计算任意形状板/壳大变形的共形几何方法

IF 1.9 4区 工程技术 Q3 ENGINEERING, MECHANICAL
Yipeng Liu, Wei Fan, Hui Ren
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引用次数: 0

摘要

求解非线性 Föppl-von Kármán(FvK)方程的高精度数值方法通常只在矩形区域等简单域中有效。计算保角几何(CCG)提供了一种将复杂曲面转换为简单域的系统方法,同时保留了正交框架,这样就可以用更有效的数值方法求解相应的 FvK 方程。符合图是通过在曲面的精细 Delauney 三角网格上求解一对拉普拉斯方程计算得出的,这种方法在数值上是稳健的,而且符合图是谐波的,随后是 C∞ 平滑的,这样就可以在规则节点上精确高效地计算高精度方法所需的所有求值和空间导数。针对壳体推导出了与 FvK 方程相对应的变分函数,使问题可以用有限元方法求解,并与商业软件 Abaqus 进行了比较;在求解 FvK 方程的横向位移和 Airy 函数时需要的自由度较少。几个基准实例验证了所提方法的有效性,目前的方法适用于计算任意形状板/浅壳的大挠度和非线性动态响应。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A Computational Conformal Geometry Approach to Calculate the Large Deformations of Plates/shells with Arbitrary Shapes
High accuracy numerical methods to solve the nonlinear Föppl-von Kármán (FvK) equations usually work well only in simple domains such as rectangular regions. Computational conformal geometry (CCG) provides a systematic method to transform complicated surfaces into simple domains, preserving the orthogonal frames, such that the corresponding FvK equations can be solved by more effective numerical methods. The conform map is calculated by solving a pair of Laplace equations on a fine Delauney triangular mesh of the surface, which is numerically robust, and the map is harmonic and subsequently C∞ smooth, such that all the evaluations and spatial derivatives required by high accuracy methods at the regular nodes can be accurately and efficiently calculated. A variational functional corresponding to the FvK equations is derived for shells, which enable the problem to be solved by the finite element methods and compared with the commercial software Abaqus; fewer degrees of freedom are required in solving the transverse displacements and Airy functions of the FvK equations. The effectiveness of the proposed approach is verified by several benchmark examples, and the current method is suitable to calculate the large deflections and nonlinear dynamical responses of plates/shallow shells with arbitrary shapes.
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来源期刊
CiteScore
4.00
自引率
10.00%
发文量
72
审稿时长
6-12 weeks
期刊介绍: The purpose of the Journal of Computational and Nonlinear Dynamics is to provide a medium for rapid dissemination of original research results in theoretical as well as applied computational and nonlinear dynamics. The journal serves as a forum for the exchange of new ideas and applications in computational, rigid and flexible multi-body system dynamics and all aspects (analytical, numerical, and experimental) of dynamics associated with nonlinear systems. The broad scope of the journal encompasses all computational and nonlinear problems occurring in aeronautical, biological, electrical, mechanical, physical, and structural systems.
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