Nonlocal isogeometric analysis for bidirectional functionally graded porous curved microbeams with arbitrary boundary conditions  

双向功能梯度多孔弯曲微梁在任意边界条件下的非局域等几何分析

作　　者：Thu-Huong Nguyen Thi Van Ke Tran Van-Minh Phung Van Hai Trinh Quoc Hoa Pham 

机构地区：[1]Faculty of Mechanical Engineering,Hanoi University of Industry,Hanoi,100000,Vietnam [2]Faculty of Mechanical Engineering,Le Quy Don Technical University,Hanoi,100000,Vietnam [3]Institute of Vehicle and Energy Engineering,Le Quy Don Technical University,Hanoi,100000,Vietnam [4]Faculty of Engineering and Technology,Nguyen Tat Thanh University,Ho Chi Minh City,700000,Vietnam

出　　处：《Acta Mechanica Sinica》2024年第8期194-218,共25页力学学报（英文版）

摘　　要：This research aims to analyze the static bending and free vibration behaviors of bidirectional functionally graded porous(BFGP)curved microbeams with elastic boundary conditions resting on a Pasternak’s elastic foundation in a hygro-thermal environment.Isogeometric analysis based on non-uniform rational B-splines,first-order shear deformation theory,nonlocal elasticity theory combined with the modified strain gradient theories,modified Timoshenko beam theory are formulated to depict bending and shear deformations of BFGP curved microbeams.Especially,because using the modified Timoshenko beam theory,this study removes the requirement for a shear correction factor and describes shear stress by zero at the upper and lower cross-sectional sites of the BFGP curved microbeam.Different from traditional boundary conditions,where the beginning and end positions of a curved beam are connected by an elastic system of straight and torsion springs.This allows for greater flexibility in controlling the stiffness of the springs to obtain arbitrary boundaries.To assess the accuracy and convergence of the proposed approach,validation numerical examples were conducted in the various examples.本研究旨在分析湿润热环境中放置在Pasternak弹性基底上的双向功能梯度多孔(BFGP)弯曲微梁在弹性边界条件下的静力弯曲和自由振动行为.基于NURBS、FSDT、MSGT和修正Timoshenko梁理论等几何分析方法(IGA)来描述BFGP弯曲微梁的弯曲和剪切变形.尤其基于修正Timoshenko梁理论的方法在本研究中可以消除对剪切修正因子的要求,并用零剪切应力描述BFGP弯曲微梁的上下横截面.与传统的边界条件不同,曲线梁的起始位置和结束位置是由直弹簧和扭转弹簧组成的弹性系统连接的.在控制弹簧刚度的条件下允许更大灵活性来获得任意边界.为了评估所提出方法的准确性和收敛性,本文还进行了各种示例的数值验证实验.

关 键 词：Bidirectional functionally graded porous material Elastic boundary condition Isogeometric analysis Curved microbeams Nonlocal elasticity theory Modified strain gradient theory 

分 类 号：O18[理学—数学] O34[理学—基础数学]