Hoop Stress

Deep induction hardening has been performed on two batches of smooth cylindrical specimens with a hardening depth respectively around 2 mm and 3 mm. The distributions of axial and circumferential residual stresses are analysed for the two specimen batches by X-ray diffraction technique. The radial normal stress field is estimated through the use of the well known Moore and Evans correction. Finally, the experimental residual stresses are compared with those obtained from a multiphysic finite element modelling of the whole induction treatment process, including electromagnetic, thermal, metallurgical and mechanical phenomena. The simulated residual stress field is in good agreement with X-ray analysis especially at depths lower than one-tenth the specimen diameter. At deeper depths, a correction of the experimental X-ray analysis has been done to obtain realistic values.

Newton's law of visocosity is a commonly used constitutive theory for deviatoric Cauchy stress tensor. In this constitutive theory originally constructed based on experimental observation, the deviatoric Cauchy stress is proportional to the symmetric part of the velocity gradient tensor. The constant of proportionality is the viscosity of the fluid. For all continuous media if the deforming matter is in thermodynamic equilibrium then all constitutive theories including those considered here must satisfy conservation and balance laws. It is well known that only the second law of thermodynamics provides possible conditions or mechanisms for deriving constitutive theories. The constitutive theory for deviatoric stress tensor used here can be shown to be a simplified form of the constitutive theory derived using conditions resulting from the entropy inequality in conjunction with the theory of generators and invariants that contains up to fifth degree terms in the components of the symmetric part of the velocity gradient tensor. In general the constitutive theory for deviatoric stress tensor is basis (covariant, contravariant, or Jaumann) dependent as it uses convected time derivatives of the Green and Almansi strain tensors of orders higher than one. However, the first convected time derivative of the Green and Almansi strain tensors are in fact symmetric part of the velocity gradient tensor which is basis independent. Thus, if the constitutive theory for deviatoric Cauchy stress tensor is only dependent on the symmetric part of the velocity gradient tensor, then it is basis independent. This is the case for the theory presented in this paper. In this paper we limit the constitutive theory for deviatoric Cauchy stress tensor to contain only up to quadratic terms in the components of the symmetric part of the velocity gradient tensor. The objective is to study the resulting flow physics due to the constitutive theory for deviatoric Cauchy stress tensor that contains up to quadratic terms in the velocity gradient tensor. Model problems consisting of fully developed flow between parallel plates, square lid-driven cavity, and asymmetric sudden expansion are used to present numerical solutions. Numerical solutions of the model problems are calculated using least squares finite element formulation based on residual functional in which the local approximations are considered in higher order scalar product spaces that permit higher order global differentiability solutions. Nonlinear system of algebraic equations are solved using Newton's linear method with line search.

This paper presents an alternative approach to constructing computer experiment designs based on stochastic process theory, specifically marked point processes with two types. The originality of this method lies in the use of Markov Chain Monte Carlo (MCMC) techniques, combined with the Metropolis-Hastings algorithm and a new dynamic called local shift dynamics. These tools enable the generation of highly flexible and adaptable experimental designs, which can be tailored to a variety of specific objectives according to experimental needs. Special attention has been given to analyzing the convergence of the Markov chain, thus ensuring the robustness and efficiency of the results obtained. Additionally, a comparative study was conducted to position our method relative to other existing computer designs. This comparison highlights the advantages and disadvantages of our approach in terms of modularity and performance.

The design and optimization of pressure vessels in boiler applications play a crucial role in the efficient performance of boilers. This paper presents a comprehensive study of the efficient design of pressure vessels for improved boiler performance. The study includes an analysis of the current design trends, materials, and manufacturing techniques used in pressure vessel design for boiler applications. Additionally, the study explores the various optimization techniques and software tools available for improving the design of pressure vessels. The optimization techniques studied include Taguchi method, response surface methodology, and genetic algorithms. The software tools analyzed include ANSYS, ABAQUS, and COMSOL Multiphysics. The study concludes with a summary of the best practices for designing and optimizing pressure vessels for improved boiler performance. The results of this study will be useful to design engineers, researchers, and manufacturers involved in the design and optimization of pressure vessels for boilers.

Autofrettage is a procedure performed to improve the durability of high pressure components. The main aim of this thesis work was to analyse the effect of autofrettage on the valve house of the cutting head assembly of a water jet cutting machine. As the stepping stone, a thick pipe, as a typical example of pressure vessels, was employed in order to study autofrettage process and its effects. Afterward, the adopted approach was applied on the valve house. Eventually, the results showed that this procedure leads to a tangible decrease in the maximum value of stress.

Background: Successful bone ingrowth around cementless implants requires adequate initial stability. Hoop stress fractures during stem insertion can potentially hinder prosthesis stability. Hypothesis: We hypothesized that an oversized radial head prosthetic stem (1 mm ''too large'' and causing a hoop stress fracture during insertion) would result in an unacceptable amount of micromotion. Materials and methods: Grit-blasted radial head prosthetic stems were implanted into cadaveric radii. Rasp and stem insertion energies were measured, along with micromotion at the stem tip. The sizes were increased until a fracture developed in the radial neck. Results: Prosthetic radial head stems that were oversized by 1 mm caused small cracks in the radial neck. Micromotion of oversized stems (42 AE 7 mm) was within the threshold conducive for bone ingrowth (<100 mm) and not significantly different from that for the maximum sized stems (50 AE 12 mm) (P ! .4). Discussion: Contrary to our hypothesis, hoop stress fractures caused by implantation of a stem oversized by 1 mm did not result in loss of stability. Stem micromotion remained within the range for bone ingrowth and was not significantly diminished after the fracture. This suggests that if a crack occurs during the final stages of stem insertion, it may be acceptable to leave the stem in place without adding a cerclage wire. Conclusion: A small radial neck fracture occurring during insertion of a radial head prosthetic stem oversized by 1 mm does not necessarily compromise initial stability.

Experimental investigation on the damage and wave propagation characteristics in PVB laminated glass panels subjected to impact loading was conducted. By applying different impact energies, the effect of two projectile configurations, a wooden post and steel ball, was studied. The effect of impact location was also investigated. The dynamic response of the panels was measured at different locations on the test panels using strain gauges. Damage and transient response and wave propagation characteristics of test panels were reported and compared. The results showed that flexural wave was the predominant wave in the response. In addition, in-plane compressive wave was also observed. It was also shown that while the projectile contact area affected the maximum transient response and crack propagation characteristics, it had a limited effect on the perforation threshold. For panels impacted at the corners, coupled strain waves were created by wave reflection processes when the waves reached the panel boundaries. Moreover, the impact velocity had a pronounced effect on peak strain and strain rates of test panels.

In this study the stress behavior of buried pipes in cohesionless soil was investigated experimentally. The parameters investigated in the laboratory tests include embedment ratio of pipe, horizontal distance of pipe to footing and the position of pipe. Hoop stresses at four positions on the borders of the pipes were measured by strain gauges. The results indicated that a significant increase in bearing capacities and decrease in pipe hoop stress when embedment ratio of pipe and horizontal distance of pipe to footing were increased. Based on the results of the laboratory model tests, the embedment ratio of pipe and the position of pipe are the main parameters that affect the hoop stresses on pipe.

In this paper, a numerical solution using finite difference method is provided to evaluate the thermo-elasto-plastic behavior of nonuniform thickness rotating annular discs made of functionally graded materials (FGMs). The plane stress geometrical conditions are considered and the disc is assumed to be composed of three layers that are perfectly-bonded. The inner layer is metallic and the outer layer is ceramic, whereas the intermediate layer is chosen to form FGM. The material properties of the intermediate layer are assumed to vary in the radial direction according to a power-law. The stress-strain model of the disc material and von Mises yielding criterion are considered in order to evaluate the elasto-plastic behaviour. For validating the proposed approach, the obtained results are compared with others available in the literature and satisfactory agreements are acquired. Finally, the effects of various geometrical and operational parameters on the thermo-elasto-plastic behavior ...

Multiple fiber-bridged matrix cracks in an unidirectionally reinforced, off-axis, ceramic matrix composite is modeled using a combination of a displacement based finite element scheme and an eigen function expansion method. All cracks are considered to run parallel to the horizontal axis, the load is applied vertically, and all fibers are oriented at an angle ϕ about the horizontal direction. It

Analytical solution to thermoelastic response of a long rod (solid cylinder) subjected to periodic boundary condition is derived. The solution to the heat conduction equation is obtained by the application of Duhamel&#39;s theorem. Manipulating on the basic equations of elasticity, the governing equation describing thermoelastic behavior of the solid cylinder is formulated in terms of the radial displacement. This equation turns out to be of type nonhomogeneous second order Cauchy-Euler. The distributions of thermally induced stress, strain and displacement are determined by the analytical solution of the governing equation. Two different periodic boundary conditions are handled. In the first, the boundary temperature is assumed to vary sinusoidal, and in the second vary periodic but decaying eventually to zero.

In the present paper double-diffusive convection, taking into account Coriolis effects, in a horizontal layer of Brinkman-anisotropic bi-disperse porous medium is analysed. Via linear instability analysis, we found that convection can set in through stationary or oscillatory motions and the critical Rayleigh numbers for the onset of stationary secondary flow (steady convection) and overstability (oscillatory convection) are determined.

Simple structural surfaces (SSS) method of analysis is comparatively easy to understand. This technique may be used as a preliminary step to carry out Finite Element Analysis. This method is particularly useful in assessing possible applied load paths. Finite element analysis (FEA) involves solution of engineering problems using computers. Finite element method provides a high level of accuracy for many types of load case and can even give a reasonable prediction of accident damage. Now a day's there are various computational solvers used for analysis. In this paper only review for element type used, constraint used, load and boundary conditions which used for static strength analysis of floor of passenger car that is pre-processing step in finite element method. This paper will help for how pre-processing is done in static stiffness analysis of the car body.

In this study, the fatigue behavior of (±55°) 3 filament wound composite pipes with a surface crack under alternating internal pressure has been investigated. Glass reinforced plastic (GRP) pipes were made of E-glass/epoxy and tested in an open-ended condition. For this study, a PLC controlled hydraulic test stand has been established. Test specimens have antisymmetric six layers which have ±55°winding angles. Fatigue tests of the pipes with a surface crack which have notch aspect ratio a/c = 0.2 and notch-to-thickness ratios a/t = 0.25, 0.38 and 0.50 in the axial direction have been carried out in accordance with ASTM D-2992. This standard allows a frequency of 25 cycles per minute and an R = 0.05 stress ratio. Tests have been performed at three different maximum stress levels, which were 50%, 40% and 30% of the ultimate hoop stress. Final failure of the GRP pipes has been examined and fatigue test results are presented by means of (S-N) curves and delamination damage zone area-cycle (A-N) curves.

In recent years, most of the sectors replace conventional materials with aluminium matrix materials. Various mechanical studies have been done, such as tensile, impact, flexural, and hardness. For the same geometrical parameters of the steel pressure vessel, FE Analysis of Structural Steel pressure vessel is carried out, and stresses for internal pressures are determined. And the Geometric Modelling is carried out in design software solid works and analyse in ANSYS workbench. The Structural analysis of pressure vessel was carried out. The validation for Hoop stress, Longitudinal stress& Maximum shear stress was done. Cylindrical pressure vessels are widely used for commercial, under water vehicles and in aerospace applications. And the Geometric Modelling is carried out in solid works. And analysed in ANSYS Workbench. The Comparison has done between FEM results and Theoretical results for Validation purposes. The Calculations for Hoop Stress, Longitudinal Stress & Maximum Shear Stress was Calculated for theoretical. The boundary conditions and dimensions for Modelling of a Pressure vessel was taken from the paper and same Boundary conditions was applied for analysis purposes. For Structural steel the design is safe because the stress value is within range of yield strength. The Material properties used are structural properties of steel for the analysis Purposes.

This document provides a learning module on tempered safety glass. In this activity, instructors demonstrate the fracture toughness of tempered glass, thereby illustrating how the glass is toughened and introducing the concept of the fractography of glass. It can be used in classrooms from elementary to college levels

High-velocity impact onto a layered glass target produces a very extensive damage pattern exhibiting many distinct morphologies. Material around the penetration cavity is finely comminuted. Under the arrested projectile, the glass is largely intact with spokelike fracture regions. Around the projectile cavity, needle fragments are formed; they are radial in outer layers and circumferential in inner layers. Extensive radial cracks occur in all layers, but the spacing and frequency of transverse fractures change in each layer. Damage from radial cracks also progresses from being hoop-stress-induced to flexural-induced through the depth of the target. Fan and dicing cracks occur near the periphery of the target. Mesoscale damage features include conventional mist and hackle markings indicating very fast cracks. The map of damage presented herein should be a valuable reference for attempts to model impact damage of glass.

Given a discret subgroup Γ ⊂ P SL(3, C), we determine the number of complex lines and complex lines in general position lying in the complement of: maximal regions on which Γ acts properly discontinuously, the Kularni's limit set of Γ and the equicontinuity set of Γ. We also provide sufficient conditions to ensure that the equicontinuity region agrees with the Kulkarni's discontinuity region and is the largest set where the group acts properly discontinuously and we provide a description of he respective limit set in terms of the elements of the group.

Filament wound hybrid composite pipes can expose to impact loading from various causes during their service life which can cause an invisible level of damage. Thus, revealing the effect of impact damage gains great importance to design hybrid composite pipes with enhanced damage tolerance. Based on this motivation, the low velocity impact (LVI) response of carbon/glass hybrid filament wound composite pipes has been studied. Hybrid pipes were produced with the winding angle of ± 55°by using glass and carbon fiber layers in various stacking sequences by filament winding method. The stacking sequence configurations were set as Carbon/ Glass/Glass (CGG), Glass/Carbon/Glass (GCG) and Glass/Glass/Carbon (GGC). Before generating impact damage, an internal pressure of 32 bar was applied to the hybrid pipes in accordance with ANSI/AWWA C950 standard and pre-stress was generated in the pipes. Following, the hybrid pipes subjected to internal pressure were subjected to low velocity impact tests at energy levels of 5, 10, 15 and 20 J. The variation of contact force versus time, contact force versus displacement and energy versus time were obtained. After the testing, the effects of stacking sequence upon damage formation and damage progression under LVI loading have been evaluated based on the obtained data and microscopic analysis. It has been found that the damage formation such as matrix cracking on outer/inner surfaces, radial cracks, delamination, transfer cracks, splitting and leakage can take place. Moreover, the hybrid pipes with CGG stacking represents higher impact resistance while the GCG stacking has a better response of damage formation since this stacking does not show leakage damage.

This paper presents the review related guideline in transient thermal analysis for top head nozzle of crack gas drier. Crack gas drier in which gases of high pressure and temperature are admitted through nozzle. When these gases are admitted then due to fluctuation of temperature and pressure there is some cracks/failures are developed in nozzle which cause damage of nozzle and reduce the life of pressure vessel. So for designing crack gas dryer this cracks/failure should be minimized. The different analysis FE methods are used for reducing the cracks/failure in crack gas dryer. By using different methods different result are obtained. In this review which method gives optimum parameters are discussed.

This paper presents an investigation into the effect of reinforcing a Plexiglas tube with fiberglass/epoxy threads wound at different angles This paper shows an experimental analysis approach to find the ultimate failure pressure of these vessels. The propert1es of the Plexiglas, fiberglass, orientation (wind) angle and the matrix were taken into account to detennine thetr effects on the ultimate failure pressure of the vessels Mandrels were wound at ±75, ±65, and ±55 degrees, and specimen were cut out from each to 19.05 centimeters long, 7 62 centimeter inner diameter and outer diameters dependent of the wind angle. The composite materia] used is an E-type Fiberglass and Epoxy Laminating Systems EZ-10 epoxy with EZ-83 hardener. The Dura-Wound Inc. Cobra Filament Winding Machine was used to wind the specimens The specimens were tested \\ith a hydrostatic test-rig to analyze the ultimate failure pressure and fat lure modes. An INSTRON machine was used to test the specimens under compression to dctennine the Young's modulus and Poisson's ratio. The experimental results mdtcate that the wind angle affects the mechanical properties and has strong effects on the failure modes of the reinforced vessels. The failure mode however does not differ by varymg the wmd angle.

The main objective of the present paper is to show an effect of pressure-dependency of the yield criterion on the development of the plastic zone and the distribution of residual stresses in a thin annular disk subject to a pressure over its inner edge during the loading stage. The Drucker–Prager yield criterion is adopted to account for the effect of the hydrostatic pressure on plastic yielding. The state of stress is supposed to be plane and the material model is perfectly plastic. A semi-analytical stress solution to the problem formulated is given and its qualitative features are emphasized. It is shown that the pressure at which plastic yielding starts and the pressure at which the entire disk becomes plastic are weakly affected by the pressure-dependency of the yield criterion. On the other hand, this dependency has a significant effect on the maximum possible pressure that can be supported by the disk. The minimum pressure at which reverse yielding occurs is also affected by ...

Deep induction hardening has been performed on two batches of smooth cylindrical specimens with a hardening depth respectively around 2 mm and 3 mm. The distributions of axial and circumferential residual stresses are analysed for the two specimen batches by X-ray diffraction technique. The radial normal stress field is estimated through the use of the well known Moore and Evans correction. Finally, the experimental residual stresses are compared with those obtained from a multiphysic finite element modelling of the whole induction treatment process, including electromagnetic, thermal, metallurgical and mechanical phenomena. The simulated residual stress field is in good agreement with X-ray analysis especially at depths lower than one-tenth the specimen diameter. At deeper depths, a correction of the experimental X-ray analysis has been done to obtain realistic values.

Emanating from the Boltzmann transport equation, a newly developed C-and F-processes heat conduction constitutive model and the associated dynamic thermoelasticity are described. The model acknowledges the notion of the simultaneous coexistence of both the slow Cattaneo-type C-processes and fast Fourier-type F-processes in the mechanisms of heat conduction. The formulation leads to a generalization of the macroscale in space one temperature theory for heat conduction in solids of the Jeffreys-type model, Cattaneo model, and the Fourier model for heat conduction in solids. This is unlike the Jeffreys-type phenomenological model which cannot reduce to the classical Fourier model (but only to a Fourier-like representation with relaxation), and the Jeffreys-type model cannot explain the underlying physics associated the C-and F-processes model. A generalized thermoelastic theory is described to study the dynamic thermoelastic behavior of solids with special features which can explain the classical and nonclassical dynamic thermoelastic theories. R.B. Hetnarski (ed.

Initial and subsequent yield surfaces for 6061 aluminum, determined by a method of automated yield stress probing, are presented in the 2D (r zz À r hz ) and 3D (r hh À r zz À r hz ) stress spaces. In the (r zz À r hz ) space, yield surfaces at small pre-strains show the noses and unapparent cross effect. At larger pre-strains, they become ellipses with positive cross effect. In the (r hh À r zz À r hz ) space, the initial yield surface is not well described by von Mises yield criterion due to material anisotropy. The yield surfaces of various torsional pre-strains show obvious rotation around the r zz axis but they do not rotate when subjected to axial pre-strains. Therefore, the rotation behavior of yield surface is pre-strain path dependent. The rotation of yield surfaces in the 3D space is the emphasis of the present paper. Coupled axial-torsional behavior subjected to torsion after axial pre-strain are also presented for the same material that is used to determine the yield surfaces. This information is useful for verification of constitutive models.

An anisotropic quadratic form of plastic strain increment is used to define the intrinsic time in the endochronic theory of plasticity. Based on this new definition, a yield function can be derived. This new version of endochronic theory can describe the expansion, translation, rotation, and distortion of the yield surface. While the initial yielding is in the form of the Mises yield criterion, the distortion of subsequent yield surfaces is expressed by the compression or sl:retching of the Mises yield surface. The effect of sharp front and blunt rear of the yield surface is considered to be of secondary importance and neglected in the interest of keeping the equations simple. This idealization will not much affect the prediction power of the model, because the plastic strain increment is in the radial direction emanating from the center of the current yield surface and is not normal to the current yield surface. In this theory, the plastic deformation is thus not sensitive to the exact shape of the yield surface. It has been shown that the proposed theory is capable of describing the experimental results of three different metals considered. The test series investigated include several different paths of prestress.

The direct detection of gravitational waves will provide valuable astrophysical information about many celestial objects. The SCHENBERG has already undergone its first test run. It is expected to have its first scientific run soon. In this work a new data analysis approach is presented, called method of independent bars, which can be used with SCHENBERG&#39;s data . We test this method through the simulation of the detection of gravitational waves. With this method we find the source&#39;s direction without the need to have all six transducers operational. Also we show that the method is a generalization of another one, already described in the literature, known as the mode channels method.

Residual stress is ubiquitous and indispensable in most biological and artificial materials, where it sustains and optimizes many biological and functional mechanisms. The theory of volume growth, starting from a stress-free initial state, is widely used to explain the creation and evolution of growthinduced residual stress and the resulting changes in shape, and to model how growing bio-tissues such as arteries and solid tumors develop a strategy of pattern creation according to geometrical and material parameters. This modelling provides promising avenues for designing and directing some appropriate morphology of a given tissue or organ and achieve some targeted biomedical function. In this paper, we rely on a modified, augmented theory to reveal how we can obtain growth-induced residual stress and pattern evolution of a layered artery by starting from an existing, non-zero initial residual stress state. We use experimentally determined residual stress distributions of aged bi-layered human aortas and quantify their influence by a magnitude factor. Our results show that initial residual stress has a more significant impact on residual stress accumulation and the subsequent evolution of patterns than geometry and material parameters. Additionally, we provide an essential explanation for growth-induced patterns driven by differential growth coupled to an initial residual stress. Finally, we show that initial residual stress is a readily available way to control growth-induced pattern creation for tissues and thus may provide a promising inspiration for biomedical engineering. Many bio-tissues, such as arteries, heart, brain, intestine and some tumors, are under significant levels of residual stresses in vivo and also once unloaded . Residual stresses are used for maintaining a self-balanced state, by transferring physical signals and regulating some specific bio-functions . It is fair to say that healthy biological performances rely heavily on appropriate levels of residual stress. Hence, a greater understanding of the role played by residual stress can lead to better design of mechanical, electrical, chemical, biological and internal environments for living organisms. In biology, residual stress is widely accepted as the result of growth and remodelling processes or of other, more involved bio-interactions. Physically, by referring to the multiplicative decomposition (MD) method of plasticity theory, and by decomposing the overall growth process into two separate parts, Rodriguez et al. were able to simulate the growth process and to explain growth-induced residual stress. The former step refers to the mass accumulation and incompatibility creation processes within two stress-free states called unconstrained growth; the later step refers to residual stress creation and compatibility restoration processes called elastic deformation. This MD model illuminates many related mathematical and mechanical studies on the growth of artery, brain, intestine, etc. . Moreover, the influence of growth factors, including differential growth extent, volume change rate, and/or growth velocity, on residual stress distribution, pattern creation and evolution has also been analysed with the MD model . Nonetheless, there still remain some limitations for this model due to its assumption that both the initial configuration and the natural configuration (or virtual configuration 21 ) remain stress-free states during the unconstrained growth process. As discussed by Johnson et al. , for residually stressed materials the stress-free state is an entirely discrete state made of a collection of nearly infinitesimal volumes, which is unattainable in practice

Many interesting shapes appearing in the biological world are formed by the onset of mechanical instability. In this work we consider how the build-up of residual stress can cause a solid to buckle. In all past studies a fictitious (virtual) stress-free state was required to calculate the residual stress. In contrast, we use a model which is simple and allows the prescription of any residual stress field. We specialize the analysis to an elastic tube subject to a two-dimensional residual stress, and find that incremental wrinkles can appear on its inner or its outer face, depending on the location of the highest value of the residual hoop stress. We further validate the predictions of the incremental theory with finite element simulations, which allow us to go beyond this threshold and predict the shape, number and amplitude of the resulting creases.

Rubber components and soft tissues are often subjected to large bending deformations &quot;in service&quot;. The circumferential line elements on the inner face of a bent block can contract up to a certain critical stretch ratio lambda_cr (say) before bifurcation occurs and axial creases appear. For several models used to describe rubber, it is found that lambda_cr = 0.56, allowing for a 44% contraction. For models used to describe arteries it is found, somewhat surprisingly, that the strain-stiffening effect promotes instability. For example, the models used for the artery of a 70 year old human predict that lambda_cr = 0.73, allowing only for a 27% contraction. Tensile experiments conducted on pig skin indicate that bending instabilities should occur even earlier there.

Within the context of finite deformation elasticity theory the problem of deforming an open sector of a thick-walled circular cylindrical tube into a complete circular cylindrical tube is analyzed. The analysis provides a means of estimating the radial and circumferential residual stress present in an intact tube, which is a problem of particular concern in dealing with the mechanical response of arteries. The initial sector is assumed to be unstressed and the stress distribution resulting from the closure of the sector is then calculated in the absence of loads on the cylindrical surfaces. Conditions on the form of the elastic strain-energy function required for existence and uniqueness of the deformed configuration are then examined. Finally, stability of the resulting finite deformation is analyzed using the theory of incremental deformations superimposed on the finite deformation, implemented in terms of the Stroh formulation. The main results are that convexity of the strain energy as a function of a certain deformation variable ensures existence and uniqueness of the residually-stressed intact tube, and that bifurcation can occur in the closing of thick, widely opened sectors, depending on the values of geometrical and physical parameters. The results are illustrated for particular choices of these parameters, based on data available in the biomechanics literature.

The generalized coupled thermoelasticity based on the Lord-Shulman (LS) model that admits the second sound effect is considered to study the dynamic thermoelastic response of functionally graded annular disk. The disk material is considered to be graded along the radial direction, where a power law distribution is assumed. The thermal and mechanical waves propagation are investigated applying a sudden thermal exposure to the boundary. The Laplace transform is used to transform the governing equations into the Laplace domain, where the Galerkin finite element method is employed to solve the system of equations in space domain. Finally, the numerical inversion of the Laplace transform is used to obtain the actual physical quantities in the time domain. The time dependent temperature, radial displacement, radial stress, and hoop stress are plotted.

Simple structural surfaces (SSS) method of analysis is comparatively easy to understand. This technique may be used as a preliminary step to carry out Finite Element Analysis. This method is particularly useful in assessing possible applied load paths. Finite element analysis (FEA) involves solution of engineering problems using computers. Finite element method provides a high level of accuracy for many types of load case and can even give a reasonable prediction of accident damage. Now a day's there are various computational solvers used for analysis. In this paper only review for element type used, constraint used, load and boundary conditions which used for static strength analysis of floor of passenger car that is pre-processing step in finite element method. This paper will help for how pre-processing is done in static stiffness analysis of the car body.

Simple structural surfaces (SSS) method of analysis is comparatively easy to understand. This technique may be used as a preliminary step to carry out Finite Element Analysis. This method is particularly useful in assessing possible applied load paths. Finite element analysis (FEA) involves solution of engineering problems using computers. Finite element method provides a high level of accuracy for many types of load case and can even give a reasonable prediction of accident damage. Now a day's there are various computational solvers used for analysis. In this paper only review for element type used, constraint used, load and boundary conditions which used for static strength analysis of floor of passenger car that is pre-processing step in finite element method. This paper will help for how pre-processing is done in static stiffness analysis of the car body.

The Korteweg-de Vries equation models unidirectional propagation of small finite amplitude long waves in a non-dispersive medium. The well-posedness, that is the existence, uniqueness of the solution, and continuous dependence on data, has been studied on unbounded, periodic, and bounded domains. This research focuses on an initial and boundary value problem (IBVP) for the Kortewegde Vries (KdV) equation posed on a bounded interval with general nonhomogeneous boundary conditions. Using Kato smoothing properties of an associated linear problem and the contraction mapping principle, the IBVP is shown to be locally well-posed given several conditions on the parameters for the boundary conditions, in the L 2 -based Sobolev space H s (0, 1) for any s ≥ 0.

An extensive parametric study on the variation of the centrifugal-force-induced stress and displacements with the inhomogeneity indexes, profile parameters and boundary conditions is conducted based on the author's recently published analytical formulas for radially functionally power-law graded rotating hyperbolic discs under axisymmetric conditions. The radial variation of the thickness of the disc is chosen to obey a hyperbolic function defined either convergent or divergent. In the present work, contrary to the published one, it is assumed that both Young's modulus and density radially vary with the same inhomogeneity index to enable to conduct a parametric study. Under this additional assumption, for the values of the chosen powerlaw indexes 5, 0, 5

Introduction: Broken glass exhibits unique fracture patterns depend upon the nature of the impact. The fracture patterns provide information like point and angle of impact, direction of force and sequence of firing. Recent studies have shown that the use of shotgun in Malaysia is increasing, yet, the relationship existing among the fracture pattern and the projectile impact factors are not well documented. The objective was to analyse the fracture characteristics on different glass types of variable thickness and distance made by shotgun ammunition. Methods: Soda lime and tempered glass panel with dimension of 12’x 12’ with 3 or 4 mm thickness were shot from various distances of 4, 6 and 8 m from the muzzle end of the shotgun. Samples were analysed under fixed parameters and observations were recorded. Results: It is found that the bullet hole diameter of 4 mm tempered glass were larger compared to 4 mm soda lime glass ranged from 14.33 to 24.17 cm as distance increased. Tempered gl...

In this paper, the analytical and numerical solutions for rotating variable-thickness solid disk and numerical solution for rotating variable-thickness annular disk are presented. The outer edge of the solid disk and the inner and outer edges of the annular disk are considered to have clamped boundary conditions. Two different cases for the radially varying thickness of the solid and annular disks are given. The numerical solution as well as the analytical solution is available for the first case of the solid disk while the analytical solution is not available for the second case of the annular disk. Both analytical and numerical results for displacement and stresses will be investigated for the first case of radially varying thickness. The accuracy of the present numerical solution is discussed and its ability of use for the second case of radially varying thickness is investigated. Finally, the distributions of displacement and stresses will be presented and the appropriate comparisons and discussions are made at the same angular velocity.

An analytical, numerical and experimental investigation was carried out to determine fracture criteria for piezoceramics with poling parallel and perpendicular to the crack faces. The asymptotic expressions of stress, strain, electric flux density and electric fields were derived. For a piezoelectric material, in addition to the usual three modes of fracture, there is a fourth mode associated with the electric field. The asymptotic expressions were used for determining the energy release rate and extending a conservative interaction energy or M-integral for calculating the intensity factors associated with piezoelectric material for energetically consistent boundary conditions on the crack faces. Tests were performed on four-point bend PZT-5H fracture specimens with the poling direction parallel to the crack faces. The specimens were analyzed numerically by means of the finite element method. Finally, a mixed mode fracture criterion for piezoelectric ceramics was developed. This cri...

In this work, we constructed the equations of generalized thermoelasticity of a homogeneous isotropic hollow cylinder. The formulation is applied in the context of the Green and Naghdi theory of types II and III. The material of the cylinder is assumed to be homogeneous isotropic both mechanically and thermally. The problem has been solved numerically using a finite-element method. Numerical results for the temperature distribution, displacement, radial stress, and hoop stress are represented graphically. Comparisons are made with the results predicted by the types II and III. The results obtained in this paper can be used to design various homogeneous thermoelastic elements under thermal load to meet special engineering requirements.

Limit elastic analysis of a functionally graded (FG) rotating disk with material grading based on modified rule of mixture (MROM) is reported in the present study. In MROM, stress to strain transfer ratio (q) is an unknown parameter which restricts the application of MROM as yield strength estimation of a material depends on this ratio. Till now the determination of stress to strain transfer ratio, which varies with size, shape, manufacturing processes and composition, is reported by means of experiments. In current work, the effective Young's modulus is calculated by two means i.e. MROM and Halpin-Tsai. Later stress to strain transfer ratio is quantified using MROM using inverse approach and then effective yield stress variation of FGM has been calculated. Different combinations of metal matrix ceramic reinforced FG material were selected. Metals having high strength to weight ratio were combined with non-oxide ceramics of low density. Variational formulation method has been employed to solve the elasticity problem of the rotating disk taking radial displacement field as unknown variable and best material combination is proposed on the basis of maximum limit elastic speed obtained.

Given a discret subgroup Γ ⊂ P SL(3, C), we determine the number of complex lines and complex lines in general position lying in the complement of: maximal regions on which Γ acts properly discontinuously, the Kularni's limit set of Γ and the equicontinuity set of Γ. We also provide sufficient conditions to ensure that the equicontinuity region agrees with the Kulkarni's discontinuity region and is the largest set where the group acts properly discontinuously and we provide a description of he respective limit set in terms of the elements of the group.

General 2D boundary value problems of piezoelectric nano-sized structures with cracks under a thermal load are analyzed by the finite element method (FEM). The size-effect phenomenon observed in nano-sized structures is described by the strain-gradient effect. The strain gradients are considered in the constitutive equations for electric displacement and the high-order stress tensor. For this model, the governing equations and the corresponding boundary conditions are derived using the variational principle. Uncoupled thermoelasticity is considered; thus, the heat conduction problem is analyzed independently of the mechanical fields in the first step. The veracity of the derived formulations and their implementation into the finite element scheme is demonstrated by some numerical examples.

S 3 o w a k l u c z o w e: monokryszta3y ferroelektryczne, wspó3czynniki piezoelektryczne, odkszta3cenia, dyfrakcja rentgenowska, pomiary. S t r e s z c z e n i e Przedstawiono procedurê pomiaru, z wykorzystaniem dyfraktometru rentgenowskiego, wspó3czynników piezoelektrycznych monokryszta3u ferroelektrycznego na przyk3adzie molibdenku gadolinu ( )3 4 2 MoO Gd . 184 Teodor Breczko, Andrzej Lempaszek Introduction Piezoelectric coefficients, also referred to as piezoelectric moduli, are among the most important quantities characterizing all piezoelectric crystals, including ferroelectric ones (RUDIAK 1982). This is connected with the fact that the matrixes of these coefficients are present in constitutive equations describing direct and converse piezoelectric effects. At the same time, the values of the above coefficients are the same for both these effects. This indicates that the direct or converse piezoelectric effect can be used for measuring matrix elements. The present paper desc...

We show that there are no new consistent cosmological perfect fluid solutions when in an open neighbourhood U of an event the fluid kinematical variables and the electric and magnetic Weyl curvature are all assumed rotationally symmetric about a common spatial axis, specialising the Weyl curvature tensor to algebraic Petrov type D. The consistent solutions of this kind are either locally rotationally symmetric, or are subcases of the Szekeres dust models. Parts of our results require the assumption of a barotropic equation of state. Additionally we demonstrate that local rotational symmetry of perfect fluid cosmologies follows from rotational symmetry of the Riemann curvature tensor and of its covariant derivatives only up to second order, thus strengthening a previous result. Preprint: uct–cosmology–99/09 PACS number(s): 04.20.-q, 98.80.Hw, 04.20.Jb

The simplified three-parameter formulation of a piezoelectric medium proposed by Gao et al. [Gao, H.J., Zhang, T.Y., Tong, P., 1997. Local and global energy release rates for an electrically yielded crack in a piezoelectric ceramic. J. Mech. Phys. Solids 45, 491-510] is extended to a four-parameter modified model in order to point out the features of a steadily propagating Griffith crack. It is assumed that the crack is electro-elastically free and the medium is subjected to a generalized electro-mechanical loading applied at infinity. The complete solution is provided under impermeable and permeable boundary conditions and results are presented in order to show the main dynamical features.

The plane problem of a Griffith crack steadily propagating in an anisotropic piezoelectric medium is investigated through an analytical approach which is new in this topic. Complete solutions are provided in the subsonic regime under permeable and impermeable boundary conditions and the combined effects of mechanical and electrical far-fields are pointed out.

Submarine-pipeline developments are moving into deeper waters. As a result, thicker pipe walls are needed and hence the quotient of the pipe diameter and its wall thickness (i.e., D t ⁄ ) reduces. On the other hand, there is a push to optimise properties and requirements for moderate water depths of several hundred metres. Design criteria in the prevailing submarine-pipeline design standard DNVGL-ST-F101 (2017) were developed for straight pipes with 15 ≤ D t ⁄ ≤ 60 but applicability is limited to D t ⁄ ≤ 45. There can be a desire to go beyond this limit when designing for moderate depths. When pipe walls are becoming thinner, this makes the pipeline more susceptible to collapse. It has been found that, in some cases, the DNVGL-ST-F101 formulations that aim at predicting the collapse pressure of relatively thin-walled pipelines can lead to nonconservative results. This is a concern when the line-pipe manufacturing technique employs cold forming—such as the cross-section expansion ste...

A new isogeometrical procedure for optimization of material composition of functionally graded structures in thermo-mechanical processes is introduced. The proposed method employs a generalized form of the standard isogeometric analysis method, allowing for gradation of material properties through patches. The variations of material properties are captured in a fully isogeometric formulation using the same NURBS basis functions employed for construction of the geometry and approximation of the solution. Subsequently, the applicates of control points that define the surfaces of volume fractions of the constituents are considered as the design variables and obtained by solving the optimization problem using a mathematical programming algorithm. Some numerical examples under thermal and mechanical loadings are considered to demonstrate the performance and applicability of the proposed method. Comparison of the obtained results with those of the other existing approaches such as finite elements and meshfree methods verifies the presented results. It will be seen that the proposed procedure considerably removes the difficulties of the existing methods and provides a promising tool for material design of functionally graded structures.