In this work, a modified surface-effect incorporated beam model based on Gurtin and Murdoch (GM) surface elasticity theory is established by satisfying the required balance equations on surfaces, which is often overlooked by researchers in this field. With the refinement, the proposed model is more rigorous in mathematics and mechanics compared with GM theory-based beam models in literature. To demonstrate the model, the problem for static bending of simply supported beam considering surface effects is solved by applying the general equations derived, and numerical results are obtained and discussed.

中文翻译：

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基于Gurtin-Murdoch表面弹性理论的改进梁模型

在这项工作中，通过满足表面上所需的平衡方程，建立了基于Gurtin和Murdoch（GM）表面弹性理论的改进的表面效应结合梁模型，该领域的研究人员常常忽略了该模型。通过改进，与文献中基于GM理论的梁模型相比，所提出的模型在数学和力学上更加严格。为了证明该模型，通过应用导出的一般方程解决了考虑表面效应的简支梁静弯曲问题，并获得了数值结果并进行了讨论。