dimensional dynamic thermal stresses in an infinite elastic slab is considered. The system of fundamental equations is solved by means of a finite difference method and evaluate numerically the stress for steel at a fixed time t and for different values of x. The results are presented in graphical form, which demonstrate a discontinuity in the stress.

Mechanical and thermal stresses in a functionally graded hollow cylinder due to radially symmetric loads

In this paper, a general analysis of one-dimensional steady-state thermal stresses in a hollow thick cylinder made of functionally graded material is developed. The temperature distribution is assumed to be a function of radius, with general thermal and mechanical boundary conditions along the inside and outside surfaces. The material properties, except Poisson's ratio, are assumed to depend on variable the r and they are expressed as power functions of r. The direct method is used to solve the heat conduction and Navier equations.

Non-linear one-dimensional continuum damage theory

The background of Non-Linear Continuum Damage Mechanics is presented for the case of one-dimensional tensile stresses. A brief critical analysis of the existing methods of non-linear damage models construction is given. A new approach to the damage theory development based on the “separability” principle is suggested. The condition of non-linearity and the criterion of long-term failure are formulated. The non-linear damage constitutive equations for static and cyclic loading, allowing one to take into account the loading history, are proposed on this basis. Within the framework of the approach suggested the problems of total and residual lifetime calculation under additional loads and partial unloads are solved. The predictions are compared with experimental data obtained using some particular heat-resistant materials.

INERTIAL EFFECTS OF A TRANSIENT THERMOELASTIC PROBLEM IN A THICK PLATE WITH AN AXISYMMETRIC TEMPERATURE

Abstract This paper concerns an axisymmetric dynamic treatment of a three-dimensional thermoelastic problem in a thick plate that is exposed to the temperature of surrounding medium depending on the position and time. In the present investigation, the Laplace transform and the convolution theorem are used, and an exact solution that is valid for the whole time interval without approximation is obtained. The thermal stresses are compared with the corresponding quasi-static stresses and the corresponding one-dimensional stresses.