Size-dependent behaviour of in-plane bi-directional functionally graded porous microplates with variable thickness based on the modified strain gradient theory and IGA

IF 6.6 1区工程技术 Q1 ENGINEERING, CIVIL Thin-Walled Structures Pub Date : 2025-03-02 DOI:10.1016/j.tws.2025.113144

Saeed Mirzaei , Mehrdad Hejazi , Reza Ansari

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Abstract

In this paper, the isogeometric analysis (IGA) is extended to study the size-dependent behavior of bending, buckling and free vibration of in-plane bi-directional functionally graded porous microplates with variable thickness. In order to capture the effect of size, the modified strain gradient elasticity theory, which has three length scale parameters, is used. Regarding to the third-order shear deformation theory, the equations of motions are derived by using the Hamilton's principle and then are discretized based on the IGA approach. The material properties vary continuously through in-plane directions by employing the rule of mixture and the porosity distribution is considered an even type. The C²-continuity requirement can be easily achieved by increasing the order of the non-uniform rational B-spline (NURBS) basis functions larger than two. The influences of the size effect, aspect ratios, boundary conditions, thickness variations, material gradations, and porosity distributions on the deflections, the fundamental natural frequencies, and the buckling load values of the rectangular, circular and elliptical microplates are studied. The obtained results are compared with the previously published studies to show the performance and efficiency of the present research.

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基于修正应变梯度理论和IGA的面内双向变厚度功能梯度多孔微板尺寸特性研究

本文将等几何分析（IGA）扩展到面内双向变厚度功能梯度多孔微板的弯曲、屈曲和自由振动的尺寸依赖行为。为了捕捉尺寸的影响，采用了具有三个长度尺度参数的修正应变梯度弹性理论。针对三阶剪切变形理论，采用Hamilton原理推导出运动方程，并采用IGA方法进行离散化。采用混合规律，材料性能沿平面方向连续变化，孔隙率分布为均匀型。通过增加大于2的非均匀有理b样条（NURBS）基函数的阶数，可以很容易地实现c2 -连续性要求。研究了尺寸效应、宽高比、边界条件、厚度变化、材料梯度和孔隙率分布对矩形、圆形和椭圆形微孔板挠度、基本固有频率和屈曲载荷值的影响。将所得结果与已发表的研究结果进行了比较，以表明本研究的性能和效率。

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来源期刊

Thin-Walled Structures 工程技术-工程：土木

CiteScore

9.60

自引率

20.30%

发文量

801

审稿时长

66 days

期刊介绍： Thin-walled structures comprises an important and growing proportion of engineering construction with areas of application becoming increasingly diverse, ranging from aircraft, bridges, ships and oil rigs to storage vessels, industrial buildings and warehouses. Many factors, including cost and weight economy, new materials and processes and the growth of powerful methods of analysis have contributed to this growth, and led to the need for a journal which concentrates specifically on structures in which problems arise due to the thinness of the walls. This field includes cold– formed sections, plate and shell structures, reinforced plastics structures and aluminium structures, and is of importance in many branches of engineering. The primary criterion for consideration of papers in Thin–Walled Structures is that they must be concerned with thin–walled structures or the basic problems inherent in thin–walled structures. Provided this criterion is satisfied no restriction is placed on the type of construction, material or field of application. Papers on theory, experiment, design, etc., are published and it is expected that many papers will contain aspects of all three.