通过变运动学有限元对多组件结构进行几何非线性静态分析

IF 2.3 3区 工程技术 Q2 MECHANICS
R. Azzara, E. Carrera, P. Chiaia, M. Filippi, A. Pagani, M. Petrolo, E. Zappino
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引用次数: 0

摘要

本文介绍了一种用于复杂几何结构非线性静力分析的多维变运动学有限元模型。该方法将高阶梁模型和经典实体有限元纳入统一框架,实现了复杂几何结构的精细建模。所提出的有限元程序遵循卡雷拉统一公式 (CUF),并使用纯位移方法。控制方程在经典连续介质力学框架内导出,并利用虚拟位移原理(PVD)建立弱式平衡方程。在 CUF 框架内,以统一的方式定义了高阶梁和六面体实体模型,并根据所用数学模型的不变量和结构近似理论编写了控制方程。在节点层面,梁和实体元素之间使用了叠加耦合技术。研究了全非线性变运动学模型对各种矩形和曲线结构进行静态分析的能力。数值结果与使用商业软件获得的解决方案进行了比较。最后,提出的方法被应用于分析工程应用中更复杂的几何结构。结果表明,在计算高度非线性变形状态和局部现象(如应力集中和屈曲)时,可变运动学模型在精度和计算效率方面都具有很强的能力。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Geometrically nonlinear static analysis of multi-component structures through variable-kinematics finite elements

Geometrically nonlinear static analysis of multi-component structures through variable-kinematics finite elements

This paper presents a multi-dimensional variable-kinematics finite element model for nonlinear static analyses of structures with complex geometries. The approach incorporates higher-order beam models and classical solid finite elements in a unified framework, enabling refined modeling of complex geometries. The finite element procedure proposed follows the Carrera Unified Formulation (CUF) and uses a pure displacement-based methodology. The governing equations are derived within the classical continuum mechanics framework, and weak-form equilibrium equations are established using the Principle of Virtual Displacements (PVD). Within the CUF framework, higher-order beam and hexahedral solid models are defined in a unified manner, and the governing equations are written in terms of invariants of mathematical models used and the theory of structures approximation. A coupling technique is used between the beam and solid elements at the nodal level using superposition. The capabilities of fully nonlinear variable-kinematics models are investigated for the static analysis of various rectangular and curved structures. The numerical results are compared with solutions obtained using commercial software. Finally, the proposed methodology is applied to analyze more complex geometries in engineering applications. The results show the capabilities of variable-kinematics models in terms of both accuracy and computational efficiency for the computation of highly nonlinear deformed states and localized phenomena, such as stress concentrations and buckling.

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来源期刊
Acta Mechanica
Acta Mechanica 物理-力学
CiteScore
4.30
自引率
14.80%
发文量
292
审稿时长
6.9 months
期刊介绍: Since 1965, the international journal Acta Mechanica has been among the leading journals in the field of theoretical and applied mechanics. In addition to the classical fields such as elasticity, plasticity, vibrations, rigid body dynamics, hydrodynamics, and gasdynamics, it also gives special attention to recently developed areas such as non-Newtonian fluid dynamics, micro/nano mechanics, smart materials and structures, and issues at the interface of mechanics and materials. The journal further publishes papers in such related fields as rheology, thermodynamics, and electromagnetic interactions with fluids and solids. In addition, articles in applied mathematics dealing with significant mechanics problems are also welcome.
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