Adaptive quadtree edge-based smoothed finite element method for limit state analysis of structures

IF 2.7 3区材料科学 Q2 ENGINEERING, MECHANICAL

International Journal of Mechanics and Materials in Design Pub Date : 2024-05-13 DOI:10.1007/s10999-024-09716-6

Phuc L. H. Ho, Changkye Lee

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Abstract

This study presents an efficient numerical approach for pseudo-lower bound limit analysis of structures. The total stress field is decomposed into two components: an elastic component associated with the safety factor and a self-equilibrating residual component. Subsequently, equilibrium conditions within the optimization problem are satisfied in a weak manner. The application of the adaptive quadtree edge-based smoothed finite element method (ES-FEM), combined with the transformation into the second-order cone programming (SOCP) form, ensures the resulting optimization problem remains minimal in size. Moreover, employing a yield stress-based adaptive strategy in the proposed procedure either accurately provides limit loads with low computational effort or effectively predicts the collapse mechanism through the concentration of elements after mesh refinement progress. The investigation of a series of numerical tests confirms the effectiveness and reliability of the proposed method.

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用于结构极限状态分析的基于边缘的自适应四叉树平滑有限元法

本研究提出了一种对结构进行伪下限极限分析的高效数值方法。总应力场被分解为两个部分：与安全系数相关的弹性部分和自平衡残余部分。随后，以弱方式满足优化问题中的平衡条件。应用基于边缘的自适应四叉树平滑有限元法（ES-FEM），并将其转换为二阶锥编程（SOCP）形式，可确保优化问题的最小规模。此外，在所提出的程序中采用基于屈服应力的自适应策略，既能以较低的计算量准确提供极限载荷，又能通过网格细化后元素的集中有效预测坍塌机制。一系列数值测试的研究证实了所提方法的有效性和可靠性。

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来源期刊

International Journal of Mechanics and Materials in Design ENGINEERING, MECHANICAL-MATERIALS SCIENCE, MULTIDISCIPLINARY

CiteScore

6.00

自引率

5.40%

发文量

审稿时长

>12 weeks

期刊介绍： It is the objective of this journal to provide an effective medium for the dissemination of recent advances and original works in mechanics and materials'' engineering and their impact on the design process in an integrated, highly focused and coherent format. The goal is to enable mechanical, aeronautical, civil, automotive, biomedical, chemical and nuclear engineers, researchers and scientists to keep abreast of recent developments and exchange ideas on a number of topics relating to the use of mechanics and materials in design. Analytical synopsis of contents: The following non-exhaustive list is considered to be within the scope of the International Journal of Mechanics and Materials in Design: Intelligent Design: Nano-engineering and Nano-science in Design; Smart Materials and Adaptive Structures in Design; Mechanism(s) Design; Design against Failure; Design for Manufacturing; Design of Ultralight Structures; Design for a Clean Environment; Impact and Crashworthiness; Microelectronic Packaging Systems. Advanced Materials in Design: Newly Engineered Materials; Smart Materials and Adaptive Structures; Micromechanical Modelling of Composites; Damage Characterisation of Advanced/Traditional Materials; Alternative Use of Traditional Materials in Design; Functionally Graded Materials; Failure Analysis: Fatigue and Fracture; Multiscale Modelling Concepts and Methodology; Interfaces, interfacial properties and characterisation. Design Analysis and Optimisation: Shape and Topology Optimisation; Structural Optimisation; Optimisation Algorithms in Design; Nonlinear Mechanics in Design; Novel Numerical Tools in Design; Geometric Modelling and CAD Tools in Design; FEM, BEM and Hybrid Methods; Integrated Computer Aided Design; Computational Failure Analysis; Coupled Thermo-Electro-Mechanical Designs.