One- and Two-Dimensional Analytical Solutions of Thermal Stress for Bimodular Functionally Graded Beams under Arbitrary Temperature Rise Modes
Abstract
:1. Introduction
2. Strain Suppression Method in One-Dimensional Case
3. Two-Dimensional Thermoelasticity Solution
3.1. Pure Bending
3.2. Lateral-Force Bending
4. Comparisons and Regression
4.1. Comparison of Two-Dimensional Pure Bending and Lateral-Force Bending Solutions
4.2. Comparison of One- and Two-Dimensional Pure Bending Solutions
4.3. Regression and Validation
5. Numerical Results and Discussions
5.1. Neutral Layer in Two Bimodular Cases
5.2. Axial Stresses in Two Bimodular Cases
5.3. Bimodular Functionally Graded Effect on Thermal Stress
6. Concluding Remarks
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
References
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Cases | Case (a) | Case (b) | Case (c) | ||||
---|---|---|---|---|---|---|---|
h1/h | 0.3585 | 0.3859 | 0.4181 | 0.6732 | 0.6277 | 0.5824 | 0.5 |
h2/h | 0.6415 | 0.6141 | 0.5819 | 0.3268 | 0.3723 | 0.4176 | 0.5 |
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Xue, X.-Y.; Wen, S.-R.; Sun, J.-Y.; He, X.-T. One- and Two-Dimensional Analytical Solutions of Thermal Stress for Bimodular Functionally Graded Beams under Arbitrary Temperature Rise Modes. Mathematics 2022, 10, 1756. https://doi.org/10.3390/math10101756
Xue X-Y, Wen S-R, Sun J-Y, He X-T. One- and Two-Dimensional Analytical Solutions of Thermal Stress for Bimodular Functionally Graded Beams under Arbitrary Temperature Rise Modes. Mathematics. 2022; 10(10):1756. https://doi.org/10.3390/math10101756
Chicago/Turabian StyleXue, Xuan-Yi, Si-Rui Wen, Jun-Yi Sun, and Xiao-Ting He. 2022. "One- and Two-Dimensional Analytical Solutions of Thermal Stress for Bimodular Functionally Graded Beams under Arbitrary Temperature Rise Modes" Mathematics 10, no. 10: 1756. https://doi.org/10.3390/math10101756