16.21 Techniques of Structural Analysis and sig Spring 2003 Unit #1 In this course we are going to focus on energy and variational methods for structural analysis. To understand the overall approach we start by con- trasting it with the alternative vector mechanics approach

Concept Question Which of the following statements is true 1. The PVD and the PMPE are equivalent 2. The PVD is more general 3. The PMPE applies to any kind of material 4. The stationary character of the potential en ergy is equivalent to the Pvd for elastic ma terials

What new element is Castigliano s Theorem introducing? 1. None, it's just a particular case of the PMPE 2. It's a totally different principle that allows to obtain solutions of elasticity problems with unprecedented accuracy and efficiency in- cluding relativistic effects

Constitutive Law(6 equations, O unknowns) C Bound dary conditions of two types Traction or natural boundary conditions: For tractions t imposed on the portion of the surface of the body aBt Displacement or essential boundary conditions: For displacement

随着生物化学、细胞生物学、应用 分子生物学、遗传工程和代谢工程等学 科和分析、检测技术的发展,工业发酵 正在发生一个从技艺走向科学的重大变 化,我国大学的发酵工程专业正在融入 生物工程专业。在生物工程受到广泛重 视的今天,有必要把工业发酵生产中的 菌种选育、发酵工艺和微生物的培养设 备作为一个整体,在科学的水平上对工 业发酵进行重新审视

Concept Question Which of the following statements is correct? Uo=U for ALL elastic materials(1 Uo=OijEij-U0 ONLY for linear elastic materials Jo=-ijEii for a nonlinear elastic material Statements(1) and 3)

采用相分析和X射线衍射技术,研究了含Ti、Nb等微合金元素的高强钢中碳氮化物的溶解行为.结果表明,加热到1250℃,未均热时,主要是面心立方结构的Ti(CN)、(TiNb)(CN)、TiC析出相;均热时间为45min,部分Ti和Nb继续溶解,析出相转为Ti(CN)、TiC为主,平均颗粒尺寸由300nm增大为323nm,此时Ti、Nb固溶已经达到平衡,固溶率分别为64.2%和85.8%.当保温80min时,析出相含量基本没有变化,但颗粒尺寸有所增加

第一节 物流设施规划与设计的含义及程序 第二节 设施系统布置设计要素与模式 第三节 物流设施布置规划的分析方法与技术 第四节 物流设施布置方案的评价与选择

Which of the following statements is correct? 1. The PVD only applies to linear elastic materials 2. The PVD applies only to elastic materials, but they can be linear or non-linear 3. The PVD applies regardless of the constitutive behavior of the material

Unit #10- Principle of minimum potential energy and Castigliano's First Theorem Principle of minimum potential energy The principle of virtual displacements applies regardless of the constitutive law. Restrict attention to elastic materials(possibly nonlinear). Start from the Pvd