Analogic Analysis of Orthotropic Plate Bending Problems With Gridwork Systems

YUAN Quan; YUAN Si

doi:10.21656/1000-0887.440232

Volume 45 Issue 5

May 2024

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2024 > 45(5): 518-528

YUAN Quan, YUAN Si. Analogic Analysis of Orthotropic Plate Bending Problems With Gridwork Systems[J]. Applied Mathematics and Mechanics, 2024, 45(5): 518-528. doi: 10.21656/1000-0887.440232

Citation:

YUAN Quan, YUAN Si. Analogic Analysis of Orthotropic Plate Bending Problems With Gridwork Systems[J]. Applied Mathematics and Mechanics, 2024, 45(5): 518-528. doi: 10.21656/1000-0887.440232

Citation:

YUAN Quan, YUAN Si. Analogic Analysis of Orthotropic Plate Bending Problems With Gridwork Systems[J]. Applied Mathematics and Mechanics, 2024, 45(5): 518-528. doi: 10.21656/1000-0887.440232

PDF( 908 KB)

Analogic Analysis of Orthotropic Plate Bending Problems With Gridwork Systems

doi: 10.21656/1000-0887.440232

YUAN Quan^,,
YUAN Si

Department of Civil Engineering, Tsinghua University, Beijing 100084, P.R.China

Received Date: 2023-07-29
Rev Recd Date: 2023-11-29
Publish Date: 2024-05-01

Abstract

Abstract

Orthotropic plates were analogized to gridwork systems, and the compatibility and incompatibility between these 2 structure types in static and dynamic analyses were discussed. The results show that, the gridwork results converge to the theoretical solution of plates through the grid refinement for compatible problems with simply supported and/or clamped boundaries. All the formulas for calculation of various internal forces were derived, and the algorithms required in solving the gridwork systems were proposed by means of the 3D structural mechanics solver. A wide range of numerical examples, including rectangular and circular plates, were given to verify the validity of the proposed theory and algorithms.
- gridwork,
- orthotropic thin plate,
- compatibility,
- 3D structural mechanics solver,
- numerical computation

FullText(HTML)

References(15)

References

[1]	TIMOSHENKO S, WOINOWSKY-KRIEGER S. Theory of Plates and Shells[M]. 2nd ed. New Jersey: McGraw-Hill, 1987.
[2]	古国纪. 交叉梁系的计算[J]. 土木工程学报, 1958, 5(3): 165-178. https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC195803000.htm GU Guoji. The analysis of caisson-beam[J]. China Civil Engineering Journal, 1958, 5(3): 165-178. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC195803000.htm
[3]	张玉敏, 鲍鹏, 崔奕. 板与交叉梁系的相似性及其简化计算[J]. 河南大学学报(自然科学版), 2002, 32(1): 83-86. doi: 10.3969/j.issn.1003-4978.2002.01.024 ZHANG Yumin, BAO Peng, CUI Yi. The theoretical similarity between a plate and a grillage beam[J]. Journal of Henan University (Natural Science), 2002, 32(1): 83-86. (in Chinese) doi: 10.3969/j.issn.1003-4978.2002.01.024
[4]	袁驷, 袁全. 交叉梁系比拟求解薄板弯曲问题的相容性及其计算[J]. 土木工程学报, 2023, 56(3): 1-8. https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC202303001.htm YUAN Si, YUAN Quan. Compatibility in analogy of gridworks to thin plate bending and its numerical solution[J]. China Civil Engineering Journal, 2023, 56(3): 1-8. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC202303001.htm
[5]	王森林, 李进宝, 马红艳, 等. 基于辛叠加方法的正交各向异性矩形悬臂薄板受迫振动解析解[J/OL]. 应用数学和力学, 2023[2023-11-29]. https://link.cnki.net/urlid/50.1060.o3.20231110.1245.002. WANG Senlin, LI Jinbao, MA Hongyan, et al. Analytical forced vibration solutions of orthotropic cantilever rectangular thin plates by the symplectic superposition method[J]. Applied Mathematics and Mechanics, 2023[2023-11-29]. https://link.cnki.net/urlid/50.1060.o3.20231110.1245.002. (in Chinese)
[6]	黄炎, 雷勇军, 申慧君. 各向异性矩形板自由振动的一般解析解法[J]. 应用数学和力学, 2006, 27(4): 411-416. doi: 10.3321/j.issn:1000-0887.2006.04.005 HUANG Yan, LEI Yongjun, SHEN Huijun. Free vibration of anisotropic rectangular plates by general analytical method[J]. Applied Mathematics and Mechanics, 2006, 27(4): 411-416. (in Chinese) doi: 10.3321/j.issn:1000-0887.2006.04.005
[7]	李晶晶, 程昌钧. 考虑高阶横向剪切正交各向异性板非线性弯曲的微分求积分析[J]. 应用数学和力学, 2004, 25(8): 801-808. doi: 10.3321/j.issn:1000-0887.2004.08.005 LI Jingjing, CHENG Changjun. Differential quadrature method for bending of orthotropic plates with finite deformation and transverse shear effects[J]. Applied Mathematics and Mechanics, 2004, 25(8): 801-808. (in Chinese) doi: 10.3321/j.issn:1000-0887.2004.08.005
[8]	黄家寅. 变厚度正交各向异性矩形板非线性非对称弯曲问题的基本方程[J]. 应用数学和力学, 2004, 25(7): 741-744. doi: 10.3321/j.issn:1000-0887.2004.07.012 HUANG Jiayin. Basic equations of the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with variable thickness[J]. Applied Mathematics and Mechanics, 2004, 25(7): 741-744. (in Chinese) doi: 10.3321/j.issn:1000-0887.2004.07.012
[9]	黄家寅. 四边固定变厚度正交各向异性矩形板的非线性非对称弯曲问题的一致有效渐近解[J]. 应用数学和力学, 2004, 25(7): 745-754. doi: 10.3321/j.issn:1000-0887.2004.07.013 HUANG Jiayin. Uniformly valid asymptotic solutions of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate of four clamped edges with variable thickness[J]. Applied Mathematics and Mechanics, 2004, 25(7): 745-754. (in Chinese) doi: 10.3321/j.issn:1000-0887.2004.07.013
[10]	额布日力吐, 冯璐, 阿拉坦仓. 四边固支正交各向异性矩形薄板弯曲问题的辛叠加方法[J]. 应用数学和力学, 2018, 39(3): 311-323. doi: 10.21656/1000-0887.380092 EBURILITU, FENG Lu, ALATANCANG. Analytical bending solutions of clamped orthotropic rectangular thin plates with the symplectic superposition method[J]. Applied Mathematics and Mechanics, 2018, 39(3): 311-323. (in Chinese) doi: 10.21656/1000-0887.380092
[11]	王新志, 赵永刚, 叶开沅, 等. 正交各向异性板的非对称大变形问题[J]. 应用数学和力学, 2002, 23(9): 881-888. doi: 10.3321/j.issn:1000-0887.2002.09.001 WANG Xinzhi, ZHAO Yonggang, YEH Kaiyuan, et al. Unsymmetrical large deformation problem of orthotropic plates[J]. 应用数学和力学, 2002, 23(9): 881-888. (in Chinese) doi: 10.3321/j.issn:1000-0887.2002.09.001
[12]	袁驷. 结构力学Ⅰ: 基础教程(第4版) 求解器[EB/OL]. V3.0. 北京: 高等教育出版社. (2018-07-13)[2023-07-29]. https://abook.hep.com.cn/12202428. YUAN Si. Structural mechanical: fundamental course (4th ed) solver[EB/OL]. V3.0. Beijing: Higer Education Press. (2018-07-13) [2023-07-29]. (in Chineses)
[13]	龙驭球, 包世华, 袁驷. 结构力学Ⅰ[M]. 4版. 北京: 高等教育出版社, 2018. LONG Yuqiu, BAO Shihua, YUAN Si. Structure Mechanics [M]. 4th ed. Beijing: Higher Education Press, 2018. (in Chinese)
[14]	袁驷. 程序结构力学[M]. 2版. 北京: 高等教育出版社, 2008. YUAN Si. Programming Structural Mechanics[M]. 2nd ed. Beijing: Higher Education Press, 2008. (in Chinese)
[15]	REDDY J N. Theory and Analysis of Elastic Plates and Shells[M]. 2nd ed. Boca Raton: CRC Press, 2007.