Analytical solution of stress in functionally graded cylindrical/spherical pressure vessel

2021 ◽  
Author(s):  
Jun Xie ◽  
Shuai Hao ◽  
Wenshuai Wang ◽  
Pengpeng Shi
Keyword(s):  
Analytical Solution ◽  
Pressure Vessel ◽  
Functionally Graded ◽  
Spherical Pressure

Distribution Parameter Optimization of an FGM Pressure Vessel

2011 ◽  
Vol 320 ◽  
pp. 404-409
Author(s):  
Ze Wu Wang ◽  
Shu Juan Gao ◽  
Qian Zhang ◽  
Pei Qi Liu ◽  
Xiao Long Jiang
Keyword(s):  
Analytical Solution ◽  
Pressure Vessel ◽  
Material Properties ◽  
Optimization Design ◽  
Optimal Solution ◽  
Functionally Graded ◽  
Material Distribution ◽  
Optimization Scheme ◽  
Graded Material ◽  
Optimal Material

Functionally graded material (FGM) is well-known as one of the most promising materials in the 21stcentury, which has become the hot issue on its mechanical behavior and composition design. The optimization design of the material distribution properties for an FGM hollow vessel subjected to internal pressure were investigated in this paper. By constructing an exponentially function determining the material properties, the general analytical solution of the stresses of the FGM pressure vessel was given based on the Euler-Cauchy formula. And then, an optimization model for obtaining the optimal material distribution of FGM vessel was proposed coupling the general finite element (FE) code. The discrepancy between the analytical solution and the numerical solution was about 2%, which verified the reliability of the proposed models, and the optimization results also proved the feasibility of proposed optimization scheme because of arriving at the optimal solution in a few iterations. Results obtained would be helpful in designing an FGM pressure vessel.

Thermomechanical Analysis of Pressure Vessels With Functionally Graded Material Coating

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Z. W. Wang ◽  
Q. Zhang ◽  
L. Z. Xia ◽  
J. T. Wu ◽  
P. Q. Liu
Keyword(s):  
Analytical Solution ◽  
Functionally Graded Material ◽  
Pressure Vessel ◽  
Thermomechanical Analysis ◽  
Thermomechanical Properties ◽  
Pressure Vessels ◽  
Functionally Graded ◽  
Fe Method ◽  
Thin Walled Structures ◽  
Graded Material

Pressure vessels covered with overlaying layer or coating are widely applied due to its strong heat resistance, corrosion resistance, and load-carrying capacity. However, limited work has been reported on investigating the thermomechanical behavior of a pressure vessel with a functionally graded material (FGM) coating. In this study, a closed-form analytical solution was first derived for calculating the stress distribution in a pressure vessel with an FGM coating subjected to an internal pressure and a thermal load. Afterwards, a numerical solution was also established for validating the analytical solution using finite element (FE) method. It was found out that the analytical solution agreed well with the numerical ones, and the thermomechanical properties of FGM coating were also discussed in detail. This work would be helpful for better understanding and scientific design of pressure vessels with an FGM coating or related thin-walled structures.

Shakedown-Ratcheting Analysis of a Spherical Pressure Vessel by Anisotropic Continuum Damage Mechanics

2018 ◽  
Author(s):  
Ali Nayebi ◽  
Azam Surmiri ◽  
Hojjatollah Rokhgireh
Keyword(s):  
Pressure Vessel ◽  
Damage Mechanics ◽  
Kinematic Hardening ◽  
Continuum Damage Mechanics ◽  
Mapping Method ◽  
Anisotropic Damage ◽  
Continuum Damage ◽  
Interaction Diagram ◽  
Plastic Shakedown ◽  
Spherical Pressure

In cyclic loading and when plastic flow occurs, discontinuities grow. In this research, interaction diagram of Bree has been developed when the spherical pressure vessel contains discontinuities such as voids and microcracks. Bree’s diagram is used for ratcheting assessment of pressurized equipment in ASME III NH. Nature of these defects leads to an anisotropic damage. Anisotropic Continuum Damage Mechanics (CDM) is considered to account effects of these discontinuities on the behavior of the structure. Shakedown – ratcheting response of a hollow sphere under constant internal pressure and cyclic thermal loadings are studied by using anisotropic CDM theory coupled with nonlinear kinematic hardening of Armstrong-Frederick m’s model (A-F). Return mapping method is used to solve numerically the developed relations. Elastic, elastic shakedown, plastic shakedown and ratcheting regions are illustrated in the modified Bree’s diagram. Influence of anisotropic damage due to the plastic deformation is studied and it was shown that the plastic shakedown region is diminished because of the developed damage.

Analytical and numerical investigation of the free vibration of functionally graded materials sandwich beams

2021 ◽  
Vol 2 (110) ◽  
pp. 72-85
Author(s):  
S.H. Bakhy ◽  
M. Al-Waily ◽  
M.A. Al-Shammari
Keyword(s):  
Analytical Solution ◽  
Free Vibration ◽  
Functionally Graded Materials ◽  
Sandwich Beam ◽  
Beam Theory ◽  
Functionally Graded ◽  
Gradient Index ◽  
Sandwich Beams ◽  
Graded Materials ◽  
The Impact

Purpose: In this study, the free vibration analysis of functionally graded materials (FGMs) sandwich beams having different core metals and thicknesses is considered. The variation of material through the thickness of functionally graded beams follows the power-law distribution. The displacement field is based on the classical beam theory. The wide applications of functionally graded materials (FGMs) sandwich structures in automotive, marine construction, transportation, and aerospace industries have attracted much attention, because of its excellent bending rigidity, low specific weight, and distinguished vibration characteristics. Design/methodology/approach: A mathematical formulation for a sandwich beam comprised of FG core with two layers of ceramic and metal, while the face sheets are made of homogenous material has been derived based on the Euler–Bernoulli beam theory. Findings: The main objective of this work is to obtain the natural frequencies of the FG sandwich beam considering different parameters. Research limitations/implications: The important parameters are the gradient index, slenderness ratio, core metal type, and end support conditions. The finite element analysis (FEA), combined with commercial Ansys software 2021 R1, is used to verify the accuracy of the obtained analytical solution results. Practical implications: It was found that the natural frequency parameters, the mode shapes, and the dynamic response are considerably affected by the index of volume fraction, the ratio as well as face FGM core constituents. Finally, the beam thickness was dividing into frequent numbers of layers to examine the impact of many layers' effect on the obtained results. Originality/value: It is concluded, that the increase in the number of layers prompts an increment within the frequency parameter results' accuracy for the selected models. Numerical results are compared to those obtained from the analytical solution. It is found that the dimensionless fundamental frequency decreases as the material gradient index increases, and there is a good agreement between two solutions with a maximum error percentage of no more than 5%.

Sign in / Sign up

Export Citation Format

Share Document