A Multi-Dimensional Lagrange Multiplier Method to Identify the Load Distribution on 3D Special-Shaped Surface in the Strength Analysis of Aircraft Structure

IF 1.4 4区工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY

International Journal of Computational Methods Pub Date : 2023-01-09 DOI:10.1142/s0219876222500542

Tong Li, Zebei Mao, Yongming Cai, Bo Wang, Liang Chen

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Abstract

In the process of aircraft structural design, the aerodynamic load and inertial load need to be distributed from single loading points to distributed finite element (FE) nodes before strength analysis. The most commonly used loading distribution method is a Multi-Point Arrangement (MPA) method, which introduces a one-dimensional Lagrange multiplier based on the principle of minimum deformation energy, and simplifies the special-shaped 3D surface in aircraft structure to a plane. However, the actual aircraft structure contains a large number of special-shaped surfaces, and the MPA method cannot accurately distribute the loads on these complex special-shaped surfaces, affecting the accuracy of strength analysis. This paper developed a new 3D load distribution method based on multi-dimensional Lagrange multipliers (MDLM), which can simultaneously achieve an efficient and accurate distribution of surface aerodynamic loads and inertial loads in all directions. Typical numerical cases showed that when an aircraft structure model is a plane, this MDLM method converges to the traditional MPA method. For 3D special-shaped surfaces, the average error of this MDLM method is 0.77–2.28%, which is significantly smaller than the average error of the traditional MPA method (3.30–7.40%).

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飞机结构强度分析中三维异形表面载荷分布识别的多维拉格朗日乘子法

在飞机结构设计过程中，在进行强度分析之前，需要将气动载荷和惯性载荷从单个载荷点分布到分布式有限元节点。最常用的载荷分布方法是多点布置（MPA）方法，该方法基于最小变形能原理引入一维拉格朗日乘子，将飞机结构中的异形三维表面简化为平面。然而，实际的飞机结构包含大量的异形表面，MPA方法无法准确地将载荷分布在这些复杂的异形表面上，影响了强度分析的准确性。本文提出了一种新的基于多维拉格朗日乘子（MDLM）的三维载荷分布方法，该方法可以同时实现表面气动载荷和惯性载荷在各个方向上的高效精确分布。典型算例表明，当飞机结构模型为平面时，该MDLM方法收敛于传统的MPA方法。对于三维异形表面，该MDLM方法的平均误差为0.77–2.28%，明显小于传统MPA方法的平均错误（3.30–7.40%）。

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

International Journal of Computational Methods ENGINEERING, MULTIDISCIPLINARY-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

3.30

自引率

17.60%

发文量

审稿时长

15 months

期刊介绍： The purpose of this journal is to provide a unique forum for the fast publication and rapid dissemination of original research results and innovative ideas on the state-of-the-art on computational methods. The methods should be innovative and of high scholarly, academic and practical value. The journal is devoted to all aspects of modern computational methods including mathematical formulations and theoretical investigations; interpolations and approximation techniques; error analysis techniques and algorithms; fast algorithms and real-time computation; multi-scale bridging algorithms; adaptive analysis techniques and algorithms; implementation, coding and parallelization issues; novel and practical applications. The articles can involve theory, algorithm, programming, coding, numerical simulation and/or novel application of computational techniques to problems in engineering, science, and other disciplines related to computations. Examples of fields covered by the journal are: Computational mechanics for solids and structures, Computational fluid dynamics, Computational heat transfer, Computational inverse problem, Computational mathematics, Computational meso/micro/nano mechanics, Computational biology, Computational penetration mechanics, Meshfree methods, Particle methods, Molecular and Quantum methods, Advanced Finite element methods, Advanced Finite difference methods, Advanced Finite volume methods, High-performance computing techniques.