Analytical Solutions and Multiscale Creep Analysis of Functionally Graded Cylindrical Pressure Vessels

This study deals with the time-dependent creep analysis of functionally graded thick-cylinders under various thermal and mechanical boundary conditions. Firstly, exact thermoelastic stress, and iterative creep solutions for a heat generating and rotating cylindrical vessel made of functionally graded thermal and mechanical properties are proposed. Equations of equilibrium, compatibility, stress-strain, and strain-displacement relations are solved to obtain closed-form initial stress and strain solutions. It is found that material gradient indices have significant influences on thermoelastic stress profiles. For creep analysis, Norton’s model is incorporated into rate forms of the above-mentioned equations to obtain time-dependent stress and strain results using an iterative method. Validity of our solutions are at first verified using finite element analysis, and numerical results found in the recent literature have been enhanced. Investigation of effects of material gradients reveals that radial variation of density and creep coefficient have significant effects on strains histories, while Young’s modulus and thermal property distributions only influence stress redistribution at an early stage of creep deformation. Next, a more realistic model of introducing microscale creep effects into a macroscopic modeling is employed to investigate the creep behavior of functionally graded hollow cylinders. Finite element (FE) simulations are employed to evaluate the position-dependent parameters associated with creep constitutive law at the microscale. A macroscopic FE model solves the non-linear boundary value problem to determine the time-varying creep stresses and strains. The framework proposed is capable of predicting the creep response of functionally graded pressure vessels based on the constitutive behavior of the creeping matrix, and volume fraction profile. Effective creep properties have been computed using three different micromechanical models and the homogenized creep response and its effect on the macroscopic behavior are compared. Considering the computational expenses associated with the large 3D finite element models, the simple 2D axisymmetric model is able to closely capture the creep behavior in such multiscale methods. Finally, a multi-objective particle swarm optimization algorithm is implemented to minimize the initial stress and final creep strain of functionally graded cylinder subjected to mechanical and thermal loads

Exact thermoelastic analysis of a thick cylindrical functionally graded material shell under unsteady heating using first order shear deformation theory

In this article, a new analytical formulation is presented for axisymmetric thick-walled FGM cylinder with power-law variation in mechanical and thermal properties under transient heating using first order shear deformation theory. Equilibrium equations are derived by virtual work principles and energy method. The unsteady heat conduction equation is solved using the method of separation of variables, generalized Bessel functions and an Eigen-function method. Validation of the analytical solutions is conducted with a finite element method (FEM). The effects of time on stress and displacement distribution are studied in detail. The numerical values used in this study are selected based on earlier studies. The influence of effect of transient heat transfer on heterogeneous thick-walled cylinder elasticity is clearly demonstrated. In particular the significant influence of time and heterogenous constant on radial displacement, hoop stress and temperature distributions is computed. The study is relevant to rocket chamber thermo-mechanics, propulsion duct thermophysical design, industrial thermal storage systems etc

Thermoelastic Stresses Alleviation for Two-Dimensional Functionally Graded Cylinders Under Asymmetric Loading

Open Access via the Taylor and Francis Agreement Funding This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.Peer reviewedPublisher PD

Bree\u27s Diagram of A Functionally Graded Thick-walled Cylinder Under Thermo-mechanical Loading Considering Nonlinear Kinematic Hardening

n this paper, elasto-plastic analysis of a thick-walled cylinder made of functionally graded materials (FGMs) subjected to constant internal pressure and cyclic temperature gradient loading is carried out using MATLAB. The material is assumed to be isotropic and independent of tem- perature with constant Poisson\u27s ratio and the material properties vary radially based on a power law volume function relation. The Von Mises’ yield criterion and the Armstrong-Frederick non- linear kinematic hardening model were implemented in this investigation. To obtain the incre- mental plastic strain, return mapping algorithm (RMA) was used. At the end, the Bree\u27s inter- action diagram is plotted in terms of non-dimensional pressure and temperature which represents an engineering index for optimum design under thermo-mechanical loading

Optimal Design of Functionally Graded Parts

Several additive manufacturing processes are capable of fabricating three-dimensional parts with complex distribution of material composition to achieve desired local properties and functions. This unique advantage could be exploited by developing and implementing methodologies capable of optimizing the distribution of material composition for one-, two-, and three-dimensional parts. This paper is the first effort to review the research works on developing these methods. The underlying components (i.e., building blocks) in all of these methods include the homogenization approach, material representation technique, finite element analysis approach, and the choice of optimization algorithm. The overall performance of each method mainly depends on these components and how they work together. For instance, if a simple one-dimensional analytical equation is used to represent the material composition distribution, the finite element analysis and optimization would be straightforward, but it does not have the versatility of a method which uses an advanced representation technique. In this paper, evolution of these methods is followed; noteworthy homogenization approaches, representation techniques, finite element analysis approaches, and optimization algorithms used/developed in these studies are described; and most powerful design methods are identified, explained, and compared against each other. Also, manufacturing techniques, capable of producing functionally graded materials with complex material distribution, are reviewed; and future research directions are discussed

Elastic Behavior of Functionally Graded Two Tangled Circles Chamber

This paper presents the numerical elastic solution for a real problem, functionally graded chamber of hydraulic gear pumps under internal pressure. Because of the similarity and complexity for the considering geometry, a bipolar cylindrical coordinate system is used to extract the governing equations. The material properties are considered to vary along the two tangled circles with a power-law function. The two coupled governing equations solved by the differential quadrature method. The results are presented for various material index and show that the complexity in considering geometry and material inhomogeneity can change the stress and displacements value through the geometry efficiently. The results and presented method in this paper for extracting and solving the problem can be used for designing similar geometry more accurate. The results of this research are compared with those reported in the previous work

Three dimensional frequency analysis of bidirectional functionally graded thick cylindrical shells using a radial point interpolation method (RPIM)

This paper considers a functionally graded (FG) shell using a meshless radial point interpolation method (RPIM). The material is assumed to be bidirectional FG, where the variation is present in both the radial and the axial directions. Based on the three-dimensional equations of motion, the frequency equations are stated using RPIM. Numerical results are presented for a thick shell for various boundary conditions. These results illustrate the influence from the material variation concerning eigenfrequencies and eigenmodes. In addition, the study shows that the RPIM is an efficient method to solve dynamical shell problems

Free vibration analysis of functionally graded shell panels with various geometric shapes in thermal environment

This paper presents free vibration analysis of functionally graded materials (FGMs) shell panels with various geometric shapes in thermal environments. The shell panels are made from a mixture of metal and ceramic. Material properties are assumed to be temperature-dependent and graded in the thickness direction according to a power law function. A formulation of eight-nodded middle surface shell elements based on Reissner-Mindlin assumptions is developed for modeling FGM shell panels under the effect of temperature, which changes nonlinearly across the thickness. Numerical results obtained by the proposed model are in good agreement with those available in the literature. The effects of geometric properties, material composition, boundary conditions and temperature on the natural frequencies are investigated