Accurate analytical post-buckling solutions for simply supported square plates under biaxial compression with varying stress ratios

IF 7.9 2区 材料科学 Q1 MATERIALS SCIENCE, MULTIDISCIPLINARY
Da-Guang Zhang
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Abstract

This study addresses the challenge of obtaining accurate analytical post-buckling solutions for simply supported square plates under biaxial compression, a long-standing problem in nonlinear plate mechanics. The research question focuses on how to rigorously capture large deflections and bending–membrane interactions to establish reliable benchmarks beyond the critical load. A series expansion method within the von Kármán framework is employed to derive analytical solutions with high numerical accuracy. Compared with existing analytical and numerical approaches, the present solutions achieve five to six significant digits of accuracy, representing a substantial improvement in precision and reliability. A comprehensive parametric study demonstrates how varying the biaxial compression ratio influences post-buckling responses, providing deeper insight into boundary-sensitive and load-dependent behaviors. The results establish new analytical benchmarks that can be directly used to validate approximate and numerical methods, thereby improving the robustness of computational models. In addition, they offer practical guidance for the safe and efficient design of thin-walled plate structures in aerospace, civil, and mechanical engineering. This work highlights both the novelty of deriving truly accurate, verifiable analytical solutions and their dual value as theoretical milestones and engineering tools.

Abstract Image

变应力比下双轴压缩简支方板后屈曲精确解析解
本研究解决了在双轴压缩下简支方形板的精确解析后屈曲解的挑战,这是非线性板力学中一个长期存在的问题。研究问题集中在如何严格捕获大挠度和弯曲膜相互作用,以建立超过临界载荷的可靠基准。采用von Kármán框架下的级数展开法,得到数值精度较高的解析解。与现有的解析和数值方法相比,本方法的精度达到了5 - 6位有效数字,在精度和可靠性方面有了很大的提高。一项全面的参数研究表明,改变双轴压缩比如何影响屈曲后响应,从而更深入地了解边界敏感和负载依赖行为。研究结果建立了新的分析基准,可直接用于验证近似和数值方法,从而提高计算模型的鲁棒性。此外,它们还为航空航天、土木和机械工程中薄壁板结构的安全高效设计提供了实用指导。这项工作强调了获得真正准确、可验证的分析解决方案的新颖性,以及它们作为理论里程碑和工程工具的双重价值。
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来源期刊
Materials & Design
Materials & Design Engineering-Mechanical Engineering
CiteScore
14.30
自引率
7.10%
发文量
1028
审稿时长
85 days
期刊介绍: Materials and Design is a multi-disciplinary journal that publishes original research reports, review articles, and express communications. The journal focuses on studying the structure and properties of inorganic and organic materials, advancements in synthesis, processing, characterization, and testing, the design of materials and engineering systems, and their applications in technology. It aims to bring together various aspects of materials science, engineering, physics, and chemistry. The journal explores themes ranging from materials to design and aims to reveal the connections between natural and artificial materials, as well as experiment and modeling. Manuscripts submitted to Materials and Design should contain elements of discovery and surprise, as they often contribute new insights into the architecture and function of matter.
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