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• 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

## 数学代写|有限元方法代写Finite Element Method代考|Uniaxial deformation

Uniaxial deformation, also referred to as the simple loading, is the type of deformation that can be described with respect to a single orientation (e.g., $x$ ). Typical examples of this type of loading are the elongation/compression of a bar by a tensile/compressive force (Fig. 2.5).

In order to describe the uniaxial deformation in a slender bar, consider an infinitesimally small segment $B C$ of length $d x$ before deformation as shown in Fig. 2.19B. Once the external load is applied in the $x$ direction, the bar deforms. Point $B$ moves to $B$ ‘ where its position change $u$ is described by the deformation vector as follows:
$$\vec{u}=u \hat{i}$$
Note that $u=u(x)$. As the point $B$ moves to the position $B$ ‘, the point $C$ moves to position $C^{\prime}$ and undergoes a position change of $u+(d u / d x) d x$. Thus, the distance between points $C B$ changes from $d x$ to $d x+(d u / d x) d x$.

Elongation/contraction along a given direction is measured by using the normal strain $\varepsilon$ which is defined as the ratio of the change in length along a given direction to the original length as follows:
$$\varepsilon=\frac{1}{d x}\left[\left(1+\frac{d u}{d x}\right) d x-d x\right]=\frac{d u}{d x}$$

## 数学代写|有限元方法代写Finite Element Method代考|Planar deformation

In some problems deformation is confined into a plane. A material point $P$ in the undeformed material will move to point $P^{\prime}$ after deformation as shown in Fig. 2.6. This deformation can be represented by a deformation vector $\vec{u}$. In case of the planar deformation depicted in Fig. 2.6, the deformation vector can be expressed in a Cartesian coordinate system as follows:
$$\vec{u}=u_{x} \hat{i}+u_{y} \hat{j}$$
where $u_{x}$ and $u_{y}$ are the projections of $\vec{u}$ on the $x$ and $y$ axes, respectively. In vector form, the deformation vector is represented as follows:
$${u}=\left{\begin{array}{ll} u_{x} & u_{y} \end{array}\right}^{T}$$

Note that, in general, the deflection components $u_{x}$ and $u_{y}$ vary from point to point inside the deforming solid. Therefore, these variables are functions of the $x$ and $y$ coordinates, $u_{x}=u_{x}(x, y)$ and $u_{y}=u_{y}(x, y)$.

Deformation of a small rectangle around the point $P$ with side lengths $d x$, $d y$ and unit depth is shown Fig. 2.6. As a result of deformation, point $A$ in the undeformed configuration moves to point $A^{\prime}$. Similarly points $B, C$, and $D$ move to $B^{\prime}, C^{\prime}$, and $D^{\prime}$ ‘.

For the two-dimensional deformation depicted in Fig. 2.6, the original length of the side $A B$ is $d x$. The length of the projection of the deformed line $A$ ‘ $B$ ‘on the $x$ axis is $\left(d x+\left(\partial u_{x} / \partial x\right) d x\right.$. Thus, by using Eq. (2.36), we can define the normal strain along the $x$ direction as follows:
$$\varepsilon_{x x}=\frac{\partial u_{x}}{\partial x}$$
It can be similarly shown that the normal strain along the $y$ direction is defined as follows:
$$\varepsilon_{y y}=\frac{\partial u_{y}}{\partial y}$$

# 有限元方法代考

## 数学代写|有限元方法代写Finite Element Method代考|Uniaxial deformation

$$\vec{u}=u \hat{i}$$

$$\varepsilon=\frac{1}{d x}\left[\left(1+\frac{d u}{d x}\right) d x-d x\right]=\frac{d u}{d x}$$

## 数学代写|有限元方法代写Finite Element Method代考|Planar deformation

$$\vec{u}=u_{x} \hat{i}+u_{y} \hat{j}$$
\left 的分隔符缺失或无法识别

$$\varepsilon_{x x}=\frac{\partial u_{x}}{\partial x}$$

$$\varepsilon_{y y}=\frac{\partial u_{y}}{\partial y}$$

## 有限元方法代写

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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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