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The reformulated micro-beam models by incorporating the general strain gradient elasticity theory (GSGET)

机译:通过结合大致应变梯度弹性理论(GSGet)来改制的微束模型

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摘要

Two independent material parameters (Lame constants) are incorporated in classical isotropic elasticity theory, while how many independent material parameters are incorporated in the higher-order isotropic elasticity theory? It is answered by Zhou's general strain gradient elasticity theory (GSGET), which firstly proved that only three material parameters are independent. In this paper, the static and dynamic analyses of micro-beam models are proposed based on the GSGET, which can capture the size effects of micro-structures. Then the variational formulations of the micro-beams including Bernoulli-Euler and Tim-oshenko beams are deduced by taking advantage of Hamilton's principle. Governing equations, initial conditions, and all possible boundary conditions are derived subsequently. What's more, the static bending and free vibration problems for a simply supported beam have been analytically solved, and the effects of normalized maximum deflection, stiffness, and natural frequency are studied by comparing the present results with the classical and couple stress results respectively. The results indicate that the GSGET should be used to characterize the size effects of mechanical properties for micro-structures.
机译:两个独立的材料参数(LAME常数)结合在经典各向同性弹性理论中,而在高阶各向同性弹性理论中结合了多少个独立的材料参数?它由周的一般应变梯度弹性理论(GSGET)回答,首先证明只有三种材料参数是独立的。本文提出了基于GSGET的微束模型的静态和动态分析,其可以捕获微结构的尺寸效应。然后通过利用汉密尔顿的原理推导出包括Bernoulli-euler和Tim-Oshenko梁的微梁的变分制剂。控制方程式,初始条件和随后导出所有可能的边界条件。更重要的是,通过分别将当前结果与经典和耦合应力结果进行比较,研究了简单支持的光束的静态弯曲和自由振动问题,以及归一化最大偏转,刚度和自然频率的影响。结果表明,GSGET应用于表征机械性能对微结构的尺寸影响。

著录项

  • 来源
    《Applied Mathematical Modelling》 |2021年第2期|448-465|共18页
  • 作者单位

    School of Civil Engineering Shandong University Jinan 250061 China;

    School of Civil Engineering Shandong University Jinan 250061 China;

    School of Mechanical Engineering Shandong University Jinan 250061 China;

    School of Civil Engineering Shandong University Jinan 250061 China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    GSGET; Bernoulli-Euler beam; Timoshenko beam; Size effect;

    机译:GSGET;伯努利 - 欧拉梁;Timoshenko梁;尺寸效应;

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