Analytical solutions for nonlinear axisymmetric deformations of circular plates by using innovative orthogonal power function series

IF 2.2 3区工程技术 Q2 MECHANICS

Archive of Applied Mechanics Pub Date : 2024-07-17 DOI:10.1007/s00419-024-02648-9

Da-Guang Zhang

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引用次数: 0

Abstract

The primary objective of this paper is to introduce innovative orthogonal power function series aimed at obtaining accurate nonlinear analytical solutions for axisymmetric circular thin plates. The main features of this paper are as follows: The deflection is expanded by the innovative orthogonal power function series. The Airy stress function, which satisfies the geometric deformation compatibility equation, responds to the nonlinear coupling relationships between the plate deflection and the in-plane force or displacement boundary conditions. The nonlinear algebraic equations are obtained by the energy variational method. Many comparisons are made with the results of related researchers. The present accurate solutions not only allow the problems to be solved perfectly and provide the most reliable basis for engineering design but also set new benchmarks for the verification of various nonlinear numerical and approximate analytical solutions. The developed methodology represents a significant improvement, providing better accuracy and computational efficiency compared to historical approaches. Therefore, the present method is more worthy of promotion.

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利用创新的正交幂函数序列分析解决圆板的非线性轴对称变形问题

本文的主要目的是引入创新的正交幂函数序列，旨在获得轴对称圆形薄板的精确非线性分析解。本文的主要特点如下：通过创新的正交幂函数数列扩展挠度。满足几何变形兼容性方程的 Airy 应力函数响应板挠度与平面内力或位移边界条件之间的非线性耦合关系。非线性代数方程由能量变分法求得。与相关研究人员的结果进行了许多比较。目前的精确解法不仅可以完美地解决这些问题，为工程设计提供最可靠的依据，而且还为验证各种非线性数值解法和近似分析解法树立了新的基准。与以往的方法相比，所开发的方法有了重大改进，提供了更高的精度和计算效率。因此，本方法更值得推广。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Archive of Applied Mechanics 物理-力学

CiteScore

4.40

自引率

10.70%

发文量

234

审稿时长

4-8 weeks

期刊介绍： Archive of Applied Mechanics serves as a platform to communicate original research of scholarly value in all branches of theoretical and applied mechanics, i.e., in solid and fluid mechanics, dynamics and vibrations. It focuses on continuum mechanics in general, structural mechanics, biomechanics, micro- and nano-mechanics as well as hydrodynamics. In particular, the following topics are emphasised: thermodynamics of materials, material modeling, multi-physics, mechanical properties of materials, homogenisation, phase transitions, fracture and damage mechanics, vibration, wave propagation experimental mechanics as well as machine learning techniques in the context of applied mechanics.