<p>Creep stresses are evaluated in a hemispherical shell made of functionally graded transversely isotropic materials under uniform external pressure. The concept of transition theory is applied to evaluate the creep stresses in the shell under external pressure. The strength and compatibility of the hemispherical shell composed of magnesium, zinc, and beryl are compared based on creep stresses. This physical problem is regulated by a non-linear differential equation obtained by substituting the derived relations in the equilibrium equation. For estimating the creep stresses in the shell, the transition function <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <mi>R</mi> </math></EquationSource> <EquationSource Format="TEX">$R$</EquationSource> </InlineEquation> is considered as the difference of radial stress <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math> <msub> <mi>T</mi> <mrow> <mi>r</mi> <mi>r</mi> </mrow> </msub> </math></EquationSource> <EquationSource Format="TEX">$T_{rr}$</EquationSource> </InlineEquation> and circumferential stress <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math> <msub> <mi>T</mi> <mrow> <mi>θ</mi> <mi>θ</mi> </mrow> </msub> </math></EquationSource> <EquationSource Format="TEX">$T_{\theta \theta } $</EquationSource> </InlineEquation>. Analytical method is applied to solve the equations by taking the critical point <InlineEquation ID="IEq4"> <EquationSource Format="MATHML"><math> <mi>P</mi> <mo stretchy="false">→</mo> <mo>−</mo> <mn>1</mn> </math></EquationSource> <EquationSource Format="TEX">$P\rightarrow -1$</EquationSource> </InlineEquation> of the governing differential equation into consideration. This study examines the hemispherical shell composed of Functionally graded transversely isotropic material, which is more robust and biocompatible than homogenous transversely isotropic material. Based on all the numerical calculations and graphs it is concluded that the circumferential and radial creep stresses are minimum for a hemispherical shell composed of functionally graded transversely isotropic material magnesium in comparison to zinc and beryl, it implies that the shell composed of (FGM) magnesium is experiencing the most stable or optimal state of deformation under the conditions of external pressure. Therefore, the hemispherical shell of functionally graded transversely isotropic material magnesium might be useful in practical applications like pressure vessels, tanks, or any spherical shell structures exposed to high pressure over long durations.</p>

Analysis of creep deformation in functionally graded hemispherical shells subjected to external pressure

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发表日期：

2025年10月9日

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Richa Sharma,
Anshu Nagar

摘要

Creep stresses are evaluated in a hemispherical shell made of functionally graded transversely isotropic materials under uniform external pressure. The concept of transition theory is applied to evaluate the creep stresses in the shell under external pressure. The strength and compatibility of the hemispherical shell composed of magnesium, zinc, and beryl are compared based on creep stresses. This physical problem is regulated by a non-linear differential equation obtained by substituting the derived relations in the equilibrium equation. For estimating the creep stresses in the shell, the transition function $R$ $R$ is considered as the difference of radial stress $T_{r r}$ $T_{rr}$ and circumferential stress $T_{θ θ}$ $T_{\theta \theta } $ . Analytical method is applied to solve the equations by taking the critical point $P \to - 1$ $P\rightarrow -1$ of the governing differential equation into consideration. This study examines the hemispherical shell composed of Functionally graded transversely isotropic material, which is more robust and biocompatible than homogenous transversely isotropic material. Based on all the numerical calculations and graphs it is concluded that the circumferential and radial creep stresses are minimum for a hemispherical shell composed of functionally graded transversely isotropic material magnesium in comparison to zinc and beryl, it implies that the shell composed of (FGM) magnesium is experiencing the most stable or optimal state of deformation under the conditions of external pressure. Therefore, the hemispherical shell of functionally graded transversely isotropic material magnesium might be useful in practical applications like pressure vessels, tanks, or any spherical shell structures exposed to high pressure over long durations.