Abstract

This study presents a novel SBFEM to model the horizontal layered bounded domain with side face load. In order to overcome the limit of original SBFEM in modelling horizontal layered domain, a novel semi-analytical technique which named as the modified SBFEM is proposed. The novel type of local coordinate system makes the original scaling centre replace by scaling line. It is more suitable for the horizontal layered model analysis. The coordinate transformation is greatly reduced by using scaling line. Basing on the principle of virtual work, the modified SBFEM displacement equation is derived. Firstly, the displacement differential equation is transformed into state equation in Hamilton system. The displacement and stress of layered bounded domain can be obtained by one time. As well as making the modified SBFEM more accessible, a new technique for the treatment of side face load is provided. Furthermore, basing on the novel side face load formulation, the displacement and stress expressions for layered bounded domain can be built. The paper fully develops the new formulations, and provides numerical examples to illustrate the accuracy and efficiency of the modified SBEFM. More importantly, the complex side face form and anisotropic material are considered. It significantly extends the application field of the modified SBFEM in solving elastostatic problem.

摘要

本研究提出了一种新颖的 SBFEM 来模拟具有侧面载荷的水平分层有界域。为了克服原始SBFEM 在模拟水平分层域方面的局限性，提出了一种新的半解析技术，命名为改进的SBFEM。新型的局部坐标系使原来的缩放中心由缩放线代替。更适用于水平分层模型分析。使用缩放线大大减少了坐标变换。基于虚功原理，推导了修正的SBFEM位移方程。首先，将位移微分方程转化为哈密顿系统中的状态方程。层状有界域的位移和应力可一次性求得。除了使修改后的 SBFEM 更易于访问外，提供了一种治疗侧面负荷的新技术。此外，基于新的侧面载荷公式，可以建立分层有界域的位移和应力表达式。本文充分开发了新公式，并提供了数值示例来说明修改后的 SBEFM 的准确性和效率。更重要的是，考虑了复杂的侧面形式和各向异性材料。它显着扩展了改进的 SBFEM 在解决弹性静力学问题方面的应用领域。并提供数值示例来说明修改后的 SBEFM 的准确性和效率。更重要的是，考虑了复杂的侧面形式和各向异性材料。它显着扩展了改进的 SBFEM 在解决弹性静力学问题方面的应用领域。并提供数值示例来说明修改后的 SBEFM 的准确性和效率。更重要的是，考虑了复杂的侧面形式和各向异性材料。它显着扩展了改进的 SBFEM 在解决弹性静力学问题方面的应用领域。