Influences of Porosity Distribution and Size-Dependent on Bending, Buckling, and Free Vibration of Bi-Directional FG Porous Microbeams With Variable Thickness and MLSPs Using the MSGT and IGA

IF 2.9 3区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal for Numerical Methods in Engineering Pub Date : 2025-07-16 DOI:10.1002/nme.70069

Saeed Mirzaei, Mehrdad Hejazi, Reza Ansari

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Abstract

In this study, the bending, buckling, and free vibration analysis of bi-directional functionally graded porous microbeams with variable thickness are investigated. By utilizing the modified strain gradient theory (MSGT) in conjunction with a sinusoidal shear deformation theory, governing equations are derived using Hamilton's principle within the framework of the non-uniform rational B-spline (NURBS)-based isogeometric analysis (IGA). In addition, the C²-continuity requirement can be easily achieved by increasing the order of the NURBS basis functions. The MLSPs and the material properties of microbeams vary along with both thickness and axial directions based on the rule of mixture scheme. To consider the effects of porosity, two even and uneven distributions are considered. After verifying the accuracy of the presented approach, the influence of the aspect ratio, gradient indices, different boundary conditions, porosity parameters, variable MLSPs, and thickness on the bending, buckling, and free vibration characteristics of microbeams are investigated.

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利用MSGT和IGA研究变厚度和MLSPs双向FG多孔微梁的弯曲、屈曲和自由振动对孔隙率分布和尺寸的影响

本文研究了变厚度双向功能梯度多孔微梁的弯曲、屈曲和自由振动特性。利用修正应变梯度理论（MSGT）结合正弦剪切变形理论，在基于非均匀有理b样条（NURBS）的等几何分析（IGA）框架下，利用Hamilton原理推导出控制方程。此外，通过增加NURBS基函数的阶数，可以很容易地实现c2 -连续性要求。基于混合方案的规律，微梁的材料性能随厚度和轴向的变化而变化。为了考虑孔隙度的影响，考虑了均匀分布和不均匀分布。在验证了该方法的准确性之后，研究了宽高比、梯度指数、不同边界条件、孔隙率参数、不同mlsp和厚度对微梁弯曲、屈曲和自由振动特性的影响。

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来源期刊

International Journal for Numerical Methods in Engineering 工程技术-工程：综合

CiteScore

5.70

自引率

6.90%

发文量

276

审稿时长

5.3 months

期刊介绍： The International Journal for Numerical Methods in Engineering publishes original papers describing significant, novel developments in numerical methods that are applicable to engineering problems. The Journal is known for welcoming contributions in a wide range of areas in computational engineering, including computational issues in model reduction, uncertainty quantification, verification and validation, inverse analysis and stochastic methods, optimisation, element technology, solution techniques and parallel computing, damage and fracture, mechanics at micro and nano-scales, low-speed fluid dynamics, fluid-structure interaction, electromagnetics, coupled diffusion phenomena, and error estimation and mesh generation. It is emphasized that this is by no means an exhaustive list, and particularly papers on multi-scale, multi-physics or multi-disciplinary problems, and on new, emerging topics are welcome.