Stress Concentration Factors
Stress Concentration Factors
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DOI：
10.1115/1.3423544
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发表时间：
1974
影响因子：
1.6
通讯作者：
R. Peterson;R. Plunkett
中科院分区：
文献类型：
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作者：
R. Peterson;R. Plunkett
克服可能的符号障碍。文中未给出专业技术问题的解决方案。相反，从张量分析、位势理论的要素开始，接着到运动学、动力学以及线性弹性的本构关系，逐步阐述了该理论的要点，在每个阶段都对大量相关论断给出了严格证明。然后，关于弹性静力学的一长章以及关于弹性动力学的另一章完成了这项工作，它可作为对弹性感兴趣的应用数学家的一本优秀教材，以及作为一本为从业者提供大量参考文献的可靠参考书。
唐纳德·E·卡尔森所著《线性热弹性》，第297 - 345页（S.N. - N. 评论）。这部分沿袭了前文的风格，给出了热弹性的基本原理，同样避免了技术问题的解决方案。它不像古尔廷的文章那样雄心勃勃，但学术性很强。虽然这位评论者认为它是文献中受欢迎的补充，但他觉得在无可置疑的经典热弹性理论中使用有争议的克劳修斯 - 杜亥姆不等式是不必要的。
盖塔诺·菲谢拉所著《弹性中的存在性定理以及具有单边约束的弹性边值问题》，第347 - 424页（W.E.O. 评论）。这两篇文章推荐给那些在现代数学分析方面有良好基础的人。第一篇文章的很大一部分致力于涉及强椭圆算子的线性边值问题解的存在性和唯一性的关键定理。这些结果被应用于一些具有双边约束的线性弹性经典问题。第二篇文章扩展了第一篇文章的分析，以便处理具有单边（即不等式）约束的问题。针对对称和非对称算子的情况，为抽象单边问题得出了一般性结果。这些结果的应用包括著名的西诺里尼问题。
P. M. 纳格迪所著《壳与板理论》，第425 - 640页（S.N. - N. 评论）。通过两种并行的方法推导出了与弹性板和壳相关的场方程。第一种称为直接法，将壳视为嵌入三维欧几里得空间的可变形二维曲面。在曲面的每个点都指定了一个称为导向矢量的可变形矢量。建立了该模型的运动学，然后通过引入接触（内）力和导向矢量偶以及一个称为固有导向矢量偶的附加矢量来讨论动力学，同时充分考虑了刚性旋转下的不变性。假定了平衡方程，并得到了它们的局部形式。最后，对于弹性壳，自由能根据表面变形度量、导向矢量及其表面梯度、温度等表示。克劳修斯 - 杜亥姆不等式的使用使得动力学量作为自由能相对于相应变形度量的梯度给出。表述清晰且系统，使整个壳理论看起来很容易。但在我看来，这种方法存在两个主要的难以克服的困难：(a) 由于自由能被写成非物理的导向矢量及其梯度的函数，人们不知道如何根据物理可测量的量来计算本构参数。（在一些特殊情况下，与三维问题的精确解进行比较可得到一些本构参数。）对导向矢量的任何物理识别都将涉及该方法想要避免的特别的和直觉的近似；(b) 假设克服了困难(a)，即使在原则上，如果使用这样一种二维理论来解决一个给定的三维壳问题，即使是对于特殊的几何形状和加载条件，似乎也不可能在该理论框架内建立对误差的严格数学估计。
overcoming possible notational barriers. No solutions of specialized technical problems are presented. Instead, the essentials of the theory are developed, beginning with tensor analysis, elements of potential theory, then moving to kinematics, dynamics, and the constitutive relation in linear elasticity, at each stage giving rigorous proofs for a large body of relevant assertions. Then a long chapter in elastostatics and another in elastodynamics complete this work which can serve as an excellent text for applied mathematicians interested in elasticity, and as a solid reference book with an extensive list of references for the practitioners. Linear Thermoelasticity by Donald E. Carlson; pp. 297-345 (reviewed by S.N.-N.). This part follows the style of the previous article, giving fundamentals in thermoelasticity, again avoiding solutions to technical problems. It is less ambitious than Gurtin's article, but scholarly done. While this reviewer finds it a welcome addition to the literature, he feels that the use of the questionable Clausius-Duhem inequality in the unquestionable classical theory of thermoelasticity is unnecessary. Existence Theorems in Elasticity and Boundary-Value Problems of Elasticity With Unilateral Constraints by Gaetano Fichera; pp. 347-424 (reviewed by W.E.O.). These two articles are recommended to those who have a good background in modern mathematical analysis. A substantial portion of the first article is devoted to key theorems on the existence and uniqueness of solutions to linear boundary-value problems involving strongly elliptic operators. Applications of these results are given for some classical problems in linear elasticity with bilateral constraints. The second article extends the analysis of the first article so as to treat problems with unilateral (i.e., inequality) constraints. General results are developed for the abstract unilateral problem in cases of both symmetric and nonsymmetric operators. Applications of these results include the famous Signorini Problem. The Theory of Shells and Plates by P. M. Naghdi; pp. 425-640 (reviewed by S.N.-N.). Field equations relating to elastic plates and shells are developed by two parallel methods. The first, called direct, views the shell as a deformable two-dimensional surface embedded in three-dimensional Euclidean space. A deformable vector called director is assigned at each point of the surface. The kinematics of this model is developed, then dynamics is discussed by the introduction of contact (internal) force and director couple, and an additional vector called intrinsic director couple, taking due account of invariance under rigid rotation. Balance equations are postulated; and their local forms are obtained. Finally, for elastic shells, the free energy is expressed in terms of surface deformation measures, the director, and its surface gradient, temperature, etc. The use of the Clausius-Duhem inequality gives dynamical quantities as gradients of the free energy with respect to the corresponding deformation measures. The presentation is clear and systematic, making the whole shell theory appear easy. But in my view, this approach involves two principally insurmountable difficulties: (a) The free energy being written as a function of the nonphysical director and its gradient, one does not know how to calculate the constitutive parameters in terms of physically measurable quantities. (In some special cases, comparison with exact solutions of three-dimensional problems gives some of the Constitutive parameters.) Any physical identification of the director will involve ad hoc and intuitive approximations which the method wants to avoid; (b) Assuming that difficulty (a) is overcome, it does not appear possible, even in principle, to establish within the framework of this theory rigorous mathematical estimates for the error, if such a two-dimensional theory is used to solve a given three-dimensional shell problem, even for specialized geometries, and loading conditions.