Indronil D
Department of Civil and Environmental Engineering, North South University, Bangladesh.
Heliyon. 2024 Aug 16;10(17):e36513. doi: 10.1016/j.heliyon.2024.e36513. eCollection 2024 Sep 15.
This paper provides a comprehensive analysis, using nonlocal stress-driven integral theory, of the static behavior of a nanoscale beam of bidirectionally graded materials. After a brief explanation of the mathematical formulation of BDFGMs, the work done and strain energy expressions derived from the displacement field are discussed. Variational formulations and Hamilton's principle are used to develop the equilibrium equation. An analytical development of the nonlocal kernel for stress-driven integral theory and formulated governing equation which was nondimensionalized later. Explicit equations for displacement and moment are obtained by solving this equation using the Laplace transformation. Three different boundary conditions are examined, and differences in the maximum displacement with respect to the nonlocal parameter and the two material FGM parameters are displayed both visually and in table form. The results exhibit excellent agreement and provide a standard for further research when they are closely compared to the existing numerical data. This work contributes to the knowledge of BDFGMs under nonlocal effects generated by stress-driven integral theory and offers solutions that have been confirmed for further investigation.
本文采用非局部应力驱动积分理论，对双向梯度材料纳米梁的静态行为进行了全面分析。在简要解释双向梯度材料的数学公式后，讨论了从位移场导出的功和应变能表达式。利用变分公式和哈密顿原理建立平衡方程。对应力驱动积分理论的非局部核进行了分析推导，并对建立的控制方程进行了无量纲化处理。通过拉普拉斯变换求解该方程，得到了位移和弯矩的显式方程。研究了三种不同的边界条件，并以直观和表格形式展示了最大位移相对于非局部参数和两种材料梯度材料参数的差异。当将结果与现有数值数据进行仔细比较时，结果显示出极好的一致性，并为进一步研究提供了标准。这项工作有助于了解应力驱动积分理论产生的非局部效应下的双向梯度材料，并提供了经证实可进一步研究的解决方案。
