assignmentutor-lab™ 为您的留学生涯保驾护航 在代写结构力学Structural Mechanics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写结构力学Structural Mechanics代写方面经验极为丰富，各种代写结构力学Structural Mechanics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|结构力学代写Structural Mechanics代考|Upthrust: Punting Safely

Other real loads that induce and depend on displacements stem from bodies immersed in fluids. In particular, Archimedes’ principle tells us that the force, or upthrust, exerted by a fluid upwards on an object fully immersed or partially submerged is equal to the weight of the displaced fluid and acts through the centroid of the displaced volume.

For example, the submerged depth of a uniform upright cube is a proportion of the overall height equal to the ratio of the cube and fluid densities. The stability of how this cube floats is treated momentarily.

First, consider the floating punt in Fig. 2.2(a). It is a low-lying, flat-hottom craft used nowadays to ferry tourist passengers around shallow tranquil town rivers. Propulsion is manually applied by an experienced chauffeur levering themselves against the river bed via a long pole. Optimal mechanical advantage comes from standing at the rear, or ‘stcrn’, of the punt, from where it is also casicst to stcer using the polc as a rudder between exertions.

The tourists are ‘evenly’ distributed within the punt for simplicity. which descends uniformly to a height $h$ above the surface before the chauffeur mounts rearwards. The downward forces are now the uniformly distributed self-weight of the punt and passengers, $W_{\mathrm{P}}$, and that of the chauffeur, $W_{\mathrm{C}}$, as shown. The punt clearly tilts in the water, becoming more submerged towards the rear. The flat bottom yields a linear depth profile which should not exceed $h$ at the stern, otherwise water is taken on board.
The length of punt, $L$, is much larger than $h$, making the tilting rotation small but not negligible because the upthrust profile depends on the submerged shape; it is small enough, however, that the punt remains horizontal for a simplified equilibrium.

Adopting $x$ as a horizontal coordinate from the bow (front) of the punt, the displacement depth profile, $d$, can be written as $d=y+x \tan \theta$, where $y$ is the bow depth and $\theta$ is the tilt rotation. Alternatively, we could assume a point of rotation at some unknown location along the punt as per the previous buried pole example.

Whatever our approach, the upthrust is equal to the displaced volume times the fluid density, $\rho$, which is equal in turn to the submerged area in profile times $\rho$ times a uniform (we assume) punt width, $w$.

But recognise that the submerged area is comprised of two prismatic sections, a rectangle, $y \times L$, and a triangle, $L \times \theta L$, assuming $\tan \theta \approx \theta$ for small angles, Fig. 2.2(b). The upthrust components from each are simpler expressions, straightforwardly located – as we did for the previous buried pole; halfway along for the rectangular part and two-thirds for the triangle.

## 物理代写|结构力学代写Structural Mechanics代考|Float or Fall Over?

We finish with a floating uniform cuboid in Fig. 2.3(a), of unit length and general height $b$ and width $a$. When the ratio of the cube density to that of the fluid is equal to $\alpha$, the specific density, the submerged depth is $\alpha b$ when perfectly upright. Note that $\alpha$ is limited to unity before the cuboid sinks.

The cuboid will bob up and down if it is moved vertically and released, and eventually settle. On the other hand, if the cuboid is tilted – from sideways wind or wave loading, we might ask if it self-rights or keels over? Experience suggests that if the cuboid is more than half submerged with its centre of mass, $\mathrm{G}$, below the water line, it will overturn if slender in height: a stick or a pen always floats horizontally. When the cuboid sits more out of the water than in it, $\mathrm{G}$ lies above the water line with a greater propensity towards toppling, we surmise.

A displaced configuration is again essential for calculating the correct upthrust. The level of movement does not have to be appreciable when considering stability, for any tendency to move away from upright will happen for any perturbation, no matter how small. We also note that the cuboid rotates about the mid-point of the original surface line where the now emerging and submerging parts, represented by the triangular portions in Fig. 2.3(b), are equal. This affords no change in the upthrust, and equilibrium of vertical forces remains assured.

For moment behaviour, consider first the tilted geometry in Fig. 2.3(c), which assumes that Gioriginally lies helow surface, i.e. $\alpha>1 / 2$. We have divided the submerged part into two; a rectangle, $\mathrm{ABCD}$, and a triangle, $\mathrm{CDE}$. The area of $\mathrm{ABCD}$ is $a \cdot(\alpha b-a \theta / 2)$ given that the right-side vertical edge in Fig. 2.3(b) rises $a \theta / 2$ above the surface – for $\theta$ small, of course. The triangular area is $a \cdot a \theta / 2$, and each upthrust force, $U_1$ and $U_2$, multiplies these areas by $\rho$, the density of the fluid (recall that the cube has unit length into the page, equating its volume and area of cross-section). Their respective centroids are marked by points $\mathrm{J}$ and $\mathrm{H}$ as shown.

# 结构力学代考

## 有限元方法代写

assignmentutor™作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

assignmentutor™您的专属作业导师
assignmentutor™您的专属作业导师