Examination of the complementary energy principle in modified couple stress theory and its application for analysis of size effects in the internal force field of functionally graded microbeams

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling Pub Date : 2024-09-01 DOI:10.1016/j.apm.2024.115662

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引用次数: 0

Abstract

The precise quantification of the internal force field in MEMS piezoresistive sensor micro structure is crucial for ensuring accurate signal output. This paper proposes and proves the complementary energy principle associated with modified couple stress theory (MCST) based on the linear elasticity assumption. And this principle is used to discuss and analyze whether there is a size effect in the internal force field of functionally graded (FG) micro beams for the MEMS piezoresistive sensor. The results show that the size effects exist in the internal forces and the stationary point coordinate x of the total moment for the micro beam. The size effects are related to the dimensionless material scale parameter l/h, the supported spring stiffness, the temperature and the support rotational movements. Intuitive explanations of the size effects are given for the internal force fields and its stationary point coordinates. Behaviors of the solutions agree with the published data when the MCST degenerates into the classical theory (CT).

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检验修正耦合应力理论中的互补能量原理及其在分析功能分级微梁内力场尺寸效应中的应用

MEMS 压阻传感器微结构中内力场的精确量化对于确保精确的信号输出至关重要。本文基于线性弹性假设，提出并证明了与修正耦合应力理论（MCST）相关的补能原理。并利用该原理讨论和分析了 MEMS 压阻传感器的功能分级（FG）微梁的内力场是否存在尺寸效应。结果表明，微梁的内力和总力矩的静止点坐标 x 都存在尺寸效应。尺寸效应与无量纲材料尺度参数 l/h、支撑弹簧刚度、温度和支撑旋转运动有关。对于内力场及其静止点坐标，给出了尺寸效应的直观解释。当 MCST 退化为经典理论（CT）时，解的行为与已公布的数据一致。

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

Applied Mathematical Modelling 数学-工程：综合

CiteScore

9.80

自引率

8.00%

发文量

508

审稿时长

43 days

期刊介绍： Applied Mathematical Modelling focuses on research related to the mathematical modelling of engineering and environmental processes, manufacturing, and industrial systems. A significant emerging area of research activity involves multiphysics processes, and contributions in this area are particularly encouraged. This influential publication covers a wide spectrum of subjects including heat transfer, fluid mechanics, CFD, and transport phenomena; solid mechanics and mechanics of metals; electromagnets and MHD; reliability modelling and system optimization; finite volume, finite element, and boundary element procedures; modelling of inventory, industrial, manufacturing and logistics systems for viable decision making; civil engineering systems and structures; mineral and energy resources; relevant software engineering issues associated with CAD and CAE; and materials and metallurgical engineering. Applied Mathematical Modelling is primarily interested in papers developing increased insights into real-world problems through novel mathematical modelling, novel applications or a combination of these. Papers employing existing numerical techniques must demonstrate sufficient novelty in the solution of practical problems. Papers on fuzzy logic in decision-making or purely financial mathematics are normally not considered. Research on fractional differential equations, bifurcation, and numerical methods needs to include practical examples. Population dynamics must solve realistic scenarios. Papers in the area of logistics and business modelling should demonstrate meaningful managerial insight. Submissions with no real-world application will not be considered.