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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (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|固体力学代写Solid Mechanics代考|DEFORMATION AND STRAIN

The overall displacement of the particles in such body is known as deformation. By deforming, the body converts work done to elastic strain energy and kinetic energy. If there is no more external force exerted on it, the body will stop deform after such energy conversion is completed. When external forces reduced, the elastic strain energy will exert elastic restoring force, which will have its work done converted to kinetic energy and moves the particles back to their original position, if the bond between particles has not been break. There are two types of deformation: rigid body motion and non-rigid body deformation.

Rigid body motion occurs when the exerted force is enough to change the motion state of a body but insufficient stress is developed to overcome its attraction force. Rigid body motion includes translation and rotation. In translation, all points on the body have displacement of same magnitude and in the same direction. In rotation, all points on the body have angular displacement of same angle and in the same direction, except the points that lie along the axis of rotation.

Non-rigid body deformation occurs when stress developed is enough to overcome the attraction force, regardless the ability of force to change a body’s motion state. This type of deformation includes distortion and dilation, which is in fact the result of differential translation and rotation. Distortion is a process where a body change its shape, while dilation is a process where a body change its volume. Fig. 3.1 shows some examples of rigid and non-rigid body deformation in a girder.
As an observable and measurable quantity, deformation is an aspect that material scientists look up to identify the material’s mechanical properties. However, direct measurement of a body’s deformation is not reliable: a very short rubber stick deforms less than a very long steel rod. One can wrongfully conclude that rubber is more rigid than steel if he interpreted test result this way. Also, when a solid is experiencing rigid body deformation, no differential deformation takes place throughout the body. Differential deformation only takes place during non-rigid body deformation, which is an indication of development of stress inside within the solid. For these reasons, strain, i.e a way to determine the severity of deformation using ratio of solid’s deformation to its original length along a specific direction, is looked up.

## 物理代写|固体力学代写Solid Mechanics代考|LAGRANGIAN DESCRIPTION

Since deformation is a result of change in velocity of points on a body, it can be expressed as a function of time. Take an infinitesimal element on a solid as shown in Fig. 3.4 as an example. When external force is exerted, the point $A$ and $B$ of this element moves with different velocity. At the time $t_l$, point $A$ reaches point $A^{\prime}$.

Lagrangian description is used to express the function of deformation based on initial condition and time. In solid mechanics, initial conditions, e.g. geometry and boundary condition, are usually specified or easy to define even if they are not and thus, Lagrangian description is a kind of expression that eases the process to determine deformation of any point. Therefore, the vector of point $A^{\prime}$ (after deformation) is interested and it can be written as:
$$a^{\prime}=a^{\prime}(x, y, z, t)$$

Since position vector $a$ is consist of position component in $\mathrm{x}, \mathrm{y}$ and $\mathrm{z}$ axes, namely $x, y$ and $z$, the function can also be written as:
$$x^{\prime}=x^{\prime}(x, y, z, t)$$
$$y^{\prime}=y^{\prime}(x, y, z, t)$$
$$z^{\prime}=z^{\prime}(x, y, z, t)$$
Let $U$ be the vector of displacement attained by a point upon exertion of force at time $t_l$, and consists of displacement components along $\mathrm{x}, \mathrm{y}$ and $\mathrm{z}$ axes, namely $u, v$ and $w$. This vector is equals to the change in position vector from initial condition to time $t_l$ :
$$[U]=\left[a^{\prime}\right]-[a]$$
The following is obtained after rewriting the displacement vector in terms of displacement components in $x, y$ and $z$ axes:
\begin{aligned} &u=x^{\prime}-x \ &v=y^{\prime}-y \ &w=z^{\prime}-z \end{aligned}

# 固体力学代考

## 物理代写|固体力学代写Solid Mechanics代考|LAGRANGIAN DESCRIPTION

$$a^{\prime}=a^{\prime}(x, y, z, t)$$

$$x^{\prime}=x^{\prime}(x, y, z, t)$$
$$y^{\prime}=y^{\prime}(x, y, z, t)$$
$$z^{\prime}=z^{\prime}(x, y, z, t)$$

$$[U]=\left[a^{\prime}\right]-[a]$$将位移矢量改写为中位移分量的形式，得到 $x, y$ 和 $z$ 坐标轴:
\begin{aligned} &u=x^{\prime}-x \ &v=y^{\prime}-y \ &w=z^{\prime}-z \end{aligned}

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## 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。

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