Integral nonlocal stress gradient elasticity of functionally graded porous Timoshenko nanobeam with symmetrical or anti‐symmetrical condition

IF 2.3 4区 工程技术 Q1 MATHEMATICS, APPLIED
Chang Li, Hai Qing
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Abstract

Utilization of symmetrical or anti‐symmetrical condition could improve the calculation efficiency. In this paper, a mathematical formulation is proposed to deal with the symmetrical or anti‐symmetrical condition in an integral nonlocal stress gradient model (INSGM), which is transformed equivalently into differential form with constitutive boundary condition as well as constitutive symmetrical or anti‐symmetrical condition. Unlike general constitutive boundary conditions, an integral item is introduced to constitutive symmetrical and anti‐symmetrical conditions, and they are opposite to each other. Based on INSGM with symmetrical or anti‐symmetrical conditions, static bending of simply‐supported (SS) and clamped‐clamped (CC) functionally graded porous Timoshenko nanobeams is investigated for symmetrical loads, including uniformly distributed load (UDL) and middle point force, as well as anti‐symmetrical loads, including anti‐symmetrical UDL and middle point moment. The exact solutions are deduced and expressed in explicit form for different boundary and loading conditions. Calculation shows that, under UDL, bending deflections of half Timoshenko nanobeams based on current model agree well with those for whole Timoshenko nanobeams based on general INSGM for both SS and CC boundary conditions. Numerical study is performed to show the effectiveness of current model.
对称或反对称条件下功能梯度多孔Timoshenko纳米梁的积分非局部应力梯度弹性
利用对称或反对称条件可以提高计算效率。本文提出了一种处理积分非局部应力梯度模型(INSGM)对称或反对称条件的数学公式,将该模型等效地转化为具有本构边界条件和本构对称或反对称条件的微分形式。与一般的本构边界条件不同,本构对称和反对称条件引入了积分项,它们是相互对立的。基于对称或反对称条件下的INSGM,研究了对称载荷(包括均匀分布载荷(UDL)和中点力)以及非对称载荷(包括非对称UDL和中点力矩)下简支(SS)和夹紧(CC)功能梯度多孔Timoshenko纳米梁的静态弯曲。推导出了不同边界和载荷条件下的精确解,并以显式形式表示出来。计算结果表明,在UDL条件下,基于当前模型的半Timoshenko纳米梁的弯曲挠度与基于通用INSGM的整个Timoshenko纳米梁的弯曲挠度在SS和CC边界条件下都具有较好的一致性。数值研究表明了该模型的有效性。
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
CiteScore
3.30
自引率
8.70%
发文量
199
审稿时长
3.0 months
期刊介绍: ZAMM is one of the oldest journals in the field of applied mathematics and mechanics and is read by scientists all over the world. The aim and scope of ZAMM is the publication of new results and review articles and information on applied mathematics (mainly numerical mathematics and various applications of analysis, in particular numerical aspects of differential and integral equations), on the entire field of theoretical and applied mechanics (solid mechanics, fluid mechanics, thermodynamics). ZAMM is also open to essential contributions on mathematics in industrial applications.
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