标题: 横向等向性半无限空间内之应力与位移
Computing Stresses and Displacements in a Trasversely Isotropic Half-Space
作者: 王承德
Wang, Cheng-Der
廖志中
Liao, Jyh-Jong
土木工程学系
关键字: 横向等向性;位移
公开日期: 1997
摘要: 传统上,一般基础材料受工程结构物所引致的位移、应力量之推估,大多假设此介质为均质、均向、线弹性之连体;然而,对于许多天然大地材料而言,由于受到生成过程或是生成过程后变形作用之影响,其力学性质如强度、变形性等…,均受方向性所控制而展现出异向性质,例如黏土之沈积作用与其随后所发生的压密特性,以及岩体受不连续性切割等…。因此,对于此类材料受外力作用后之位移、应力分布的估计,宜考虑因异向性质所造成的影响。在工程实务上,异向性土壤/岩石若以其明显之地质构造或弹性对称方向为座标轴,一般可分为正交性或横向等向性材料。本论文系针对横向等向性半无限空间之弹性载重问题来加以解析与探讨,主要工作项目包括:(一)重新推导点荷重之位移与应力基本解;(二)推导埋置于地表下之非对称形荷重(有限线载重、均布与线性分布矩形载重、均布与线性分布三角形载重)的位移与应力解;(三)扩充三角形荷重解,用以计算质内受不规则形荷重所引致的位移与应力;(四)制作影响图,用以计算介质内承受不规则形地表荷重所产生的应力、内部位移及地表位移。本论文所推导出的解析解,与少数仅存的现有异向性解符合,且将解化简成均向性的情形,亦与许多均向性解相符;由一系列的参数研究显示,所得的位移与应力分布深受不同荷重模式、介质种类与异向性程度之影响,且其与以传统均向性理论所做的评估有相当大的差异;至于在估算横向等向性半无限空间内受不规则形荷童作用下的位移与应力值方面,本文所提出的解析解法与图解法,其计算结果于精度上均可达至工程实务的要求,且能够有效率地成为数值方法外的多重选择。
Conventionally, the linear elastic and isotropic theory has been extensively used for the calculation of displacements and stresses in a loaded soil or rock. However, many soils and rocks exhibit some degrees of anisotropy in their response to deformations and stresses. Anisotropic soils/rocks are often modeled as orthotropic or transversely isotropic materials. In this dissertation, several closed-form solutions and influence charts were presented for calculating the induced displacements and stresses in a horizontal transversely isotropic half-space subjected to applied loads. The major work includes (1) rederiving the displacement and stress solutions induced by a point load; (2) solving the displacements and stresses due to various buried asymmteric loads (finite line loads, uniform/linearly varying rectangular loads, and uniform/linearly varying triangular loads); (3) extending the triangular loading solutions to calculate the displacements and stresses subjected to an arbitrarily-shaped load; (4) constructing influence charts for computing the stresses and displacements induced by an arbitrarily-shaped load.
A series ofparametric studies were conducted to verif/the derived closed-fonnsolutions, and investigate the effect of the loading types, and the type and degree of material anisotropy on the displacements and stresses. The results indicate that (1) the displacement and stress in a transversely isotropic half-space can be correctly calculated by these presented solutions; (2) the displacement and stress accounted for anisotropy are quite different from those by isotropic solutions. Computing the stress and displacement in a transversely isotropic half-space subjected to uniform/non-uniform loads on an irregular shape, a triangulating technique and a graphical method provide results with reasonable accuracy. The two methods are practical and can be the alternatives of numerical methods.
URI: http://140.113.39.130/cdrfb3/record/nctu/#NT863015010
http://hdl.handle.net/11536/63253
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